Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target
>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target
>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I suspect the distribution is somewhat skewed for some people (those who
claim "I always miss to the left", etc), in which case probably setting a
perfect double and then shooting slightly towards one ball or the other
might maximise hitting probability (if the skew is in terms of the average
being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit
with a pretty wide spread for many. Too many data points required to measure
it though (and, of course, if you take enough data in a short time to plot
the distribution, the distribution usually changes as you are collecting
data!).

Cheers,
Jenny


On 10 May 2010 00:07, KEITH AITON <> wrote:

> I'm not 'having a go' at anyone, but is there any evidence to support the
> assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
> > To: .uk
> > Subject: Re: [Croquet] Maximising chances of hitting a double target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around the intended
> target then you are best to line up a perfect double (I.e. So that the gap
> is exactly one ball diameter) and then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of going through
> the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when shooting at a huge
> target, even though there is a hole in the middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a sloping East
> boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk <
> croquet-.uk>
> > To: Notts List <.uk>
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double target; e.g.
> > choosing where to put your ball when taking a lift shot, or running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect" double;
> > i.e. if my ball misses one target by a millimetre it hits the other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double on the
> > East boundary (Rover high) and lined up a target with a deliberate small
> > gap. This was because my shooting was a bit rough that day and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and assuming
> > that my shooting is normally distributed abou tthe centre of my target,
> > what's the correct way of choosing how wide a gap to leave in the
> > double? (Shoudl I be trying, for instance, to make the odds of missing
> > through the middle equal to the odds of missing on one side or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target
>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I suspect the distribution is somewhat skewed for some people (those who
claim "I always miss to the left", etc), in which case probably setting a
perfect double and then shooting slightly towards one ball or the other
might maximise hitting probability (if the skew is in terms of the average
being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit
with a pretty wide spread for many. Too many data points required to measure
it though (and, of course, if you take enough data in a short time to plot
the distribution, the distribution usually changes as you are collecting
data!).

Cheers,
Jenny


On 10 May 2010 00:07, KEITH AITON <> wrote:

> I'm not 'having a go' at anyone, but is there any evidence to support the
> assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
> > To: .uk
> > Subject: Re: [Croquet] Maximising chances of hitting a double target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around the intended
> target then you are best to line up a perfect double (I.e. So that the gap
> is exactly one ball diameter) and then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of going through
> the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when shooting at a huge
> target, even though there is a hole in the middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a sloping East
> boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk <
> croquet-.uk>
> > To: Notts List <.uk>
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double target; e.g.
> > choosing where to put your ball when taking a lift shot, or running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect" double;
> > i.e. if my ball misses one target by a millimetre it hits the other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double on the
> > East boundary (Rover high) and lined up a target with a deliberate small
> > gap. This was because my shooting was a bit rough that day and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and assuming
> > that my shooting is normally distributed abou tthe centre of my target,
> > what's the correct way of choosing how wide a gap to leave in the
> > double? (Shoudl I be trying, for instance, to make the odds of missing
> > through the middle equal to the odds of missing on one side or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Thank you, Dave.

However I was aware of, and understood, what you had said.

I would like to see proof that (when shooting at a rather distant
two-ball target) there is a greater probability of hitting it if the
two balls are less than a ball's width apart than if they were
slightly more than a ball's width apart.

JR.


On 09/05/2010, at 9:23 PM, David Maugham wrote:

> On 09/05/2010 12:15, johnriches wrote:
>> In other words, if you (or some other reasonably good player) were to
>> take, say, 20 shots at the middle ball, would you be willing to
>> pay me
>> $1 every time one of the end balls was roqueted if I agreed to pay
>> you
>> $1 every time the middle ball of the five was roqueted? I suspect
>> that
>> I might come out in front. [For the purpose of the exercise, if
>> it were
>> attempted in practice, the 2nd and 4th balls should be removed,
>> and of
>> course you could claim a roquet on only the first ball contacted.]
>>
>> I am not saying you are wrong, but I would like to be convinced.
>
> You're comparing shooting at a single ball with shooting at two
> balls with a gap bigger than a ball. I specifically said that it
> was possible to have a higher probability by shooting at the gap in
> such a situation:
>
>>> Note that this is different from having a target with a gap,
>>> where you
>>> do not have choice of placement of the striker's ball, in which case
>>> shooting at the middle may well be better than shooting at one of
>>> the
>>> balls.
>
> REW wanted to compare shooting at a "perfect" double (i.e. one
> where the gap is a hairs breadth smaller than a ball) with a double
> where the gap is bigger than a ball.
>
> Dave
>


NOTE: Views expressed in this email are my own personal opinions and
do not necessarily represent those of the ACA.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target
>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I suspect the distribution is somewhat skewed for some people (those who
claim "I always miss to the left", etc), in which case probably setting a
perfect double and then shooting slightly towards one ball or the other
might maximise hitting probability (if the skew is in terms of the average
being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit
with a pretty wide spread for many. Too many data points required to measure
it though (and, of course, if you take enough data in a short time to plot
the distribution, the distribution usually changes as you are collecting
data!).

Cheers,
Jenny


On 10 May 2010 00:07, KEITH AITON <> wrote:

> I'm not 'having a go' at anyone, but is there any evidence to support the
> assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
> > To: .uk
> > Subject: Re: [Croquet] Maximising chances of hitting a double target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around the intended
> target then you are best to line up a perfect double (I.e. So that the gap
> is exactly one ball diameter) and then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of going through
> the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when shooting at a huge
> target, even though there is a hole in the middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a sloping East
> boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk <
> croquet-.uk>
> > To: Notts List <.uk>
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double target; e.g.
> > choosing where to put your ball when taking a lift shot, or running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect" double;
> > i.e. if my ball misses one target by a millimetre it hits the other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double on the
> > East boundary (Rover high) and lined up a target with a deliberate small
> > gap. This was because my shooting was a bit rough that day and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and assuming
> > that my shooting is normally distributed abou tthe centre of my target,
> > what's the correct way of choosing how wide a gap to leave in the
> > double? (Shoudl I be trying, for instance, to make the odds of missing
> > through the middle equal to the odds of missing on one side or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Thank you, Dave.

However I was aware of, and understood, what you had said.

I would like to see proof that (when shooting at a rather distant
two-ball target) there is a greater probability of hitting it if the
two balls are less than a ball's width apart than if they were
slightly more than a ball's width apart.

JR.


On 09/05/2010, at 9:23 PM, David Maugham wrote:

> On 09/05/2010 12:15, johnriches wrote:
>> In other words, if you (or some other reasonably good player) were to
>> take, say, 20 shots at the middle ball, would you be willing to
>> pay me
>> $1 every time one of the end balls was roqueted if I agreed to pay
>> you
>> $1 every time the middle ball of the five was roqueted? I suspect
>> that
>> I might come out in front. [For the purpose of the exercise, if
>> it were
>> attempted in practice, the 2nd and 4th balls should be removed,
>> and of
>> course you could claim a roquet on only the first ball contacted.]
>>
>> I am not saying you are wrong, but I would like to be convinced.
>
> You're comparing shooting at a single ball with shooting at two
> balls with a gap bigger than a ball. I specifically said that it
> was possible to have a higher probability by shooting at the gap in
> such a situation:
>
>>> Note that this is different from having a target with a gap,
>>> where you
>>> do not have choice of placement of the striker's ball, in which case
>>> shooting at the middle may well be better than shooting at one of
>>> the
>>> balls.
>
> REW wanted to compare shooting at a "perfect" double (i.e. one
> where the gap is a hairs breadth smaller than a ball) with a double
> where the gap is bigger than a ball.
>
> Dave
>


NOTE: Views expressed in this email are my own personal opinions and
do not necessarily represent those of the ACA. On Sun, 09 May 2010 13:18:42 +0100, Jenny Clarke <> wrote:
> I suspect the distribution is somewhat skewed for some people (those who
> claim "I always miss to the left", etc), in which case probably setting a
> perfect double and then shooting slightly towards one ball or the other
> might maximise hitting probability (if the skew is in terms of the
> average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people, albeit
> with a pretty wide spread for many. Too many data points required to
> measure it though ...

If the target is far enough away (or the ground bumpy enough, or the
shooter inaccurate enough) that the normal distribution curve is nearly
flat over the width of 6 balls, would it not be better to leave a 2
ball-width gap rather than (a shade under) 1 ball-width?

Theoretically this gives two separate targets, each 3 balls wide, rather
than one 5 balls wide.

Colin McKenzie (who went through the middle of such a target yesterday,
but usually misses on the outside).

--
Frightening isn't the same as dangerous.

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target
>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I suspect the distribution is somewhat skewed for some people (those who
claim "I always miss to the left", etc), in which case probably setting a
perfect double and then shooting slightly towards one ball or the other
might maximise hitting probability (if the skew is in terms of the average
being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit
with a pretty wide spread for many. Too many data points required to measure
it though (and, of course, if you take enough data in a short time to plot
the distribution, the distribution usually changes as you are collecting
data!).

Cheers,
Jenny


On 10 May 2010 00:07, KEITH AITON <> wrote:

> I'm not 'having a go' at anyone, but is there any evidence to support the
> assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
> > To: .uk
> > Subject: Re: [Croquet] Maximising chances of hitting a double target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around the intended
> target then you are best to line up a perfect double (I.e. So that the gap
> is exactly one ball diameter) and then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of going through
> the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when shooting at a huge
> target, even though there is a hole in the middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a sloping East
> boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk <
> croquet-.uk>
> > To: Notts List <.uk>
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double target; e.g.
> > choosing where to put your ball when taking a lift shot, or running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect" double;
> > i.e. if my ball misses one target by a millimetre it hits the other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double on the
> > East boundary (Rover high) and lined up a target with a deliberate small
> > gap. This was because my shooting was a bit rough that day and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and assuming
> > that my shooting is normally distributed abou tthe centre of my target,
> > what's the correct way of choosing how wide a gap to leave in the
> > double? (Shoudl I be trying, for instance, to make the odds of missing
> > through the middle equal to the odds of missing on one side or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Thank you, Dave.

However I was aware of, and understood, what you had said.

I would like to see proof that (when shooting at a rather distant
two-ball target) there is a greater probability of hitting it if the
two balls are less than a ball's width apart than if they were
slightly more than a ball's width apart.

JR.


On 09/05/2010, at 9:23 PM, David Maugham wrote:

> On 09/05/2010 12:15, johnriches wrote:
>> In other words, if you (or some other reasonably good player) were to
>> take, say, 20 shots at the middle ball, would you be willing to
>> pay me
>> $1 every time one of the end balls was roqueted if I agreed to pay
>> you
>> $1 every time the middle ball of the five was roqueted? I suspect
>> that
>> I might come out in front. [For the purpose of the exercise, if
>> it were
>> attempted in practice, the 2nd and 4th balls should be removed,
>> and of
>> course you could claim a roquet on only the first ball contacted.]
>>
>> I am not saying you are wrong, but I would like to be convinced.
>
> You're comparing shooting at a single ball with shooting at two
> balls with a gap bigger than a ball. I specifically said that it
> was possible to have a higher probability by shooting at the gap in
> such a situation:
>
>>> Note that this is different from having a target with a gap,
>>> where you
>>> do not have choice of placement of the striker's ball, in which case
>>> shooting at the middle may well be better than shooting at one of
>>> the
>>> balls.
>
> REW wanted to compare shooting at a "perfect" double (i.e. one
> where the gap is a hairs breadth smaller than a ball) with a double
> where the gap is bigger than a ball.
>
> Dave
>


NOTE: Views expressed in this email are my own personal opinions and
do not necessarily represent those of the ACA. On Sun, 09 May 2010 13:18:42 +0100, Jenny Clarke <> wrote:
> I suspect the distribution is somewhat skewed for some people (those who
> claim "I always miss to the left", etc), in which case probably setting a
> perfect double and then shooting slightly towards one ball or the other
> might maximise hitting probability (if the skew is in terms of the
> average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people, albeit
> with a pretty wide spread for many. Too many data points required to
> measure it though ...

If the target is far enough away (or the ground bumpy enough, or the
shooter inaccurate enough) that the normal distribution curve is nearly
flat over the width of 6 balls, would it not be better to leave a 2
ball-width gap rather than (a shade under) 1 ball-width?

Theoretically this gives two separate targets, each 3 balls wide, rather
than one 5 balls wide.

Colin McKenzie (who went through the middle of such a target yesterday,
but usually misses on the outside).

--
Frightening isn't the same as dangerous.

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I believe my shooting is either on/very close, OR I miss by a foot or more. So I'm not sure a normal distribution describes these results well.

Of course, those where I miss by a foot or more aren't going to hit a double target anyway - and perhaps the ones which are on/ very close may follow a normal distribution of their own around the aim line.

regards
Martin French
07718 630804
----- Original Message -----
From: Jenny Clarke
To: KEITH AITON
Cc: Notts List ; Samir (Corda) (UK) Patel
Sent: Sunday, May 09, 2010 1:18 PM
Subject: Re: [Croquet] Maximising chances of hitting a double target


I suspect the distribution is somewhat skewed for some people (those who claim "I always miss to the left", etc), in which case probably setting a perfect double and then shooting slightly towards one ball or the other might maximise hitting probability (if the skew is in terms of the average being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit with a pretty wide spread for many. Too many data points required to measure it though (and, of course, if you take enough data in a short time to plot the distribution, the distribution usually changes as you are collecting data!).

Cheers,
Jenny



On 10 May 2010 00:07, KEITH AITON <> wrote:

I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target

>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target
>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I suspect the distribution is somewhat skewed for some people (those who
claim "I always miss to the left", etc), in which case probably setting a
perfect double and then shooting slightly towards one ball or the other
might maximise hitting probability (if the skew is in terms of the average
being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit
with a pretty wide spread for many. Too many data points required to measure
it though (and, of course, if you take enough data in a short time to plot
the distribution, the distribution usually changes as you are collecting
data!).

Cheers,
Jenny


On 10 May 2010 00:07, KEITH AITON <> wrote:

> I'm not 'having a go' at anyone, but is there any evidence to support the
> assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
> > To: .uk
> > Subject: Re: [Croquet] Maximising chances of hitting a double target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around the intended
> target then you are best to line up a perfect double (I.e. So that the gap
> is exactly one ball diameter) and then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of going through
> the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when shooting at a huge
> target, even though there is a hole in the middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a sloping East
> boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk <
> croquet-.uk>
> > To: Notts List <.uk>
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double target; e.g.
> > choosing where to put your ball when taking a lift shot, or running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect" double;
> > i.e. if my ball misses one target by a millimetre it hits the other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double on the
> > East boundary (Rover high) and lined up a target with a deliberate small
> > gap. This was because my shooting was a bit rough that day and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and assuming
> > that my shooting is normally distributed abou tthe centre of my target,
> > what's the correct way of choosing how wide a gap to leave in the
> > double? (Shoudl I be trying, for instance, to make the odds of missing
> > through the middle equal to the odds of missing on one side or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Thank you, Dave.

However I was aware of, and understood, what you had said.

I would like to see proof that (when shooting at a rather distant
two-ball target) there is a greater probability of hitting it if the
two balls are less than a ball's width apart than if they were
slightly more than a ball's width apart.

JR.


On 09/05/2010, at 9:23 PM, David Maugham wrote:

> On 09/05/2010 12:15, johnriches wrote:
>> In other words, if you (or some other reasonably good player) were to
>> take, say, 20 shots at the middle ball, would you be willing to
>> pay me
>> $1 every time one of the end balls was roqueted if I agreed to pay
>> you
>> $1 every time the middle ball of the five was roqueted? I suspect
>> that
>> I might come out in front. [For the purpose of the exercise, if
>> it were
>> attempted in practice, the 2nd and 4th balls should be removed,
>> and of
>> course you could claim a roquet on only the first ball contacted.]
>>
>> I am not saying you are wrong, but I would like to be convinced.
>
> You're comparing shooting at a single ball with shooting at two
> balls with a gap bigger than a ball. I specifically said that it
> was possible to have a higher probability by shooting at the gap in
> such a situation:
>
>>> Note that this is different from having a target with a gap,
>>> where you
>>> do not have choice of placement of the striker's ball, in which case
>>> shooting at the middle may well be better than shooting at one of
>>> the
>>> balls.
>
> REW wanted to compare shooting at a "perfect" double (i.e. one
> where the gap is a hairs breadth smaller than a ball) with a double
> where the gap is bigger than a ball.
>
> Dave
>


NOTE: Views expressed in this email are my own personal opinions and
do not necessarily represent those of the ACA. On Sun, 09 May 2010 13:18:42 +0100, Jenny Clarke <> wrote:
> I suspect the distribution is somewhat skewed for some people (those who
> claim "I always miss to the left", etc), in which case probably setting a
> perfect double and then shooting slightly towards one ball or the other
> might maximise hitting probability (if the skew is in terms of the
> average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people, albeit
> with a pretty wide spread for many. Too many data points required to
> measure it though ...

If the target is far enough away (or the ground bumpy enough, or the
shooter inaccurate enough) that the normal distribution curve is nearly
flat over the width of 6 balls, would it not be better to leave a 2
ball-width gap rather than (a shade under) 1 ball-width?

Theoretically this gives two separate targets, each 3 balls wide, rather
than one 5 balls wide.

Colin McKenzie (who went through the middle of such a target yesterday,
but usually misses on the outside).

--
Frightening isn't the same as dangerous.

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I believe my shooting is either on/very close, OR I miss by a foot or more. So I'm not sure a normal distribution describes these results well.

Of course, those where I miss by a foot or more aren't going to hit a double target anyway - and perhaps the ones which are on/ very close may follow a normal distribution of their own around the aim line.

regards
Martin French
07718 630804
----- Original Message -----
From: Jenny Clarke
To: KEITH AITON
Cc: Notts List ; Samir (Corda) (UK) Patel
Sent: Sunday, May 09, 2010 1:18 PM
Subject: Re: [Croquet] Maximising chances of hitting a double target


I suspect the distribution is somewhat skewed for some people (those who claim "I always miss to the left", etc), in which case probably setting a perfect double and then shooting slightly towards one ball or the other might maximise hitting probability (if the skew is in terms of the average being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit with a pretty wide spread for many. Too many data points required to measure it though (and, of course, if you take enough data in a short time to plot the distribution, the distribution usually changes as you are collecting data!).

Cheers,
Jenny



On 10 May 2010 00:07, KEITH AITON <> wrote:

I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target

>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I have to agree with David that the maths is clearly in favour of
leaving the 'perfect double' - i.e. a gap of exactly one ball's width.
However, if I am shooting from some distance away (say 2 x my critical
distance), so that the distribution curve is flattish, then I will
generally aim to leave a gap of a fraction over 1 ball. This is not
because I doubt the math, but because it is difficult to judge exactly
one ball's gap, and I would rather err on the side of making the gap a
fraction too big, rather than a fraction too small.

I've always thought the more interesting question is the one David
avoided - i.e. with a target with a given gap > 1 ball's width, at what
point is it better to aim at one of the balls, rather than at the gap?

Regards

Jeff

On 09/05/2010 15:07, Martin French wrote:
> I believe my shooting is either on/very close, OR I miss by a foot or
> more. So I'm not sure a normal distribution describes these results well.
> Of course, those where I miss by a foot or more aren't going to hit a
> double target anyway - and perhaps the ones which are on/ very close may
> follow a normal distribution of their own around the aim line.
> regards
> Martin French
> 07718 630804
>
> ----- Original Message -----
> *From:* Jenny Clarke
> *To:* KEITH AITON
> *Cc:* Notts List ; Samir
> (Corda) (UK) Patel
> *Sent:* Sunday, May 09, 2010 1:18 PM
> *Subject:* Re: [Croquet] Maximising chances of hitting a double target
>
> I suspect the distribution is somewhat skewed for some people (those
> who claim "I always miss to the left", etc), in which case probably
> setting a perfect double and then shooting slightly towards one ball
> or the other might maximise hitting probability (if the skew is in
> terms of the average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people,
> albeit with a pretty wide spread for many. Too many data points
> required to measure it though (and, of course, if you take enough
> data in a short time to plot the distribution, the distribution
> usually changes as you are collecting data!).
>
> Cheers,
> Jenny
>
>
> On 10 May 2010 00:07, KEITH AITON <
> > wrote:
>
> I'm not 'having a go' at anyone, but is there any evidence to
> support the assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
>
> > To: .uk
>
> > Subject: Re: [Croquet] Maximising chances of hitting a double
> target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around
> the intended target then you are best to line up a perfect
> double (I.e. So that the gap is exactly one ball diameter) and
> then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of
> going through the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when
> shooting at a huge target, even though there is a hole in the
> middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a
> sloping East boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk
>
> > >
> > To: Notts List <.uk
> >
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double
> target; e.g.
> > choosing where to put your ball when taking a lift shot, or
> running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect"
> double;
> > i.e. if my ball misses one target by a millimetre it hits the
> other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double
> on the
> > East boundary (Rover high) and lined up a target with a
> deliberate small
> > gap. This was because my shooting was a bit rough that day
> and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and
> assuming
> > that my shooting is normally distributed abou tthe centre of
> my target,
> > what's the correct way of choosing how wide a gap to leave in
> the
> > double? (Shoudl I be trying, for instance, to make the odds
> of missing
> > through the middle equal to the odds of missing on one side
> or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target
>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I suspect the distribution is somewhat skewed for some people (those who
claim "I always miss to the left", etc), in which case probably setting a
perfect double and then shooting slightly towards one ball or the other
might maximise hitting probability (if the skew is in terms of the average
being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit
with a pretty wide spread for many. Too many data points required to measure
it though (and, of course, if you take enough data in a short time to plot
the distribution, the distribution usually changes as you are collecting
data!).

Cheers,
Jenny


On 10 May 2010 00:07, KEITH AITON <> wrote:

> I'm not 'having a go' at anyone, but is there any evidence to support the
> assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
> > To: .uk
> > Subject: Re: [Croquet] Maximising chances of hitting a double target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around the intended
> target then you are best to line up a perfect double (I.e. So that the gap
> is exactly one ball diameter) and then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of going through
> the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when shooting at a huge
> target, even though there is a hole in the middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a sloping East
> boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk <
> croquet-.uk>
> > To: Notts List <.uk>
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double target; e.g.
> > choosing where to put your ball when taking a lift shot, or running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect" double;
> > i.e. if my ball misses one target by a millimetre it hits the other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double on the
> > East boundary (Rover high) and lined up a target with a deliberate small
> > gap. This was because my shooting was a bit rough that day and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and assuming
> > that my shooting is normally distributed abou tthe centre of my target,
> > what's the correct way of choosing how wide a gap to leave in the
> > double? (Shoudl I be trying, for instance, to make the odds of missing
> > through the middle equal to the odds of missing on one side or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Thank you, Dave.

However I was aware of, and understood, what you had said.

I would like to see proof that (when shooting at a rather distant
two-ball target) there is a greater probability of hitting it if the
two balls are less than a ball's width apart than if they were
slightly more than a ball's width apart.

JR.


On 09/05/2010, at 9:23 PM, David Maugham wrote:

> On 09/05/2010 12:15, johnriches wrote:
>> In other words, if you (or some other reasonably good player) were to
>> take, say, 20 shots at the middle ball, would you be willing to
>> pay me
>> $1 every time one of the end balls was roqueted if I agreed to pay
>> you
>> $1 every time the middle ball of the five was roqueted? I suspect
>> that
>> I might come out in front. [For the purpose of the exercise, if
>> it were
>> attempted in practice, the 2nd and 4th balls should be removed,
>> and of
>> course you could claim a roquet on only the first ball contacted.]
>>
>> I am not saying you are wrong, but I would like to be convinced.
>
> You're comparing shooting at a single ball with shooting at two
> balls with a gap bigger than a ball. I specifically said that it
> was possible to have a higher probability by shooting at the gap in
> such a situation:
>
>>> Note that this is different from having a target with a gap,
>>> where you
>>> do not have choice of placement of the striker's ball, in which case
>>> shooting at the middle may well be better than shooting at one of
>>> the
>>> balls.
>
> REW wanted to compare shooting at a "perfect" double (i.e. one
> where the gap is a hairs breadth smaller than a ball) with a double
> where the gap is bigger than a ball.
>
> Dave
>


NOTE: Views expressed in this email are my own personal opinions and
do not necessarily represent those of the ACA. On Sun, 09 May 2010 13:18:42 +0100, Jenny Clarke <> wrote:
> I suspect the distribution is somewhat skewed for some people (those who
> claim "I always miss to the left", etc), in which case probably setting a
> perfect double and then shooting slightly towards one ball or the other
> might maximise hitting probability (if the skew is in terms of the
> average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people, albeit
> with a pretty wide spread for many. Too many data points required to
> measure it though ...

If the target is far enough away (or the ground bumpy enough, or the
shooter inaccurate enough) that the normal distribution curve is nearly
flat over the width of 6 balls, would it not be better to leave a 2
ball-width gap rather than (a shade under) 1 ball-width?

Theoretically this gives two separate targets, each 3 balls wide, rather
than one 5 balls wide.

Colin McKenzie (who went through the middle of such a target yesterday,
but usually misses on the outside).

--
Frightening isn't the same as dangerous.

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I believe my shooting is either on/very close, OR I miss by a foot or more. So I'm not sure a normal distribution describes these results well.

Of course, those where I miss by a foot or more aren't going to hit a double target anyway - and perhaps the ones which are on/ very close may follow a normal distribution of their own around the aim line.

regards
Martin French
07718 630804
----- Original Message -----
From: Jenny Clarke
To: KEITH AITON
Cc: Notts List ; Samir (Corda) (UK) Patel
Sent: Sunday, May 09, 2010 1:18 PM
Subject: Re: [Croquet] Maximising chances of hitting a double target


I suspect the distribution is somewhat skewed for some people (those who claim "I always miss to the left", etc), in which case probably setting a perfect double and then shooting slightly towards one ball or the other might maximise hitting probability (if the skew is in terms of the average being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit with a pretty wide spread for many. Too many data points required to measure it though (and, of course, if you take enough data in a short time to plot the distribution, the distribution usually changes as you are collecting data!).

Cheers,
Jenny



On 10 May 2010 00:07, KEITH AITON <> wrote:

I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target

>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I have to agree with David that the maths is clearly in favour of
leaving the 'perfect double' - i.e. a gap of exactly one ball's width.
However, if I am shooting from some distance away (say 2 x my critical
distance), so that the distribution curve is flattish, then I will
generally aim to leave a gap of a fraction over 1 ball. This is not
because I doubt the math, but because it is difficult to judge exactly
one ball's gap, and I would rather err on the side of making the gap a
fraction too big, rather than a fraction too small.

I've always thought the more interesting question is the one David
avoided - i.e. with a target with a given gap > 1 ball's width, at what
point is it better to aim at one of the balls, rather than at the gap?

Regards

Jeff

On 09/05/2010 15:07, Martin French wrote:
> I believe my shooting is either on/very close, OR I miss by a foot or
> more. So I'm not sure a normal distribution describes these results well.
> Of course, those where I miss by a foot or more aren't going to hit a
> double target anyway - and perhaps the ones which are on/ very close may
> follow a normal distribution of their own around the aim line.
> regards
> Martin French
> 07718 630804
>
> ----- Original Message -----
> *From:* Jenny Clarke
> *To:* KEITH AITON
> *Cc:* Notts List ; Samir
> (Corda) (UK) Patel
> *Sent:* Sunday, May 09, 2010 1:18 PM
> *Subject:* Re: [Croquet] Maximising chances of hitting a double target
>
> I suspect the distribution is somewhat skewed for some people (those
> who claim "I always miss to the left", etc), in which case probably
> setting a perfect double and then shooting slightly towards one ball
> or the other might maximise hitting probability (if the skew is in
> terms of the average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people,
> albeit with a pretty wide spread for many. Too many data points
> required to measure it though (and, of course, if you take enough
> data in a short time to plot the distribution, the distribution
> usually changes as you are collecting data!).
>
> Cheers,
> Jenny
>
>
> On 10 May 2010 00:07, KEITH AITON <
> > wrote:
>
> I'm not 'having a go' at anyone, but is there any evidence to
> support the assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
>
> > To: .uk
>
> > Subject: Re: [Croquet] Maximising chances of hitting a double
> target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around
> the intended target then you are best to line up a perfect
> double (I.e. So that the gap is exactly one ball diameter) and
> then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of
> going through the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when
> shooting at a huge target, even though there is a hole in the
> middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a
> sloping East boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk
>
> > >
> > To: Notts List <.uk
> >
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double
> target; e.g.
> > choosing where to put your ball when taking a lift shot, or
> running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect"
> double;
> > i.e. if my ball misses one target by a millimetre it hits the
> other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double
> on the
> > East boundary (Rover high) and lined up a target with a
> deliberate small
> > gap. This was because my shooting was a bit rough that day
> and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and
> assuming
> > that my shooting is normally distributed abou tthe centre of
> my target,
> > what's the correct way of choosing how wide a gap to leave in
> the
> > double? (Shoudl I be trying, for instance, to make the odds
> of missing
> > through the middle equal to the odds of missing on one side
> or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

I'm not a mathematician or statistician, but I think I have a reasonable understanding of odds.



The answer to your question is entirely dependent upon the individuals shooting over the given distance.



For example, for a good shot over a short distance, the answer will always be to have the gap at one ball apart. For worse shots over longer distance, the answer will be to have the gap two balls apart.



To try and explain the above, the trade off between having a "target" of 5 balls compared with a "target" of 6 balls changes depending on your likelihood of going through the middle.



How you determine the gap for any given distance is just down to understanding your own ability, like so many other aspects of the game.



Chris

> Date: Sun, 9 May 2010 08:06:10 +0100
> From:
> To: .uk
> Subject: [Croquet] Maximising chances of hitting a double target
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target
>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I suspect the distribution is somewhat skewed for some people (those who
claim "I always miss to the left", etc), in which case probably setting a
perfect double and then shooting slightly towards one ball or the other
might maximise hitting probability (if the skew is in terms of the average
being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit
with a pretty wide spread for many. Too many data points required to measure
it though (and, of course, if you take enough data in a short time to plot
the distribution, the distribution usually changes as you are collecting
data!).

Cheers,
Jenny


On 10 May 2010 00:07, KEITH AITON <> wrote:

> I'm not 'having a go' at anyone, but is there any evidence to support the
> assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
> > To: .uk
> > Subject: Re: [Croquet] Maximising chances of hitting a double target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around the intended
> target then you are best to line up a perfect double (I.e. So that the gap
> is exactly one ball diameter) and then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of going through
> the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when shooting at a huge
> target, even though there is a hole in the middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a sloping East
> boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk <
> croquet-.uk>
> > To: Notts List <.uk>
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double target; e.g.
> > choosing where to put your ball when taking a lift shot, or running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect" double;
> > i.e. if my ball misses one target by a millimetre it hits the other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double on the
> > East boundary (Rover high) and lined up a target with a deliberate small
> > gap. This was because my shooting was a bit rough that day and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and assuming
> > that my shooting is normally distributed abou tthe centre of my target,
> > what's the correct way of choosing how wide a gap to leave in the
> > double? (Shoudl I be trying, for instance, to make the odds of missing
> > through the middle equal to the odds of missing on one side or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Thank you, Dave.

However I was aware of, and understood, what you had said.

I would like to see proof that (when shooting at a rather distant
two-ball target) there is a greater probability of hitting it if the
two balls are less than a ball's width apart than if they were
slightly more than a ball's width apart.

JR.


On 09/05/2010, at 9:23 PM, David Maugham wrote:

> On 09/05/2010 12:15, johnriches wrote:
>> In other words, if you (or some other reasonably good player) were to
>> take, say, 20 shots at the middle ball, would you be willing to
>> pay me
>> $1 every time one of the end balls was roqueted if I agreed to pay
>> you
>> $1 every time the middle ball of the five was roqueted? I suspect
>> that
>> I might come out in front. [For the purpose of the exercise, if
>> it were
>> attempted in practice, the 2nd and 4th balls should be removed,
>> and of
>> course you could claim a roquet on only the first ball contacted.]
>>
>> I am not saying you are wrong, but I would like to be convinced.
>
> You're comparing shooting at a single ball with shooting at two
> balls with a gap bigger than a ball. I specifically said that it
> was possible to have a higher probability by shooting at the gap in
> such a situation:
>
>>> Note that this is different from having a target with a gap,
>>> where you
>>> do not have choice of placement of the striker's ball, in which case
>>> shooting at the middle may well be better than shooting at one of
>>> the
>>> balls.
>
> REW wanted to compare shooting at a "perfect" double (i.e. one
> where the gap is a hairs breadth smaller than a ball) with a double
> where the gap is bigger than a ball.
>
> Dave
>


NOTE: Views expressed in this email are my own personal opinions and
do not necessarily represent those of the ACA. On Sun, 09 May 2010 13:18:42 +0100, Jenny Clarke <> wrote:
> I suspect the distribution is somewhat skewed for some people (those who
> claim "I always miss to the left", etc), in which case probably setting a
> perfect double and then shooting slightly towards one ball or the other
> might maximise hitting probability (if the skew is in terms of the
> average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people, albeit
> with a pretty wide spread for many. Too many data points required to
> measure it though ...

If the target is far enough away (or the ground bumpy enough, or the
shooter inaccurate enough) that the normal distribution curve is nearly
flat over the width of 6 balls, would it not be better to leave a 2
ball-width gap rather than (a shade under) 1 ball-width?

Theoretically this gives two separate targets, each 3 balls wide, rather
than one 5 balls wide.

Colin McKenzie (who went through the middle of such a target yesterday,
but usually misses on the outside).

--
Frightening isn't the same as dangerous.

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I believe my shooting is either on/very close, OR I miss by a foot or more. So I'm not sure a normal distribution describes these results well.

Of course, those where I miss by a foot or more aren't going to hit a double target anyway - and perhaps the ones which are on/ very close may follow a normal distribution of their own around the aim line.

regards
Martin French
07718 630804
----- Original Message -----
From: Jenny Clarke
To: KEITH AITON
Cc: Notts List ; Samir (Corda) (UK) Patel
Sent: Sunday, May 09, 2010 1:18 PM
Subject: Re: [Croquet] Maximising chances of hitting a double target


I suspect the distribution is somewhat skewed for some people (those who claim "I always miss to the left", etc), in which case probably setting a perfect double and then shooting slightly towards one ball or the other might maximise hitting probability (if the skew is in terms of the average being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit with a pretty wide spread for many. Too many data points required to measure it though (and, of course, if you take enough data in a short time to plot the distribution, the distribution usually changes as you are collecting data!).

Cheers,
Jenny



On 10 May 2010 00:07, KEITH AITON <> wrote:

I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target

>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I have to agree with David that the maths is clearly in favour of
leaving the 'perfect double' - i.e. a gap of exactly one ball's width.
However, if I am shooting from some distance away (say 2 x my critical
distance), so that the distribution curve is flattish, then I will
generally aim to leave a gap of a fraction over 1 ball. This is not
because I doubt the math, but because it is difficult to judge exactly
one ball's gap, and I would rather err on the side of making the gap a
fraction too big, rather than a fraction too small.

I've always thought the more interesting question is the one David
avoided - i.e. with a target with a given gap > 1 ball's width, at what
point is it better to aim at one of the balls, rather than at the gap?

Regards

Jeff

On 09/05/2010 15:07, Martin French wrote:
> I believe my shooting is either on/very close, OR I miss by a foot or
> more. So I'm not sure a normal distribution describes these results well.
> Of course, those where I miss by a foot or more aren't going to hit a
> double target anyway - and perhaps the ones which are on/ very close may
> follow a normal distribution of their own around the aim line.
> regards
> Martin French
> 07718 630804
>
> ----- Original Message -----
> *From:* Jenny Clarke
> *To:* KEITH AITON
> *Cc:* Notts List ; Samir
> (Corda) (UK) Patel
> *Sent:* Sunday, May 09, 2010 1:18 PM
> *Subject:* Re: [Croquet] Maximising chances of hitting a double target
>
> I suspect the distribution is somewhat skewed for some people (those
> who claim "I always miss to the left", etc), in which case probably
> setting a perfect double and then shooting slightly towards one ball
> or the other might maximise hitting probability (if the skew is in
> terms of the average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people,
> albeit with a pretty wide spread for many. Too many data points
> required to measure it though (and, of course, if you take enough
> data in a short time to plot the distribution, the distribution
> usually changes as you are collecting data!).
>
> Cheers,
> Jenny
>
>
> On 10 May 2010 00:07, KEITH AITON <
> > wrote:
>
> I'm not 'having a go' at anyone, but is there any evidence to
> support the assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
>
> > To: .uk
>
> > Subject: Re: [Croquet] Maximising chances of hitting a double
> target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around
> the intended target then you are best to line up a perfect
> double (I.e. So that the gap is exactly one ball diameter) and
> then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of
> going through the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when
> shooting at a huge target, even though there is a hole in the
> middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a
> sloping East boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk
>
> > >
> > To: Notts List <.uk
> >
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double
> target; e.g.
> > choosing where to put your ball when taking a lift shot, or
> running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect"
> double;
> > i.e. if my ball misses one target by a millimetre it hits the
> other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double
> on the
> > East boundary (Rover high) and lined up a target with a
> deliberate small
> > gap. This was because my shooting was a bit rough that day
> and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and
> assuming
> > that my shooting is normally distributed abou tthe centre of
> my target,
> > what's the correct way of choosing how wide a gap to leave in
> the
> > double? (Shoudl I be trying, for instance, to make the odds
> of missing
> > through the middle equal to the odds of missing on one side
> or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

I'm not a mathematician or statistician, but I think I have a reasonable understanding of odds.



The answer to your question is entirely dependent upon the individuals shooting over the given distance.



For example, for a good shot over a short distance, the answer will always be to have the gap at one ball apart. For worse shots over longer distance, the answer will be to have the gap two balls apart.



To try and explain the above, the trade off between having a "target" of 5 balls compared with a "target" of 6 balls changes depending on your likelihood of going through the middle.



How you determine the gap for any given distance is just down to understanding your own ability, like so many other aspects of the game.



Chris

> Date: Sun, 9 May 2010 08:06:10 +0100
> From:
> To: .uk
> Subject: [Croquet] Maximising chances of hitting a double target
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Colin McKenzie wrote:
>
> If the target is far enough away (or the ground bumpy enough, or the
> shooter inaccurate enough) that the normal distribution curve is
> nearly flat over the width of 6 balls, would it not be better to leave
> a 2 ball-width gap rather than (a shade under) 1 ball-width?
>
> Theoretically this gives two separate targets, each 3 balls wide,
> rather than one 5 balls wide.
>
> Colin McKenzie (who went through the middle of such a target
> yesterday, but usually misses on the outside).
>
Yes, I agree with this; if the distribution is completely flat (i.e. if
your shooting is completely random within this range) then this is
clearly better to have a 2 ball gap. There's also clearly no advantage
to having less than a one ball gap, but I'm unsure where to go between
these limits. I imagine there's some relationship between the standard
deviation and the optimal gap, but I'm not as adept at statistical
theory as I once was.

Dave M is right to say that different criteria apply to the relatd
question of whether to shoot at a single ball or the gap when aiming at
an imperfect double.

There's another related question, which is to do with how much of a gap
to leave to avoid an attractive double target when making leaves.

Keith is right to question the suggestion that shooting is "Normally
Distributed" around a mean. I didn't assume it to be true; just
suggested it as a basis for a calculation.

Another interesting thought based on target size. most people probably
feel they could shoot a ball from corner 1 to go off the lawn in the
corner 2 area without a problem; with far more confidence than - say -
hitting an 7 yard roquet. And yet the latter is a slightly larger target.

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target
>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I suspect the distribution is somewhat skewed for some people (those who
claim "I always miss to the left", etc), in which case probably setting a
perfect double and then shooting slightly towards one ball or the other
might maximise hitting probability (if the skew is in terms of the average
being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit
with a pretty wide spread for many. Too many data points required to measure
it though (and, of course, if you take enough data in a short time to plot
the distribution, the distribution usually changes as you are collecting
data!).

Cheers,
Jenny


On 10 May 2010 00:07, KEITH AITON <> wrote:

> I'm not 'having a go' at anyone, but is there any evidence to support the
> assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
> > To: .uk
> > Subject: Re: [Croquet] Maximising chances of hitting a double target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around the intended
> target then you are best to line up a perfect double (I.e. So that the gap
> is exactly one ball diameter) and then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of going through
> the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when shooting at a huge
> target, even though there is a hole in the middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a sloping East
> boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk <
> croquet-.uk>
> > To: Notts List <.uk>
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double target; e.g.
> > choosing where to put your ball when taking a lift shot, or running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect" double;
> > i.e. if my ball misses one target by a millimetre it hits the other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double on the
> > East boundary (Rover high) and lined up a target with a deliberate small
> > gap. This was because my shooting was a bit rough that day and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and assuming
> > that my shooting is normally distributed abou tthe centre of my target,
> > what's the correct way of choosing how wide a gap to leave in the
> > double? (Shoudl I be trying, for instance, to make the odds of missing
> > through the middle equal to the odds of missing on one side or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Thank you, Dave.

However I was aware of, and understood, what you had said.

I would like to see proof that (when shooting at a rather distant
two-ball target) there is a greater probability of hitting it if the
two balls are less than a ball's width apart than if they were
slightly more than a ball's width apart.

JR.


On 09/05/2010, at 9:23 PM, David Maugham wrote:

> On 09/05/2010 12:15, johnriches wrote:
>> In other words, if you (or some other reasonably good player) were to
>> take, say, 20 shots at the middle ball, would you be willing to
>> pay me
>> $1 every time one of the end balls was roqueted if I agreed to pay
>> you
>> $1 every time the middle ball of the five was roqueted? I suspect
>> that
>> I might come out in front. [For the purpose of the exercise, if
>> it were
>> attempted in practice, the 2nd and 4th balls should be removed,
>> and of
>> course you could claim a roquet on only the first ball contacted.]
>>
>> I am not saying you are wrong, but I would like to be convinced.
>
> You're comparing shooting at a single ball with shooting at two
> balls with a gap bigger than a ball. I specifically said that it
> was possible to have a higher probability by shooting at the gap in
> such a situation:
>
>>> Note that this is different from having a target with a gap,
>>> where you
>>> do not have choice of placement of the striker's ball, in which case
>>> shooting at the middle may well be better than shooting at one of
>>> the
>>> balls.
>
> REW wanted to compare shooting at a "perfect" double (i.e. one
> where the gap is a hairs breadth smaller than a ball) with a double
> where the gap is bigger than a ball.
>
> Dave
>


NOTE: Views expressed in this email are my own personal opinions and
do not necessarily represent those of the ACA. On Sun, 09 May 2010 13:18:42 +0100, Jenny Clarke <> wrote:
> I suspect the distribution is somewhat skewed for some people (those who
> claim "I always miss to the left", etc), in which case probably setting a
> perfect double and then shooting slightly towards one ball or the other
> might maximise hitting probability (if the skew is in terms of the
> average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people, albeit
> with a pretty wide spread for many. Too many data points required to
> measure it though ...

If the target is far enough away (or the ground bumpy enough, or the
shooter inaccurate enough) that the normal distribution curve is nearly
flat over the width of 6 balls, would it not be better to leave a 2
ball-width gap rather than (a shade under) 1 ball-width?

Theoretically this gives two separate targets, each 3 balls wide, rather
than one 5 balls wide.

Colin McKenzie (who went through the middle of such a target yesterday,
but usually misses on the outside).

--
Frightening isn't the same as dangerous.

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I believe my shooting is either on/very close, OR I miss by a foot or more. So I'm not sure a normal distribution describes these results well.

Of course, those where I miss by a foot or more aren't going to hit a double target anyway - and perhaps the ones which are on/ very close may follow a normal distribution of their own around the aim line.

regards
Martin French
07718 630804
----- Original Message -----
From: Jenny Clarke
To: KEITH AITON
Cc: Notts List ; Samir (Corda) (UK) Patel
Sent: Sunday, May 09, 2010 1:18 PM
Subject: Re: [Croquet] Maximising chances of hitting a double target


I suspect the distribution is somewhat skewed for some people (those who claim "I always miss to the left", etc), in which case probably setting a perfect double and then shooting slightly towards one ball or the other might maximise hitting probability (if the skew is in terms of the average being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit with a pretty wide spread for many. Too many data points required to measure it though (and, of course, if you take enough data in a short time to plot the distribution, the distribution usually changes as you are collecting data!).

Cheers,
Jenny



On 10 May 2010 00:07, KEITH AITON <> wrote:

I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target

>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I have to agree with David that the maths is clearly in favour of
leaving the 'perfect double' - i.e. a gap of exactly one ball's width.
However, if I am shooting from some distance away (say 2 x my critical
distance), so that the distribution curve is flattish, then I will
generally aim to leave a gap of a fraction over 1 ball. This is not
because I doubt the math, but because it is difficult to judge exactly
one ball's gap, and I would rather err on the side of making the gap a
fraction too big, rather than a fraction too small.

I've always thought the more interesting question is the one David
avoided - i.e. with a target with a given gap > 1 ball's width, at what
point is it better to aim at one of the balls, rather than at the gap?

Regards

Jeff

On 09/05/2010 15:07, Martin French wrote:
> I believe my shooting is either on/very close, OR I miss by a foot or
> more. So I'm not sure a normal distribution describes these results well.
> Of course, those where I miss by a foot or more aren't going to hit a
> double target anyway - and perhaps the ones which are on/ very close may
> follow a normal distribution of their own around the aim line.
> regards
> Martin French
> 07718 630804
>
> ----- Original Message -----
> *From:* Jenny Clarke
> *To:* KEITH AITON
> *Cc:* Notts List ; Samir
> (Corda) (UK) Patel
> *Sent:* Sunday, May 09, 2010 1:18 PM
> *Subject:* Re: [Croquet] Maximising chances of hitting a double target
>
> I suspect the distribution is somewhat skewed for some people (those
> who claim "I always miss to the left", etc), in which case probably
> setting a perfect double and then shooting slightly towards one ball
> or the other might maximise hitting probability (if the skew is in
> terms of the average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people,
> albeit with a pretty wide spread for many. Too many data points
> required to measure it though (and, of course, if you take enough
> data in a short time to plot the distribution, the distribution
> usually changes as you are collecting data!).
>
> Cheers,
> Jenny
>
>
> On 10 May 2010 00:07, KEITH AITON <
> > wrote:
>
> I'm not 'having a go' at anyone, but is there any evidence to
> support the assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
>
> > To: .uk
>
> > Subject: Re: [Croquet] Maximising chances of hitting a double
> target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around
> the intended target then you are best to line up a perfect
> double (I.e. So that the gap is exactly one ball diameter) and
> then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of
> going through the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when
> shooting at a huge target, even though there is a hole in the
> middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a
> sloping East boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk
>
> > >
> > To: Notts List <.uk
> >
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double
> target; e.g.
> > choosing where to put your ball when taking a lift shot, or
> running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect"
> double;
> > i.e. if my ball misses one target by a millimetre it hits the
> other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double
> on the
> > East boundary (Rover high) and lined up a target with a
> deliberate small
> > gap. This was because my shooting was a bit rough that day
> and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and
> assuming
> > that my shooting is normally distributed abou tthe centre of
> my target,
> > what's the correct way of choosing how wide a gap to leave in
> the
> > double? (Shoudl I be trying, for instance, to make the odds
> of missing
> > through the middle equal to the odds of missing on one side
> or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

I'm not a mathematician or statistician, but I think I have a reasonable understanding of odds.



The answer to your question is entirely dependent upon the individuals shooting over the given distance.



For example, for a good shot over a short distance, the answer will always be to have the gap at one ball apart. For worse shots over longer distance, the answer will be to have the gap two balls apart.



To try and explain the above, the trade off between having a "target" of 5 balls compared with a "target" of 6 balls changes depending on your likelihood of going through the middle.



How you determine the gap for any given distance is just down to understanding your own ability, like so many other aspects of the game.



Chris

> Date: Sun, 9 May 2010 08:06:10 +0100
> From:
> To: .uk
> Subject: [Croquet] Maximising chances of hitting a double target
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Colin McKenzie wrote:
>
> If the target is far enough away (or the ground bumpy enough, or the
> shooter inaccurate enough) that the normal distribution curve is
> nearly flat over the width of 6 balls, would it not be better to leave
> a 2 ball-width gap rather than (a shade under) 1 ball-width?
>
> Theoretically this gives two separate targets, each 3 balls wide,
> rather than one 5 balls wide.
>
> Colin McKenzie (who went through the middle of such a target
> yesterday, but usually misses on the outside).
>
Yes, I agree with this; if the distribution is completely flat (i.e. if
your shooting is completely random within this range) then this is
clearly better to have a 2 ball gap. There's also clearly no advantage
to having less than a one ball gap, but I'm unsure where to go between
these limits. I imagine there's some relationship between the standard
deviation and the optimal gap, but I'm not as adept at statistical
theory as I once was.

Dave M is right to say that different criteria apply to the relatd
question of whether to shoot at a single ball or the gap when aiming at
an imperfect double.

There's another related question, which is to do with how much of a gap
to leave to avoid an attractive double target when making leaves.

Keith is right to question the suggestion that shooting is "Normally
Distributed" around a mean. I didn't assume it to be true; just
suggested it as a basis for a calculation.

Another interesting thought based on target size. most people probably
feel they could shoot a ball from corner 1 to go off the lawn in the
corner 2 area without a problem; with far more confidence than - say -
hitting an 7 yard roquet. And yet the latter is a slightly larger target.

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Hi all,

I think some of what Chris wrote, and possibly also Colin and John, is
based on the common fallacy that shooting at a single ball, your
target is 3 balls wide. This is based on the idea that your ball could
hit the target ball in the middle, or just graze it on the left or
right, making a picture three balls wide. However, the middle of the
SB must hit a target 2 balls wide - somewhere from half a ball's width
to the left of the target to half a ball to the right. This is the
real width of the target.

Two balls can never make a target bigger than twice the size of a
single ball target. So a perfect double is a target 4 balls wide.

Similarly, the real width of your target when shooting at the peg is
the diameter of one ball plus the diameter of the peg.

Jonathan




On 9 May 2010 17:45, chris clarke <> wrote:
> Rob,
> I'm not a mathematician or statistician, but I think I have a reasonable
> understanding of odds.
>
> The answer to your question is entirely dependent upon the individuals
> shooting over the given distance.
>
> For example, for a good shot over a short distance, the answer will always
> be to have the gap at one ball apart. For worse shots over longer distance,
> the answer will be to have the gap two balls apart.
>
> To try and explain the above, the trade off between having a "target" of 5
> balls compared with a "target" of 6 balls changes depending on your
> likelihood of going through the middle.
>
> How you determine the gap for any given distance is just down to
> understanding your own ability, like so many other aspects of the game.
>
> Chris
>
>> Date: Sun, 9 May 2010 08:06:10 +0100
>> From:
>> To: .uk
>> Subject: [Croquet] Maximising chances of hitting a double target
>>
>> Perhaps a question for mathematicians or statisticans.
>>
>> Sometimes you get a choice of how big to make a double target; e.g.
>> choosing where to put your ball when taking a lift shot, or running a
>> hoop undercontrol after which you have a long shot at a double.
>>
>> Historically I;ve usually tried to line up for the "perfect" double;
>> i.e. if my ball misses one target by a millimetre it hits the other
>> target by a millimetre.
>>
>> However the other day, I took a lift from A baulk at a double on the
>> East boundary (Rover high) and lined up a target with a deliberate small
>> gap. This was because my shooting was a bit rough that day and I felt
>> this maximised my chances.
>>
>> So a theoretical question. If all other things are equal, and assuming
>> that my shooting is normally distributed abou tthe centre of my target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>>
>> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.

Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)

If your shooting is normally distributed, then the probability of
hitting is the area under the graph encompassed by the target balls
(plus half a ball's width either side). This will always be maximal when
you include the peak of the graph, so the greatest chance of hitting
should always include hitting exactly the middle of the target.

I.e. you shouldn't leave a gap, if you are making the double yourself.
Indeed, doing so, and missing through the gap is an eponymous error
(Hogan).

Note that this is different from having a target with a gap, where you
do not have choice of placement of the striker's ball, in which case
shooting at the middle may well be better than shooting at one of the
balls.

Dave


_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Dave,

I am interested in the mathematics you are referring to.
It seems to me that the steepness of the peak would need to be
considered, and also the distance away of the two target balls.

If, say, 5 balls were placed in line on the north boundary so that
there were no gaps between them, it seems that for your theory to
be correct, then if I shoot from A-baulk and aim at the 3rd (centre)
ball, my chance of hitting it would need to be about twice as great
as my chance of hitting either the 1st or 5th ball (i.e. either of
the two end balls in the line). That may well be true for a good
roqueter, but I am not so sure it would be so for one who is more
likely to spray the shots along the line.

In other words, if you (or some other reasonably good player) were to
take, say, 20 shots at the middle ball, would you be willing to pay
me $1 every time one of the end balls was roqueted if I agreed to pay
you $1 every time the middle ball of the five was roqueted? I
suspect that I might come out in front. [For the purpose of the
exercise, if it were attempted in practice, the 2nd and 4th balls
should be removed, and of course you could claim a roquet on only the
first ball contacted.]

I am not saying you are wrong, but I would like to be convinced.

JR.

On 09/05/2010, at 5:23 PM, David Maugham wrote:

> On Sun, 2010-05-09 at 08:06 +0100, Rob Edlin-White wrote:
>> So a theoretical question. If all other things are equal, and
>> assuming
>> that my shooting is normally distributed abou tthe centre of my
>> target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of
>> missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>
> If your shooting is normally distributed, then the probability of
> hitting is the area under the graph encompassed by the target balls
> (plus half a ball's width either side). This will always be maximal
> when
> you include the peak of the graph, so the greatest chance of hitting
> should always include hitting exactly the middle of the target.
>
> I.e. you shouldn't leave a gap, if you are making the double yourself.
> Indeed, doing so, and missing through the gap is an eponymous error
> (Hogan).
>
> Note that this is different from having a target with a gap, where you
> do not have choice of placement of the striker's ball, in which case
> shooting at the middle may well be better than shooting at one of the
> balls.
>
> Dave
>
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Your chances of hitting in are much better if you leave a gap of 0.99 of
a ballwidth between the 2 balls - rather than no gap.
The striker's ball cannot pass through the gap and therefore has a 3.99
ballwidths target - compared to 3.0.

Martyn

-----Original Message-----
From: croquet-.uk
[mailto:croquet-.uk] On Behalf Of Rob
Edlin-White
Sent: Sunday, 9 May 2010 5:06 PM
To: Notts List
Subject: [Croquet] Maximising chances of hitting a double target


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small

gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.

Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.

This ignores
- psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
- aiming (I you may find aiming at a gap quite disconcerting)
- matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).

Samir


-----
Sent from Blackberry Wireless

----- Original Message -----
From: croquet-.uk
To: Notts List <.uk>
Sent: Sun May 09 08:06:10 2010
Subject: [Croquet] Maximising chances of hitting a double target


*** WARNING ***

This message has originated outside your organisation,
either from an external partner or the Global Internet.
Keep this in mind if you answer this message.


Perhaps a question for mathematicians or statisticans.

Sometimes you get a choice of how big to make a double target; e.g.
choosing where to put your ball when taking a lift shot, or running a
hoop undercontrol after which you have a long shot at a double.

Historically I;ve usually tried to line up for the "perfect" double;
i.e. if my ball misses one target by a millimetre it hits the other
target by a millimetre.

However the other day, I took a lift from A baulk at a double on the
East boundary (Rover high) and lined up a target with a deliberate small
gap. This was because my shooting was a bit rough that day and I felt
this maximised my chances.

So a theoretical question. If all other things are equal, and assuming
that my shooting is normally distributed abou tthe centre of my target,
what's the correct way of choosing how wide a gap to leave in the
double? (Shoudl I be trying, for instance, to make the odds of missing
through the middle equal to the odds of missing on one side or the
other? And if so, how do I estimate the target width to do this?)

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. On 09/05/2010 12:15, johnriches wrote:
> In other words, if you (or some other reasonably good player) were to
> take, say, 20 shots at the middle ball, would you be willing to pay me
> $1 every time one of the end balls was roqueted if I agreed to pay you
> $1 every time the middle ball of the five was roqueted? I suspect that
> I might come out in front. [For the purpose of the exercise, if it were
> attempted in practice, the 2nd and 4th balls should be removed, and of
> course you could claim a roquet on only the first ball contacted.]
>
> I am not saying you are wrong, but I would like to be convinced.

You're comparing shooting at a single ball with shooting at two balls with a gap bigger than a ball.
I specifically said that it was possible to have a higher probability by shooting at the gap in such
a situation:

>> Note that this is different from having a target with a gap, where you
>> do not have choice of placement of the striker's ball, in which case
>> shooting at the middle may well be better than shooting at one of the
>> balls.

REW wanted to compare shooting at a "perfect" double (i.e. one where the gap is a hairs breadth
smaller than a ball) with a double where the gap is bigger than a ball.

Dave

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target
>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I suspect the distribution is somewhat skewed for some people (those who
claim "I always miss to the left", etc), in which case probably setting a
perfect double and then shooting slightly towards one ball or the other
might maximise hitting probability (if the skew is in terms of the average
being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit
with a pretty wide spread for many. Too many data points required to measure
it though (and, of course, if you take enough data in a short time to plot
the distribution, the distribution usually changes as you are collecting
data!).

Cheers,
Jenny


On 10 May 2010 00:07, KEITH AITON <> wrote:

> I'm not 'having a go' at anyone, but is there any evidence to support the
> assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
> > To: .uk
> > Subject: Re: [Croquet] Maximising chances of hitting a double target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around the intended
> target then you are best to line up a perfect double (I.e. So that the gap
> is exactly one ball diameter) and then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of going through
> the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when shooting at a huge
> target, even though there is a hole in the middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a sloping East
> boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk <
> croquet-.uk>
> > To: Notts List <.uk>
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double target; e.g.
> > choosing where to put your ball when taking a lift shot, or running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect" double;
> > i.e. if my ball misses one target by a millimetre it hits the other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double on the
> > East boundary (Rover high) and lined up a target with a deliberate small
> > gap. This was because my shooting was a bit rough that day and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and assuming
> > that my shooting is normally distributed abou tthe centre of my target,
> > what's the correct way of choosing how wide a gap to leave in the
> > double? (Shoudl I be trying, for instance, to make the odds of missing
> > through the middle equal to the odds of missing on one side or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Thank you, Dave.

However I was aware of, and understood, what you had said.

I would like to see proof that (when shooting at a rather distant
two-ball target) there is a greater probability of hitting it if the
two balls are less than a ball's width apart than if they were
slightly more than a ball's width apart.

JR.


On 09/05/2010, at 9:23 PM, David Maugham wrote:

> On 09/05/2010 12:15, johnriches wrote:
>> In other words, if you (or some other reasonably good player) were to
>> take, say, 20 shots at the middle ball, would you be willing to
>> pay me
>> $1 every time one of the end balls was roqueted if I agreed to pay
>> you
>> $1 every time the middle ball of the five was roqueted? I suspect
>> that
>> I might come out in front. [For the purpose of the exercise, if
>> it were
>> attempted in practice, the 2nd and 4th balls should be removed,
>> and of
>> course you could claim a roquet on only the first ball contacted.]
>>
>> I am not saying you are wrong, but I would like to be convinced.
>
> You're comparing shooting at a single ball with shooting at two
> balls with a gap bigger than a ball. I specifically said that it
> was possible to have a higher probability by shooting at the gap in
> such a situation:
>
>>> Note that this is different from having a target with a gap,
>>> where you
>>> do not have choice of placement of the striker's ball, in which case
>>> shooting at the middle may well be better than shooting at one of
>>> the
>>> balls.
>
> REW wanted to compare shooting at a "perfect" double (i.e. one
> where the gap is a hairs breadth smaller than a ball) with a double
> where the gap is bigger than a ball.
>
> Dave
>


NOTE: Views expressed in this email are my own personal opinions and
do not necessarily represent those of the ACA. On Sun, 09 May 2010 13:18:42 +0100, Jenny Clarke <> wrote:
> I suspect the distribution is somewhat skewed for some people (those who
> claim "I always miss to the left", etc), in which case probably setting a
> perfect double and then shooting slightly towards one ball or the other
> might maximise hitting probability (if the skew is in terms of the
> average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people, albeit
> with a pretty wide spread for many. Too many data points required to
> measure it though ...

If the target is far enough away (or the ground bumpy enough, or the
shooter inaccurate enough) that the normal distribution curve is nearly
flat over the width of 6 balls, would it not be better to leave a 2
ball-width gap rather than (a shade under) 1 ball-width?

Theoretically this gives two separate targets, each 3 balls wide, rather
than one 5 balls wide.

Colin McKenzie (who went through the middle of such a target yesterday,
but usually misses on the outside).

--
Frightening isn't the same as dangerous.

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I believe my shooting is either on/very close, OR I miss by a foot or more. So I'm not sure a normal distribution describes these results well.

Of course, those where I miss by a foot or more aren't going to hit a double target anyway - and perhaps the ones which are on/ very close may follow a normal distribution of their own around the aim line.

regards
Martin French
07718 630804
----- Original Message -----
From: Jenny Clarke
To: KEITH AITON
Cc: Notts List ; Samir (Corda) (UK) Patel
Sent: Sunday, May 09, 2010 1:18 PM
Subject: Re: [Croquet] Maximising chances of hitting a double target


I suspect the distribution is somewhat skewed for some people (those who claim "I always miss to the left", etc), in which case probably setting a perfect double and then shooting slightly towards one ball or the other might maximise hitting probability (if the skew is in terms of the average being left or right of centre).

I would expect pretty much a normal distribution for most people, albeit with a pretty wide spread for many. Too many data points required to measure it though (and, of course, if you take enough data in a short time to plot the distribution, the distribution usually changes as you are collecting data!).

Cheers,
Jenny



On 10 May 2010 00:07, KEITH AITON <> wrote:

I'm not 'having a go' at anyone, but is there any evidence to support the assumption that shooting follows a normal distribution?

Keith

> Date: Sun, 9 May 2010 12:25:32 +0100
> From:
> To: .uk
> Subject: Re: [Croquet] Maximising chances of hitting a double target

>
>
> Rob,
>
> Assuming your shooting follows a normal distribution around the intended target then you are best to line up a perfect double (I.e. So that the gap is exactly one ball diameter) and then aim at the middle of it.
>
> Increasing the gap will give you a greater probability of going through the hole than of grazing the outside of the target.
>
> This ignores
> - psychological issues (you may be more confident when shooting at a huge target, even though there is a hole in the middle)
> - aiming (I you may find aiming at a gap quite disconcerting)
> - matters of gravity (if you're lining up a "double" down a sloping East boundary, you want to leave a smaller gap).
>
> Samir
>
>
> -----
> Sent from Blackberry Wireless
>
> ----- Original Message -----
> From: croquet-.uk
> To: Notts List <.uk>
> Sent: Sun May 09 08:06:10 2010
> Subject: [Croquet] Maximising chances of hitting a double target
>
>
> *** WARNING ***
>
> This message has originated outside your organisation,
> either from an external partner or the Global Internet.
> Keep this in mind if you answer this message.
>
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. I have to agree with David that the maths is clearly in favour of
leaving the 'perfect double' - i.e. a gap of exactly one ball's width.
However, if I am shooting from some distance away (say 2 x my critical
distance), so that the distribution curve is flattish, then I will
generally aim to leave a gap of a fraction over 1 ball. This is not
because I doubt the math, but because it is difficult to judge exactly
one ball's gap, and I would rather err on the side of making the gap a
fraction too big, rather than a fraction too small.

I've always thought the more interesting question is the one David
avoided - i.e. with a target with a given gap > 1 ball's width, at what
point is it better to aim at one of the balls, rather than at the gap?

Regards

Jeff

On 09/05/2010 15:07, Martin French wrote:
> I believe my shooting is either on/very close, OR I miss by a foot or
> more. So I'm not sure a normal distribution describes these results well.
> Of course, those where I miss by a foot or more aren't going to hit a
> double target anyway - and perhaps the ones which are on/ very close may
> follow a normal distribution of their own around the aim line.
> regards
> Martin French
> 07718 630804
>
> ----- Original Message -----
> *From:* Jenny Clarke
> *To:* KEITH AITON
> *Cc:* Notts List ; Samir
> (Corda) (UK) Patel
> *Sent:* Sunday, May 09, 2010 1:18 PM
> *Subject:* Re: [Croquet] Maximising chances of hitting a double target
>
> I suspect the distribution is somewhat skewed for some people (those
> who claim "I always miss to the left", etc), in which case probably
> setting a perfect double and then shooting slightly towards one ball
> or the other might maximise hitting probability (if the skew is in
> terms of the average being left or right of centre).
>
> I would expect pretty much a normal distribution for most people,
> albeit with a pretty wide spread for many. Too many data points
> required to measure it though (and, of course, if you take enough
> data in a short time to plot the distribution, the distribution
> usually changes as you are collecting data!).
>
> Cheers,
> Jenny
>
>
> On 10 May 2010 00:07, KEITH AITON <
> > wrote:
>
> I'm not 'having a go' at anyone, but is there any evidence to
> support the assumption that shooting follows a normal distribution?
>
> Keith
>
> > Date: Sun, 9 May 2010 12:25:32 +0100
> > From:
>
> > To: .uk
>
> > Subject: Re: [Croquet] Maximising chances of hitting a double
> target
>
> >
> >
> > Rob,
> >
> > Assuming your shooting follows a normal distribution around
> the intended target then you are best to line up a perfect
> double (I.e. So that the gap is exactly one ball diameter) and
> then aim at the middle of it.
> >
> > Increasing the gap will give you a greater probability of
> going through the hole than of grazing the outside of the target.
> >
> > This ignores
> > - psychological issues (you may be more confident when
> shooting at a huge target, even though there is a hole in the
> middle)
> > - aiming (I you may find aiming at a gap quite disconcerting)
> > - matters of gravity (if you're lining up a "double" down a
> sloping East boundary, you want to leave a smaller gap).
> >
> > Samir
> >
> >
> > -----
> > Sent from Blackberry Wireless
> >
> > ----- Original Message -----
> > From: croquet-.uk
>
> > >
> > To: Notts List <.uk
> >
> > Sent: Sun May 09 08:06:10 2010
> > Subject: [Croquet] Maximising chances of hitting a double target
> >
> >
> > *** WARNING ***
> >
> > This message has originated outside your organisation,
> > either from an external partner or the Global Internet.
> > Keep this in mind if you answer this message.
> >
> >
> > Perhaps a question for mathematicians or statisticans.
> >
> > Sometimes you get a choice of how big to make a double
> target; e.g.
> > choosing where to put your ball when taking a lift shot, or
> running a
> > hoop undercontrol after which you have a long shot at a double.
> >
> > Historically I;ve usually tried to line up for the "perfect"
> double;
> > i.e. if my ball misses one target by a millimetre it hits the
> other
> > target by a millimetre.
> >
> > However the other day, I took a lift from A baulk at a double
> on the
> > East boundary (Rover high) and lined up a target with a
> deliberate small
> > gap. This was because my shooting was a bit rough that day
> and I felt
> > this maximised my chances.
> >
> > So a theoretical question. If all other things are equal, and
> assuming
> > that my shooting is normally distributed abou tthe centre of
> my target,
> > what's the correct way of choosing how wide a gap to leave in
> the
> > double? (Shoudl I be trying, for instance, to make the odds
> of missing
> > through the middle equal to the odds of missing on one side
> or the
> > other? And if so, how do I estimate the target width to do this?)
> >
> > _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Rob,

I'm not a mathematician or statistician, but I think I have a reasonable understanding of odds.



The answer to your question is entirely dependent upon the individuals shooting over the given distance.



For example, for a good shot over a short distance, the answer will always be to have the gap at one ball apart. For worse shots over longer distance, the answer will be to have the gap two balls apart.



To try and explain the above, the trade off between having a "target" of 5 balls compared with a "target" of 6 balls changes depending on your likelihood of going through the middle.



How you determine the gap for any given distance is just down to understanding your own ability, like so many other aspects of the game.



Chris

> Date: Sun, 9 May 2010 08:06:10 +0100
> From:
> To: .uk
> Subject: [Croquet] Maximising chances of hitting a double target
>
> Perhaps a question for mathematicians or statisticans.
>
> Sometimes you get a choice of how big to make a double target; e.g.
> choosing where to put your ball when taking a lift shot, or running a
> hoop undercontrol after which you have a long shot at a double.
>
> Historically I;ve usually tried to line up for the "perfect" double;
> i.e. if my ball misses one target by a millimetre it hits the other
> target by a millimetre.
>
> However the other day, I took a lift from A baulk at a double on the
> East boundary (Rover high) and lined up a target with a deliberate small
> gap. This was because my shooting was a bit rough that day and I felt
> this maximised my chances.
>
> So a theoretical question. If all other things are equal, and assuming
> that my shooting is normally distributed abou tthe centre of my target,
> what's the correct way of choosing how wide a gap to leave in the
> double? (Shoudl I be trying, for instance, to make the odds of missing
> through the middle equal to the odds of missing on one side or the
> other? And if so, how do I estimate the target width to do this?)
>
> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Colin McKenzie wrote:
>
> If the target is far enough away (or the ground bumpy enough, or the
> shooter inaccurate enough) that the normal distribution curve is
> nearly flat over the width of 6 balls, would it not be better to leave
> a 2 ball-width gap rather than (a shade under) 1 ball-width?
>
> Theoretically this gives two separate targets, each 3 balls wide,
> rather than one 5 balls wide.
>
> Colin McKenzie (who went through the middle of such a target
> yesterday, but usually misses on the outside).
>
Yes, I agree with this; if the distribution is completely flat (i.e. if
your shooting is completely random within this range) then this is
clearly better to have a 2 ball gap. There's also clearly no advantage
to having less than a one ball gap, but I'm unsure where to go between
these limits. I imagine there's some relationship between the standard
deviation and the optimal gap, but I'm not as adept at statistical
theory as I once was.

Dave M is right to say that different criteria apply to the relatd
question of whether to shoot at a single ball or the gap when aiming at
an imperfect double.

There's another related question, which is to do with how much of a gap
to leave to avoid an attractive double target when making leaves.

Keith is right to question the suggestion that shooting is "Normally
Distributed" around a mean. I didn't assume it to be true; just
suggested it as a basis for a calculation.

Another interesting thought based on target size. most people probably
feel they could shoot a ball from corner 1 to go off the lawn in the
corner 2 area without a problem; with far more confidence than - say -
hitting an 7 yard roquet. And yet the latter is a slightly larger target.

_______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. Hi all,

I think some of what Chris wrote, and possibly also Colin and John, is
based on the common fallacy that shooting at a single ball, your
target is 3 balls wide. This is based on the idea that your ball could
hit the target ball in the middle, or just graze it on the left or
right, making a picture three balls wide. However, the middle of the
SB must hit a target 2 balls wide - somewhere from half a ball's width
to the left of the target to half a ball to the right. This is the
real width of the target.

Two balls can never make a target bigger than twice the size of a
single ball target. So a perfect double is a target 4 balls wide.

Similarly, the real width of your target when shooting at the peg is
the diameter of one ball plus the diameter of the peg.

Jonathan




On 9 May 2010 17:45, chris clarke <> wrote:
> Rob,
> I'm not a mathematician or statistician, but I think I have a reasonable
> understanding of odds.
>
> The answer to your question is entirely dependent upon the individuals
> shooting over the given distance.
>
> For example, for a good shot over a short distance, the answer will always
> be to have the gap at one ball apart. For worse shots over longer distance,
> the answer will be to have the gap two balls apart.
>
> To try and explain the above, the trade off between having a "target" of 5
> balls compared with a "target" of 6 balls changes depending on your
> likelihood of going through the middle.
>
> How you determine the gap for any given distance is just down to
> understanding your own ability, like so many other aspects of the game.
>
> Chris
>
>> Date: Sun, 9 May 2010 08:06:10 +0100
>> From:
>> To: .uk
>> Subject: [Croquet] Maximising chances of hitting a double target
>>
>> Perhaps a question for mathematicians or statisticans.
>>
>> Sometimes you get a choice of how big to make a double target; e.g.
>> choosing where to put your ball when taking a lift shot, or running a
>> hoop undercontrol after which you have a long shot at a double.
>>
>> Historically I;ve usually tried to line up for the "perfect" double;
>> i.e. if my ball misses one target by a millimetre it hits the other
>> target by a millimetre.
>>
>> However the other day, I took a lift from A baulk at a double on the
>> East boundary (Rover high) and lined up a target with a deliberate small
>> gap. This was because my shooting was a bit rough that day and I felt
>> this maximised my chances.
>>
>> So a theoretical question. If all other things are equal, and assuming
>> that my shooting is normally distributed abou tthe centre of my target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>>
>> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe. At the last USCA Selection 8s I had two good days of making roquets and
two dreadful days. On the dreadful days when shooting at the middle of wide
doubles (up to a half a yard gap at 18+ yards) I did not go through the
gap once. I either roqueted or missed outside the balls. This summer I will
video three sets of 10 attempts and share results. Chris' comment on
understanding ones ability is spot on. If you're a top 20 player you'll likely
have a small gap. If you struggle like me, the gap can be wider. Bob K.


In a message dated 5/9/2010 11:52:36 A.M. Eastern Daylight Time,
writes:

Hi all,

I think some of what Chris wrote, and possibly also Colin and John, is
based on the common fallacy that shooting at a single ball, your
target is 3 balls wide. This is based on the idea that your ball could
hit the target ball in the middle, or just graze it on the left or
right, making a picture three balls wide. However, the middle of the
SB must hit a target 2 balls wide - somewhere from half a ball's width
to the left of the target to half a ball to the right. This is the
real width of the target.

Two balls can never make a target bigger than twice the size of a
single ball target. So a perfect double is a target 4 balls wide.

Similarly, the real width of your target when shooting at the peg is
the diameter of one ball plus the diameter of the peg.

Jonathan




On 9 May 2010 17:45, chris clarke <> wrote:
> Rob,
> I'm not a mathematician or statistician, but I think I have a reasonable
> understanding of odds.
>
> The answer to your question is entirely dependent upon the individuals
> shooting over the given distance.
>
> For example, for a good shot over a short distance, the answer will
always
> be to have the gap at one ball apart. For worse shots over longer
distance,
> the answer will be to have the gap two balls apart.
>
> To try and explain the above, the trade off between having a "target" of
5
> balls compared with a "target" of 6 balls changes depending on your
> likelihood of going through the middle.
>
> How you determine the gap for any given distance is just down to
> understanding your own ability, like so many other aspects of the game.
>
> Chris
>
>> Date: Sun, 9 May 2010 08:06:10 +0100
>> From:
>> To: .uk
>> Subject: [Croquet] Maximising chances of hitting a double target
>>
>> Perhaps a question for mathematicians or statisticans.
>>
>> Sometimes you get a choice of how big to make a double target; e.g.
>> choosing where to put your ball when taking a lift shot, or running a
>> hoop undercontrol after which you have a long shot at a double.
>>
>> Historically I;ve usually tried to line up for the "perfect" double;
>> i.e. if my ball misses one target by a millimetre it hits the other
>> target by a millimetre.
>>
>> However the other day, I took a lift from A baulk at a double on the
>> East boundary (Rover high) and lined up a target with a deliberate small
>> gap. This was because my shooting was a bit rough that day and I felt
>> this maximised my chances.
>>
>> So a theoretical question. If all other things are equal, and assuming
>> that my shooting is normally distributed abou tthe centre of my target,
>> what's the correct way of choosing how wide a gap to leave in the
>> double? (Shoudl I be trying, for instance, to make the odds of missing
>> through the middle equal to the odds of missing on one side or the
>> other? And if so, how do I estimate the target width to do this?)
>>
>> _______________________________________________
___________________________________________________

Posted on the Croquet mailing list. Go to http://nottingham-lists.org.uk/mailman/listinfo/croquet to subscribe.