Margin of Error

[JoeW]

Can someone point me to a thread or a web site that discusses the size of the contact point for different angles and the margin of error for different distances.

I am looking for the margin of error for different shots over different distances.

For instance on a straight in shot the size of the contact point is .xx while on a 30 degree cut shot the size of the contact point is .xx

On a 30 degree cut shot that is 6" from the pocket the contact point is .xx with .yy margin of error.

On a 30 degree cut shot that is 24 inches from the corner pocket the size of the contact point is .xx with .yy margin of error on a standard table with zz size pockets.

What I am attempting to determine is how accuate the player must be in order to make different shots. While this has probably been combined into a degree of difficulty equation that is not what I am looking for.

What I am attemptng to do is to state how accurate one must be to make X shot. Somthing like, "The player must hit within 1/64 of an inch of the correct aiming lines to make xx shot over yy distance with the CB at zz distance."

To make my point, I think that all I really need is some estimate of the margin of error for something like a 30 degree cut shot with OB 24 inches from a 4.5 inch pocket and the cb 36 inches away from the OB. One must aim the CB at a contact point that is x in diameter.

The reason for my request is that I have an idea about how the mind aims a shot that I will present here on AZB but to make the argument I need to precede it with the accuracy requirements to make a particular shot.

Nothing like jumping into the aiming controversy. Of course my perspective is that of psychology, not physics. I suspect the physics guys and others will take me to task so I need to be prepared.

Any help is appreciated.

 

[Patrick Johnson]

Can someone point me to a thread or a web site that discusses the size of the contact point for different angles and the margin of error for different distances.

I am looking for the margin of error for different shots over different distances.

For instance on a straight in shot the size of the contact point is .xx while on a 30 degree cut shot the size of the contact point is .xx

On a 30 degree cut shot that is 6" from the pocket the contact point is .xx with .yy margin of error.

On a 30 degree cut shot that is 24 inches from the corner pocket the size of the contact point is .xx with .yy margin of error on a standard table with zz size pockets.

What I am attempting to determine is how accuate the player must be in order to make different shots. While this has probably been combined into a degree of difficulty equation that is not what I am looking for.

What I am attemptng to do is to state how accurate one must be to make X shot. Somthing like, "The player must hit within 1/64 of an inch of the correct aiming lines to make xx shot over yy distance with the CB at zz distance."

To make my point, I think that all I really need is some estimate of the margin of error for something like a 30 degree cut shot with OB 24 inches from a 4.5 inch pocket and the cb 36 inches away from the OB. One must aim the CB at a contact point that is x in diameter.

The reason for my request is that I have an idea about how the mind aims a shot that I will present here on AZB but to make the argument I need to precede it with the accuracy requirements to make a particular shot.

Nothing like jumping into the aiming controversy. Of course my perspective is that of psychology, not physics. I suspect the physics guys and others will take me to task so I need to be prepared.

Any help is appreciated.

Here's a matrix of actual OB contact area sizes for various pocket sizes and distances, Joe.



Somebody else will have to give you the formula to figure out how much they're reduced by viewing them at an angle (for various cut angles).

pj
chgo

 

[Scott Lee]

Joe...Your post makes no sense to me. Are you talking about the size of the contact point between the tip and CB (which is 3mm or 1/8"), or the size of the contact point between the CB & OB (which is infinitely smaller)? IMO, the size doesn't change, whether the shot is straight in or any cut angle. Margin of error depends mostly on pocket size. Aim in the center of the pocket, and it makes no difference.

Scott Lee
www.poolknowledge.com

Can someone point me to a thread or a web site that discusses the size of the contact point for different angles and the margin of error for different distances.

I am looking for the margin of error for different shots over different distances.

For instance on a straight in shot the size of the contact point is .xx while on a 30 degree cut shot the size of the contact point is .xx

On a 30 degree cut shot that is 6" from the pocket the contact point is .xx with .yy margin of error.

On a 30 degree cut shot that is 24 inches from the corner pocket the size of the contact point is .xx with .yy margin of error on a standard table with zz size pockets.

What I am attempting to determine is how accuate the player must be in order to make different shots. While this has probably been combined into a degree of difficulty equation that is not what I am looking for.

What I am attemptng to do is to state how accurate one must be to make X shot. Somthing like, "The player must hit within 1/64 of an inch of the correct aiming lines to make xx shot over yy distance with the CB at zz distance."

To make my point, I think that all I really need is some estimate of the margin of error for something like a 30 degree cut shot with OB 24 inches from a 4.5 inch pocket and the cb 36 inches away from the OB. One must aim the CB at a contact point that is x in diameter.

The reason for my request is that I have an idea about how the mind aims a shot that I will present here on AZB but to make the argument I need to precede it with the accuracy requirements to make a particular shot.

Nothing like jumping into the aiming controversy. Of course my perspective is that of psychology, not physics. I suspect the physics guys and others will take me to task so I need to be prepared.

Any help is appreciated.

 

[Still_Learning]

Jack Koehler's (sp?) book on the science of pocket billiards has a table showing the margin of error, in fractions of a degree, for any shot based on both distance from CB to OB and distance from OB to pocket. It does not, however, give variations for different pocket sizes, and I'm not even sure it specifies what pocket size the information was based on.

 

[Patrick Johnson]

Joe, here's a little help for adjusting "target size" for the angled perspective you get with cut angles. Maybe you can extrapolate (interpolate?) for angles in between these.

3/4 CB/OB overlap = 14.48 degrees cut angle: reduce target size by -3%
1/2 CB/OB overlap = 30.00 degrees cut angle: reduce target size by -15%
1/4 CB/OB overlap = 48.59 degrees cut angle: reduce target size by -34%

Hope this helps.

pj
chgo

 

[JoeW]

Thank you one and all. I think that I have what I need.

Scott, it seems to me that when you hit an OB head on the margin of error for the contact point is a larger diameter than if the cb strikes the contact point at an angle. I seem to remember someone saying that these contact points were different diameters. This may or may not be the case and so I thought I would ask. PJ matrix is what I was looking for, though I may not have stated it as well as it could be stated. My apologies for the confusion.

Apparently with a 5 inch pocket and the OB at 24 inches the margin of error on the contact point is 1/8 inch or .125
when there is 48 inches to the pocket the margin of error on the contact point is 1/16 inch or .0625

Using PJ cut angle reductions the margin of error on the contact point for a 24 inch 1/2 ball hit is reduced by .125 - (.15 X .125) = .10 or 3/32 inch"

for a 48 inch 1/2 ball hit the margin of error is reduced by .0626 - (.0625 X .34) = 041 or 3 /64 of an inch.

These are estimates and of course do not consider many other factors. None-the-less it gives some idea of the margins of error at the contact point.

 

[Patrick Johnson]

Thank you one and all. I think that I have what I need.

Scott, it seems to me that when you hit an OB head on the contact point is a larger diameter than if the cb strikes it at an angle. I seem to remember someone saying that these contact points were different diameters.

I think Scott's talking about the size of the area on both balls that are actually in contact at impact (due to the slight compression of the balls). You and I are talking about the size of the target area on the OB that must be hit to pocket the ball (including margin for error due to pocket size being greater than ball diameter).

pj
chgo

 

[JoeW]

I think Scott's talking about the size of the area on both balls that are actually in contact at impact (due to the slight compression of the balls). You and I are talking about the size of the target area on the OB that must be hit to pocket the ball (including margin for error due to pocket size being greater than ball diameter).

pj
chgo

Ahhhh -- thank you for the clarification. That is exactly what I was looking for. Now I see the confusion.

Assuming that my extrapolations are reasonable approximations I can now show what the player must be able to "see" from different CB distances. A figure that displays the actual target will assist with presenting some information of how the eye can calclate hitting this target when there is no actual target on a pool ball.

From what I have been studying I think that the eye actually needs to calculate the various angles that will result in the CB -OB contact. A person may say that they look at a contact point but I think that neuropsych input may lead to the idea that what the mind does is attempt to determine the intersection of lines.

I suspect that people who think they are doing something else are deceiving themselves because the brain has ways of perceiving.

 

[JoeW]

Jack Koehler's (sp?) book on the science of pocket billiards has a table showing the margin of error, in fractions of a degree, for any shot based on both distance from CB to OB and distance from OB to pocket. It does not, however, give variations for different pocket sizes, and I'm not even sure it specifies what pocket size the information was based on.

Thanks I have Jack's book. I knew it was somewhere like that should have thought of him.

Joe

 

[Bob Jewett]

Here's a matrix of actual OB contact area sizes for various pocket sizes and distances, Joe.

View attachment 74511

Somebody else will have to give you the formula to figure out how much they're reduced by viewing them at an angle (for various cut angles).

pj
chgo

A reasonable approximation is to multiply them by the cosine* of the cut angle.
Cut cosine
0 -- 1.00
30 -- 0.87
45 -- 0.71
60 -- 0.50
80 -- 0.17

The target for an 80-degree cut is only 1/6 as large as the same-length straight-in. Up to about a half-ball cut, the target is not much reduced.

A similar topic is discussed in http://www.sfbilliards.com/articles/1994-04.pdf which doesn't discuss the size of the target at the object ball but does discuss how accurately your bridge must be placed for any particular shot including a simple way to graphically include the cut angle in the required accuracy calculation. It turns out that for a spot shot, your bridge has to be within 1/32nd of an inch of the correct place.

* (If you go to the google search page, and type in "cosine(30 degrees)" as the thing to be searched for, google will give you the value of that expression.)

 

[Bob Jewett]

I think Scott's talking about the size of the area on both balls that are actually in contact at impact (due to the slight compression of the balls). You and I are talking about the size of the target area on the OB that must be hit to pocket the ball (including margin for error due to pocket size being greater than ball diameter).

pj
chgo

Yes, I think that's true. Depending on the shot, either of these two sizes can be larger.

 

[Jal]

...What I am attemptng to do is to state how accurate one must be to make X shot. Somthing like, "The player must hit within 1/64 of an inch of the correct aiming lines to make xx shot over yy distance with the CB at zz distance."

To make my point, I think that all I really need is some estimate of the margin of error for something like a 30 degree cut shot with OB 24 inches from a 4.5 inch pocket and the cb 36 inches away from the OB. One must aim the CB at a contact point that is x in diameter.

If you want an "exact" formula (perfect spheres, sans throw) that includes CB-OB distance in the mix, I have it. While it's relatively simple, it does contain trig functions.

Jim