How Many Angles Is Enough?

[Patrick Johnson]

Whenever the subject of "x angles" aiming systems comes up (and when doesn't it?), a predictable bone of contention is exactly how many angles are necessary to make all possible shots, taking into account the "margin of error" provided by pockets being bigger than balls. I don't think it's ever been answered in those terms, and it's easy to do, so here's the answer in a nutshell:

For a wide range of pocket widths (4.5 to 5.5 inches), an aiming system needs only 6-8 cut angles in each direction to make all balls within 1 foot of pockets.

So far, so good, but that number multiplies quickly as shots get longer.

To make all balls within 3 feet of pockets, 18-24 cut angles in each direction are needed. And for all balls within 5 feet of pockets, 30-40 cut angles in each direction.

The systems we hear about all have 10 cut angles or less, which means 2/3 of 3-foot shots and 4/5 of 5-foot shots can only be made with some kind of adjustment from the system.

I'm not making a point, just passing along the information for future reference because I happened to be thinking about it. The math for this is simple - anybody's welcome to it.

pj
chgo

 

[klockdoc]

Whenever the subject of "x angles" aiming systems comes up (and when doesn't it?), a predictable bone of contention is exactly how many angles are necessary to make all possible shots, taking into account the "margin of error" provided by pockets being bigger than balls. I don't think it's ever been answered in those terms, and it's easy to do, so here's the answer in a nutshell:

For a wide range of pocket widths (4.5 to 5.5 inches), an aiming system needs only 6-8 cut angles in each direction to make all balls within 1 foot of pockets.

So far, so good, but that number multiplies quickly as shots get longer.

To make all balls within 3 feet of pockets, 18-24 cut angles in each direction are needed. And for all balls within 5 feet of pockets, 30-40 cut angles in each direction.

The systems we hear about all have 10 cut angles or less, which means 2/3 of 3-foot shots and 4/5 of 5-foot shots can only be made with some kind of adjustment from the system.

I'm not making a point, just passing along the information for future reference because I happened to be thinking about it. The math for this is simple - anybody's welcome to it.

pj
chgo

Why would there be more angles to a shot at 1 foot, if the cue ball was brought back to the same original angle, but 5 foot away???

The length of the shot has changed, but the angles stay consistent, don't they???

 

[RRfireblade]

Why would there be more angles to a shot at 1 foot, if the cue ball was brought back to the same original angle, but 5 foot away???

The length of the shot has changed, but the angles stay consistent, don't they???

Yes but the margin for error is greater as your closer and less as you get farther from the hole requiring more precision.

 

[av84fun]

Extremely interesting data. While I digest it, let me ask you this. What is the width of the surface of the CB/OB when they contact each other. In other words, when the two balls are touching each other, what is the width of the surface that is in contact with the other ball?

It's hard to tell just by looking and I thought you would know.

Thanks!
Jim

 

[predator]

What if you're shooting over a ball draw shot with heavy right spin with the cue stick elevated? How can anything other than experience and feel work on that one?

 

[WesleyW]

Patrick, nice information, but you are making 1 big mistake. You don't need all the angles to make the balls. There are 6 holes in the table, not 1. Every hole requires different angles. The further the distance AND the bigger the angle (I've calculated it, the bigger the angle, the difficult the shot, because of lesser margin error, for example the angle of a half ball hit is only 30 degrees, but the angle of an almost full ball miss is almost 90 degrees), the more angles you need. When this occures, you can choose an easier hole to make that ball, so you don't need all the angles. Ofcourse you will say, what if other balls blocking the easier holes? Then you need to play safety and don't make the ball, that also requires lesser angles.

So a few angles (perhaps 10-12) will be enough to win the game.

 

[SpiderWebComm]

Just to make the new aiming thread complete....

I know there's a difference between cut angles and aim, but it seems PJ is connecting the two. However, you can always shoot 1-aim and make everything.

 

[Patrick Johnson]

Extremely interesting data. While I digest it, let me ask you this. What is the width of the surface of the CB/OB when they contact each other. In other words, when the two balls are touching each other, what is the width of the surface that is in contact with the other ball?

It's hard to tell just by looking and I thought you would know.

Thanks!
Jim

I think it's small enough to be practically zero. Why?

pj
chgo

 

[Patrick Johnson]

Just to make the new aiming thread complete....

I know there's a difference between cut angles and aim, but it seems PJ is connecting the two. However, you can always shoot 1-aim and make everything.

Why so cryptic? Wouldn't it be easier to just say what "1-aim" means?

pj
chgo

 

[Patrick Johnson]

... You don't need all the angles to make the balls. There are 6 holes in the table, not 1.

You let your aiming system dictate which pocket you'll shoot at?

pj
chgo

 

[Patrick Johnson]

Why would there be more angles to a shot at 1 foot, if the cue ball was brought back to the same original angle, but 5 foot away???

The length of the shot has changed, but the angles stay consistent, don't they???

I don't know what "more angles to a shot" means, but here's a brief explanation:

Because pockets are bigger than balls, OB contact points are really "contact areas" whose size is determined by the amount of "slop" available in the pockets (you can miss the "ideal" contact point by a small amount and still put the ball in a pocket). In order to be able to send the OB to any place on the table so that any possible shot can be made ("100% shotmaking"), these contact areas must cover the entire OB equator leaving no gaps. Each gap between a system's contact areas = an area of the table that the OB can't be sent to using the system, an area that might just contain the pocket for your shot.

The closer OBs are to pockets, the bigger these contact areas are (because pockets are "bigger" when OBs are closer) and fewer of them are needed to cover the entire OB equator. Conversely, the farther OBs are from pockets, the smaller these contact areas are and more of them are needed to cover all the possible shots.

pj
chgo

 

[WesleyW]

You let your aiming system dictate which pocket you'll shoot at?

pj
chgo

Yes, you should always choose the most easiest pocket to shoot at. To contain position, you can use english.

 

[Patrick Johnson]

Me:
You let your aiming system dictate which pocket you'll shoot at?

WesleyW:
Yes, you should always choose the most easiest pocket to shoot at. To contain position, you can use english.

That's enough reason to not use that system. I'd never use a system that couldn't make any shot that I choose.

pj
chgo

 

[Bob Jewett]

Yes, you should always choose the most easiest pocket to shoot at. To contain position, you can use english.

This is one of the most remarkable statements I've ever seen on pool forums. Have you ever played one pocket?

 

[Bob Jewett]

Just to make the new aiming thread complete....

I know there's a difference between cut angles and aim, but it seems PJ is connecting the two. However, you can always shoot 1-aim and make everything.

I think Pat's trying to discuss geometry and physics, not psychology and mesmerism.

Has Hal said whether it's OK for you to discuss his systems after he's dead? Do you intend to then?

 

[klockdoc]

I don't know what "more angles to a shot" means, but here's a brief explanation:

Because pockets are bigger than balls, OB contact points are really "contact areas" whose size is determined by the amount of "slop" available in the pockets (you can miss the "ideal" contact point by a small amount and still put the ball in a pocket). In order to be able to send the OB to any place on the table so that any possible shot can be made ("100% shotmaking"), these contact areas must cover the entire OB equator leaving no gaps. Each gap between a system's contact areas = an area of the table that the OB can't be sent to using the system, an area that might just contain the pocket for your shot.

The closer OBs are to pockets, the bigger these contact areas are (because pockets are "bigger" when OBs are closer) and fewer of them are needed to cover the entire OB equator. Conversely, the farther OBs are from pockets, the smaller these contact areas are and more of them are needed to cover all the possible shots.

pj
chgo

Thank you for the explanation

 

[Patrick Johnson]

Thank you for the explanation

My pleasure.

pj
chgo

 

[shakes]

Whenever the subject of "x angles" aiming systems comes up (and when doesn't it?), a predictable bone of contention is exactly how many angles are necessary to make all possible shots, taking into account the "margin of error" provided by pockets being bigger than balls. I don't think it's ever been answered in those terms, and it's easy to do, so here's the answer in a nutshell:

For a wide range of pocket widths (4.5 to 5.5 inches), an aiming system needs only 6-8 cut angles in each direction to make all balls within 1 foot of pockets.

So far, so good, but that number multiplies quickly as shots get longer.

To make all balls within 3 feet of pockets, 18-24 cut angles in each direction are needed. And for all balls within 5 feet of pockets, 30-40 cut angles in each direction.

The systems we hear about all have 10 cut angles or less, which means 2/3 of 3-foot shots and 4/5 of 5-foot shots can only be made with some kind of adjustment from the system.

I'm not making a point, just passing along the information for future reference because I happened to be thinking about it. The math for this is simple - anybody's welcome to it.

pj
chgo

Great post! I've been working on this conundrum myself, as I have seen and used one of the systems, and was curious as to why it worked. Was I making the adjustments subconsciously, or was the system working. One of the important differences in the aiming systems that I've noticed is that they teach AIM points, not CONTACT points.

If you'll take a wooden dowel and put it on the edge of the object ball, with the other end pivoting in place, (The edge of the object ball is an aim point, the pivot acting as the center of the cue ball you are aiming through) and bring the object ball straight back to the pivot, you will notice that as the object ball gets closer, the dowel will push out further to the side, thus changing the actual angle of cut. I'm trying to draw out my thoughts on the wei table, and hopefully I will have that up soon, but the systems could be sound, I just don't know how many angles are necessary. It could be 6, it could be 10. But I don't think an infinite number are necessary. JMO.

 

[Patrick Johnson]

I don't think an infinite number [of aim points] are necessary. JMO.

You're right in more ways than one. An infinite number isn't necessary to make all possible shots without adjustment (50 will probably be enough - see my numbers above), and only a few are necessary to make all possible shots with adjustment (this is how I think these systems actually work).

pj
chgo

 

[shakes]

You're right in more ways than one. An infinite number isn't necessary to make all possible shots without adjustment (50 will probably be enough - see my numbers above), and only a few are necessary to make all possible shots with adjustment (this is how I think these systems actually work).

pj
chgo

Of course, but what I'm saying is that as long as you are using the aim points, not contact points, that the "systems" do the adjusting themselves just by the change in distance and angles. I don't think you would need anymore than 10 or 12 spots. Being as we are working with spheres, the adjustments are inherent as long as you are using the same aim point.