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View Full Version : How Many Angles Is Enough?


Patrick Johnson
11-28-2007, 11:37 PM
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
11-29-2007, 12:48 AM
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
11-29-2007, 01:40 AM
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
11-29-2007, 01:56 AM
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
11-29-2007, 02:22 AM
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
11-29-2007, 03:48 AM
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
11-29-2007, 05:49 AM
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
11-29-2007, 06:52 AM
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
11-29-2007, 06:55 AM
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
11-29-2007, 07:06 AM
... 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
11-29-2007, 07:34 AM
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
11-29-2007, 09:30 AM
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
11-29-2007, 09:43 AM
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
11-29-2007, 10:46 AM
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
11-29-2007, 10:49 AM
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
11-29-2007, 10:55 AM
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
11-29-2007, 11:26 AM
Thank you for the explanation
My pleasure.

pj
chgo

shakes
11-29-2007, 11:41 AM
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
11-29-2007, 11:49 AM
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
11-29-2007, 11:56 AM
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.

jondrums
11-29-2007, 12:02 PM
Hi PJ - thanks for the great data! This has really got me thinking a little further... I now wonder what happens if you constrain all cuts to 45degrees or less - (the angle of a 1/4 ball hit). My thought is, that as you go above 45 degrees you need lots more aiming points, because the resultant cut is more and more sensitive to aim.

45deg represents a shot most people will take, above that, with the OB 5 feet from the pocket, I start thinking safe...

I'll do this calculation a little later today if you don't get to it. I'm also planning to replicate your original calc. to make sure we're comparing apples to apples.

Jon

Patrick Johnson
11-29-2007, 12:25 PM
... 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.

This is a common misconception about these kinds of systems. It's simply not true.

pj
chgo

seymore15074
11-29-2007, 01:16 PM
Omg Pat, where are these crazy numbers coming from?! :p

You know at x ft, if you try and say there are 100 angles needed, that I could easily set down the cue ball x ft from the pocket that isn't one of those 100, right? (which is supporting what you are saying, anyway)

That's like saying .9 is the smallest number less than 1... Unless you go with .99, .999, .9999, etc...there are literally an infinite number of angles in pool, you can divide them up forever (even though eventually they will be "accurate-enough" for the game).

Patrick Johnson
11-29-2007, 02:03 PM
... I could easily set down the cue ball x ft from the pocket that isn't one of those 100, right?
... you can divide them up forever (even though eventually they will be "accurate-enough" for the game).

Did you notice that you contradicted yourself here? Yes, they eventually get accurate enough - that's why there are no angles that miss when you have enough angles.

pj
chgo

Bob Jewett
11-29-2007, 02:55 PM
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.
No, yours is a common misconception. Each of your spots sends the object ball along only a single direction relative to the path of the incoming cue ball. If you can do the geometry, you can figure out the exact degrees in the cut angle. That hit gets that cut angle, and only that cut angle unless you depart from the system according to feel and subconscious corrections.