Proof discrete aiming methods can't work

[AuntyDan]

When I was at college one of the very few things I remember from my Applied Engineering mathematics classes was this:

In order to differentiate between a Mathematician and an Engineer you draw a line in front of them. Two paces beyond that line you put a beautiful and naked member of the opposite sex. You instruct them that in order to take advantage of this situation they are to take one pace forward, then 1/2 a pace, then 1/4, 1/8, 1/16, 1/32 and so forth. The Mathematician will state that they have already calculated there are an infinite number of fractions so therefore the task is impossible and not worth even attempting.

The Engineer will say "OK, so I might not get all the way there, but I'll get close enough."

 

[Patrick Johnson]

When I was at college one of the very few things I remember from my Applied Engineering mathematics classes was this:

In order to differentiate between a Mathematician and an Engineer you draw a line in front of them. Two paces beyond that line you put a beautiful and naked member of the opposite sex. You instruct them that in order to take advantage of this situation they are to take one pace forward, then 1/2 a pace, then 1/4, 1/8, 1/16, 1/32 and so forth. The Mathematician will state that they have already calculated there are an infinite number of fractions so therefore the task is impossible and not worth even attempting.

The Engineer will say "OK, so I might not get all the way there, but I'll get close enough."

LOL. That's a good analogy for these "approximation" systems - especially because it points out that they can work even if they're not perfect.

Nothing is perfect. Even systems like ghost ball that "get you all the way there" don't work without some help from our "instincts" - no sign lights up to tell us when we're perfectly aligned; we have to rely on our imperfect experience and visualization skills for that.

pj
chgo

 

[Quatsch83]

First, we are very limited in the range of degrees that we can hit a ball. It doesn't matter if the angle can be split into degrees, minutes and seconds and endless fractions of a second because the width of the pocket and the shape of the balls both create slop. A fairly small number of angles will pocket almost all straight in shots if we can actually hit these angles. Sailor Barge was reputed to break the cue ball down into sixteen target spots. Those sixteen spots will make over 90% of shots if not all shots, or will at least provide a shot that can be made if you choose to shoot it.

Technically there is an infinite number of angles that will pocket a straight-in shot

 

[Patrick Johnson]

Without allowing for blocking balls I used software to test and found that 13 to 15 aim points would pocket any typical shot on the table assuming we had made some effort to play shape.

Here's a chart showing the minimum number of aim points within 1/8 of a ball circumference (up to 45 degrees of cut angle, or half of all possible shots).



The green-shaded boxes show which combinations of pocket size and OB-pocket distance work with 15 or fewer aim points. For average size pockets (4.5 to 5.0 inches) you need more aim points when you get beyond 3.5-4.5 feet from the pocket. So your estimate that "any typical shot" works is overstated, but not ridiculous.

But even if this isn't a ridiculous estimate, it's still very misleading about aiming systems because actual aiming systems aren't described this way - they're described as the number of aim points they produce in total for either 1/4 of a ball's circumference (left or right cuts) or 1/2 of a ball's circumference (left and right cuts). To compare your estimate apples-to-apples with a real aiming system, we have to double or quadruple the number of aim points - an aiming system would have to have a minimum of 30 or 60 total aim points for half of them to cover most "typical" shots (green boxes above).

pj
chgo

 

[mattiefingaz]

If pool is geometry so is soccer

I agree completely...If of course your foot is a a near perfect sphere, and the collision made by the ball after contacting your foot meet against the completely near perfect sphere of your oponents body part. Oh yeah, and you're only operating on one plane.

The situation isn't quite as bad as your description might imply, especially when the OB is closer to the pocket (where the pocket is "bigger"). However, you overall message is valid, IMO. Here's a pertinent quote from my fractional-ball aiming FAQ page:

For a given shot, with N different lines of aim, assuming you can hit where you are aiming, the object ball can go only in N different directions. Depending on where a pocket is and how far it is from the object ball, the cut shot may or may not be makable with one of the selected aiming lines.

Even with English effects (squirt, curve, and throw) and cling (collision-induced throw), the object ball can still go only in N different directions for N lines of aim for a given cue stick elevation and shot speed, and for given ball and table conditions.

See TP A.13 for background and specific results. Here are some highlights (for people who don't like the math):

• To be able to pocket an object ball into a pocket about 3 feet away, with an average angle to the pocket, and for any cut angle, the required number of aiming lines is about 19!
• If you consider cut shots only within a typical range (e.g., 7.5 to 52.5 degrees), and use only three equally spaced lines of aim (e.g., the 15, 30, and 45 degree aims):
  • If the object ball is less than a foot from the pocket, every shot can be pocketed with the three lines of aim.
  • If the object ball is more than two feet from the pocket, less than 50% of all cut shots in the limited range can be pocketed with only three lines of aim.

Now, I still think the three fractional aiming references (1/4, 1/2, and 3/4) are very useful because they are very easy to visualize. And having easy to identify references is always useful (e.g., as with the tangent line and the 30 degree direction for predicting CB motion), so I agree 100% that the aim points (from fractional-ball aiming or any other system) provide a good framework from within to work, especially for people that have difficulty aiming accurately and consistently.

Regards,
Dave

Dr. Dave you're going to have to spot ME the 5 up, and maybe the last 2.

Good days all.

Mattie

 

[ShootingArts]

obvious issue

Here's a chart showing the minimum number of aim points within 1/8 of a ball circumference (up to 45 degrees of cut angle, or half of all possible shots).

View attachment 108877

The green-shaded boxes show which combinations of pocket size and OB-pocket distance work with 15 or fewer aim points. For average size pockets (4.5 to 5.0 inches) you need more aim points when you get beyond 3.5-4.5 feet from the pocket. So your estimate that "any typical shot" works is overstated, but not ridiculous.

But even if this isn't a ridiculous estimate, it's still very misleading about aiming systems because actual aiming systems aren't described this way - they're described as the number of aim points they produce in total for either 1/4 of a ball's circumference (left or right cuts) or 1/2 of a ball's circumference (left and right cuts). To compare your estimate apples-to-apples with a real aiming system, we have to double or quadruple the number of aim points - an aiming system would have to have a minimum of 30 or 60 total aim points for half of them to cover most "typical" shots (green boxes above).

pj
chgo

pj,

The obvious issue is what is a typical shot. Here was my standard which you quoted and then ignored.

"Without allowing for blocking balls I used software to test and found that 13 to 15 aim points would pocket any typical shot on the table assuming we had made some effort to play shape."

Your findings from your chart, even if they were accurate, assumes that all shots on your chart would be shot an equal number of times, far from typical play! I challenge you to watch a few eight, nine, and ten ball matches and record the shots taken when the player had made an effort to play shape and did not hook themselves, my criteria. Count how many of those shots could have been made using only fifteen aim points and how many would be missed. Those fifteen aim points actually are infinite* since they are fifteen aim points on the face of the object ball facing the cue ball. Once you escape from theoryland and look at real typical shots your figures will have to be drastically revised.

*How did your model account for these fifteen points being relative to cue ball position?

Hu

 

[Patrick Johnson]

pj,

The obvious issue is what is a typical shot. Here was my standard which you quoted and then ignored.

"Without allowing for blocking balls I used software to test and found that 13 to 15 aim points would pocket any typical shot on the table assuming we had made some effort to play shape."

I didn't ignore it - you apparently missed how I took it into account.

*How did your model account for these fifteen points being relative to cue ball position?

By assuming each shot was no more than a 45-degree cut.

pj
chgo

 

[ShootingArts]

I would pursue this

I didn't ignore it - you apparently missed how I took it into account.



By assuming each shot was no more than a 45-degree cut.

pj
chgo

pj,

I would pursue this but your replies aren't relevant to my questions. Same old same old, you put garbage in and come out with garbage figures that look pretty on a chart but are actually meaningless. You don't have the equipment, software, or knowledge needed to accurately determine the things you are stating. You are reaching 2D conclusions about a 3D world.

Hu

 

[dr_dave]

You are reaching 2D conclusions about a 3D world.

Three lines of aim in the 3D world are still only three lines of aim. With only three different lines of aim, the CB can only go in three different directions (for a given CB and OB location). Right?

Regards,
Dave

 

[ShootingArts]

(for a given CB and OB location).

Three lines of aim in the 3D world are still only three lines of aim. With only three different lines of aim, the CB can only go in three different directions (for a given CB and OB location). Right?

Regards,
Dave

Dave,

Obviously I can split hairs and say that speed, cue stick angle, and spin can change the directions but I'm going to agree that your basic statement is true. However, every time you change the angle between the cue ball and object ball you now have three totally different locations. The original goal of my tests was testing the validity of SAM. I had to conclude that for the vast majority of shots that are actually played on a table in a game, SAM will indeed pocket the balls.

Once we realize that the three spots you mention or the fifteen spots I mention are actually an infinite number of spots varying with the angle between the cue ball and object ball we have made a big step. From what pj has indicated in his posts, these spots are defined at the beginning of his modeling and never change other than some might be hidden or exposed on different shots. That is a gross error in itself. Secondly, I have seen no indication that the actual shapes of the ball and pockets have been considered. A ball readily glances off of a point and goes in the hole. It doesn't go in when you simply say 2.25 inches overlaps a mathematical model 4.5 inch hole.

Bottom line is that 2D modeling of 3D activities simply doesn't work in this case. I could model this successfully but it would take months and a lot of dollars. Every new shot requires recalculating the acceptable amount the object ball can overlap each point and the fifteen points on the cue ball have to be relocated for every shot. Doing anything less is to start with invalid data. The final thing is that typical shots have to be defined. The easiest way to define these is to break down real matches from video. When we consider every shot physically possible to be attempted on a table in calculating the success of a system we are again putting in bad data. People aren't attempting the vast majority of theoretically possible shots.

Assuming a roughly pocket speed shot, just at a WAG I'd say that 3/16 of the diameter of the object ball can overlap the point and the ball still fall. That is 3/16 diameter on each side, total 3/8 the diameter of the object ball can overlap. If this assumption is correct then the effective width of the object ball at the pocket is only 1.4 inches for it to bounce out of the pocket. Perhaps reality is a little more, perhaps a little less, either way that is a far cry from 2.25 inches.

Anytime someone wants to put their worksheets, beginning data, and assumptions on the table for us all to examine I will be happy to consider their information. All assumptions used in the start of the project must be either proven or discarded by the end of the project.

Hu

 

[Patrick Johnson]

You don't have the equipment, software, or knowledge needed to accurately determine the things you are stating.

LOL. This is simple stuff, Hu. You don't even need a calculator - just pi and basic math.

You are reaching 2D conclusions about a 3D world.

You're overcomplicating to avoid real discussion of your spurious claims.

pj
chgo

 

[ShootingArts]

proving my point

LOL. This is simple stuff, Hu. You don't even need a calculator - just pi and basic math.

You're overcomplicating to avoid real discussion of your spurious claims.

pj
chgo

pj,

You are just proving that you have no comprehension of what is needed to reach any valid conclusions.

Hu

 

[dr_dave]

Hu,

I agree with PJ that you are trying to make this much more complicated than it actually is. In 3D (or in 2D diagrams), for a given CB and OB location, 3 (or 13, or N) well-defined lines of aim can send the OB in only 3 (or 13, or N) directions. If the CB or OB are moved to different positions relative to each other and the pocket, the limited lines of aim can still only send the OB in a limited number of directions. Sometimes, one or more of these directions might result in the ball being pocketed; but with a slightly different shot angle, maybe none of the lines would work.

Now, none of this logic applies to a system where you vary something based on feel (e.g., the "pivot" in CTE). In these cases, you can create an infinite number of aiming lines. The lines-of-aim logic applies only to systems where there is a well-defined, precise, and repeatable procedure for lining up a shot without feel or intuition (e.g., fractional-ball aiming).

Regards,
Dave

Dave,

Obviously I can split hairs and say that speed, cue stick angle, and spin can change the directions but I'm going to agree that your basic statement is true. However, every time you change the angle between the cue ball and object ball you now have three totally different locations. The original goal of my tests was testing the validity of SAM. I had to conclude that for the vast majority of shots that are actually played on a table in a game, SAM will indeed pocket the balls.

Once we realize that the three spots you mention or the fifteen spots I mention are actually an infinite number of spots varying with the angle between the cue ball and object ball we have made a big step. From what pj has indicated in his posts, these spots are defined at the beginning of his modeling and never change other than some might be hidden or exposed on different shots. That is a gross error in itself. Secondly, I have seen no indication that the actual shapes of the ball and pockets have been considered. A ball readily glances off of a point and goes in the hole. It doesn't go in when you simply say 2.25 inches overlaps a mathematical model 4.5 inch hole.

Bottom line is that 2D modeling of 3D activities simply doesn't work in this case. I could model this successfully but it would take months and a lot of dollars. Every new shot requires recalculating the acceptable amount the object ball can overlap each point and the fifteen points on the cue ball have to be relocated for every shot. Doing anything less is to start with invalid data. The final thing is that typical shots have to be defined. The easiest way to define these is to break down real matches from video. When we consider every shot physically possible to be attempted on a table in calculating the success of a system we are again putting in bad data. People aren't attempting the vast majority of theoretically possible shots.

Assuming a roughly pocket speed shot, just at a WAG I'd say that 3/16 of the diameter of the object ball can overlap the point and the ball still fall. That is 3/16 diameter on each side, total 3/8 the diameter of the object ball can overlap. If this assumption is correct then the effective width of the object ball at the pocket is only 1.4 inches for it to bounce out of the pocket. Perhaps reality is a little more, perhaps a little less, either way that is a far cry from 2.25 inches.

Anytime someone wants to put their worksheets, beginning data, and assumptions on the table for us all to examine I will be happy to consider their information. All assumptions used in the start of the project must be either proven or discarded by the end of the project.

Hu

 

[softshot]

. In 3D (or in 2D diagrams), for a given CB and OB location, 3 (or 13, or N) well-defined lines of aim can send the OB in only 3 (or 13, or N) directions. If the CB or OB are moved to different positions relative to each other and the pocket, the limited lines of aim can still only send the OB in a limited number of directions.

There is a difference between infinite angles and infinite effective angles.. the number of effective angles is finite because you are dealing with an known space with known targets.. and the projectile is roughly half the size of any given target..

there is a margin for error built into the game..

how many effective aim points there are can be debated .. but saying they are infinite is wrong based upon the reality of a pool table..

 

[cookie man]

Hu,

I agree with PJ that you are trying to make this much more complicated than it actually is. In 3D (or in 2D diagrams), for a given CB and OB location, 3 (or 13, or N) well-defined lines of aim can send the OB in only 3 (or 13, or N) directions. If the CB or OB are moved to different positions relative to each other and the pocket, the limited lines of aim can still only send the OB in a limited number of directions. Sometimes, one or more of these directions might result in the ball being pocketed; but with a slightly different shot angle, maybe none of the lines would work.

Now, none of this logic applies to a system where you vary something based on feel (e.g., the "pivot" in CTE). In these cases, you can create an infinite number of aiming lines. The lines-of-aim logic applies only to systems where there is a well-defined, precise, and repeatable procedure for lining up a shot without feel or intuition (e.g., fractional-ball aiming).

Regards,
Dave

You seem to have alot of opinions on CTE for a very little, extremely little knowledge of it.

 

[ShootingArts]

garbage in, garbage out

Dave,

20+25=47 within a range of +Y,-X. True or false?

When you answer that question and fourteen more similar to it correctly without defining Y and X then I will acknowledge that I am overcomplicating things. Until then I'll remember that the R&D corporation I was vice president of for awhile lost millions when the Fed's chose to ignore variables and dump the renewable energy research funds into technology that looked great, until the variables were added. As we told them to begin with, the few btu's of geothermal energy they were planning to use disappeared when they tried to transport it for actual use. However they spent four years and many millions proving what we already knew because we had included the variables while they simply looked at raw, vastly simplified, numbers.

Oversimplifying things does often result in garbage data. Ignoring the fact that the fifteen points on the ball are relative to the face viewed and the fact that balls are round results in bogus results.

Hu

Hu,

I agree with PJ that you are trying to make this much more complicated than it actually is. In 3D (or in 2D diagrams), for a given CB and OB location, 3 (or 13, or N) well-defined lines of aim can send the OB in only 3 (or 13, or N) directions. If the CB or OB are moved to different positions relative to each other and the pocket, the limited lines of aim can still only send the OB in a limited number of directions. Sometimes, one or more of these directions might result in the ball being pocketed; but with a slightly different shot angle, maybe none of the lines would work.

Now, none of this logic applies to a system where you vary something based on feel (e.g., the "pivot" in CTE). In these cases, you can create an infinite number of aiming lines. The lines-of-aim logic applies only to systems where there is a well-defined, precise, and repeatable procedure for lining up a shot without feel or intuition (e.g., fractional-ball aiming).

Regards,
Dave

 

[dr_dave]

Oversimplifying things does often result in garbage data. Ignoring the fact that the fifteen points on the ball are relative to the face viewed and the fact that balls are round results in bogus results.

Are you implying that PJ and I haven't taken into account the roundness of the balls? You apparently have very little faith in us.

Regards,
Dave

 

[dr_dave]

There is a difference between infinite angles and infinite effective angles.. the number of effective angles is finite because you are dealing with an known space with known targets.. and the projectile is roughly half the size of any given target..

there is a margin for error built into the game..

how many effective aim points there are can be debated .. but saying they are infinite is wrong based upon the reality of a pool table..

With a system like fractional-ball aiming, there are only a finite number of clearly defined aiming lines for a given CB and OB location. If you adjust or compensate between these fixed reference directions based on feel or intuition, then you can create an infinite number of aiming lines. Some (an infinite number) of these lines will send the OB into the pocket, and many (also an infinite number) won't. With only a finite number of possible aiming lines, one or more might send the OB into a pocket, but it is also possible that none will (depending on the angle and distance to the pocket, and the effective size of the pocket at that angle).

I hope that's more clear,
Dave

 

[dr_dave]

You seem to have alot of opinions on CTE for a very little, extremely little knowledge of it.

If you think something I wrote is a misrepresentation of CTE (e.g., the "pivot" requiring some "judgment" or "feel"), I would be happy to hear your thoughts on the matter, since you seem to be a devote CTE user (which I am not). It seems to me that Spidey describes the "pivot" (or the effective point of the "pivot") changing with shot distance. Wouldn't that require some "judgment" or "feel?"

Thank you,
Dave

 

[SpiderWebComm]

For all of these diagrams, math, extreme knowledge of everything pool related....

It'd be really cool if everyone in these aiming threads posted a video of them running some balls in 14.1 or running racks of 9/10-ball. Before everyone cries about how that has nothing to do with pool knowledge, I say that's h0rsesh1t... it has everything to do with it. I just wanna know out of all these experts and know-everythings..... who can actually play and who hides the fact they can't play by maintaining a superior internet pool identity through superior debate and posts.

I've seen so many proof posts and examples of stuff that mostly doesn't apply to the core knowledge (with people projecting as they know and really don't), that my head is spinning. Since this thread keeps getting bumped with back-and-forths from people who are experts online--- I'm curious as to how these experts really play.

I'd bet anything no one would ever post any videos because it'd likely blow their perceived "expert" identity.