Support for Fractional Aiming

[CueAndMe]

Patrick, I don't understand the angle numbers you came up with. Here's the same diagram with the angles that I came up with for each point. It's not perfect but probably within a degree using the aiming table.



Here are the resulting shots using all 9 of these aims from 3 diamonds away from a "pocket." The compression of aiming points towards the edge using the circumference divisions offsets the equator division angles perhaps too much.
Page 2 represents the 1/8 circumference divisions only.

CueTable Help

 

[Patrick Johnson]

Patrick, I don't understand the angle numbers you came up with.

Then I guess I don't understand what you meant by this:

Using equator aiming fractions, angles expand as you move away from center ball up to the edge. So having a built in way of offsetting this expansion would be advantageous. When you divide the periphery instead, the aims compress into a smaller area as you move away from center.

What do the phrases in blue mean?

pj
chgo

 

[CueAndMe]

equator aiming fractions- the divisions that we normally talk about when describing fractional aims, using the center line of the ball and dividing that.

dividing the periphery- using the curved line that is the perimeter of the ball and dividing that curved line instead of the straight line that is the equator

If you look at the original post's diagram and the plotting of the 9 balls, you'll notice an increasing spread between the balls.

But for the angles under 30 degrees, I don't think this expansion/spreading is significant. So I'm wrong in assuming that this expansion of angles needs to be offset. They are pretty evenly spaced as they are.

And using the divisions in my last post(of the perimeter) you can see that the compression of angles that occurs (using fractions of the perimeter) is perhaps not all that helpful.

That said, I think it's easier to visualize the perimeter points. Maybe that's just me though.

 

[Bob Jewett]

Then I guess I don't understand what you meant by this: ... What do the phrases in blue mean?

This point is illustrated in http://www.sfbilliards.com/Western_fractions_bw.gif which was drawn about 100 years ago. It's from Western's book on the relationship of fullness of hit to carom angle. It's the finest gradation of fractional aiming I've seen in print, except for a continuous graph, such as that in http://www.sfbilliards.com/fract.pdf

 

[CueAndMe]

Thanks Bob. I just want to clarify that my image of the perimeter being divided is viewed from table level, not from above.
I'm trying to figure out if this makes a difference for aiming targets.
The 100 year old illustration, if I'm understanding it, is viewed from above, and shows the resulting angles from aiming at the equator divisions?

 

[CueAndMe]

Revised image showing top and bottom of object ball:

 

[Patrick Johnson]

Patrick, I don't understand the angle numbers you came up with. Here's the same diagram with the angles that I came up with for each point. It's not perfect but probably within a degree using the aiming table.

View attachment 74753

If I understand you now, I think you must have divided the cut angles between a full hit and a half-ball hit into eighths. In that case, here's a table of cut angles measured three different ways.

On the left, circled in black, are the cut angles (measured from the line between CB/OB centers) from dividing 1/4 of the ball's circumference into 8 equal sections (your "dividing the periphery"?). They range from 0 degrees to 45 degrees.

In the middle, circled in red, are the cut angles (measured from the line between CB/GhostBall centers) from dividing the CB/OB overlaps between a full hit and a half-ball hit into eighths (your "equator fractions"?). They range from 0 degrees to 30 degrees. I believe these are the angles your drawing approximates.

On the right, circled in blue, are the same cut angles as those circled in red, except measured from the line between CB/OB centers. The angles circled in blue are for a CB at a distance of 48 inches from the OB (about what your CueTable diagram shows). At that distance this range of cut angles is compressed by a total of about 2/3 of one degree. At a CB/OB distance of 12 inches (the leftmost blue column) this range of cut angles is compressed by a total of about 2-2/3 degrees.



How's that for anal?

pj
chgo

 

[Patrick Johnson]

Thanks Bob. I just want to clarify that my image of the perimeter being divided is viewed from table level, not from above.
I'm trying to figure out if this makes a difference for aiming targets.

I don't think so. The targets should transpose identically.

The 100 year old illustration, if I'm understanding it, is viewed from above, and shows the resulting angles from aiming at the equator divisions?

So you're saying aim the CB center at these divisions equally spaced around the circumference? Here's a visual of the actual contact points that would result from this method (blue lines) vs. normal fractional aiming (red lines):



The fractional aiming contact points stay pretty evenly spaced around the circumference up to a half-ball hit, so this (exponential?) alternative isn't as good (I think you came to the same conclusion).

pj
chgo

 

[Dead Crab]

That's the system I use (peripheral). Not only can you use the angle from ball center, but also the distance up from the table.

For example, 10 degree cut point is about 2mm off the table, 15 degrees is about 4mm, 20 degrees, 8mm.

I've got about a 1mm nap in my cloth, so a 10 degree cut is just where there is light visible between the cloth and ball.

For the shallow cuts where the cloth and ball are indistinguishable I either reference off the 10-degree aim point (6-9 degree cuts), or off the top-ball-vertical axis (0-5 degree cuts).

With this approach, confidence in the aim point is very high for angles up to 30 degrees.

If you want to get comfortable estimating 4mm or 8mm, get some machine screws with thread diameters this size. Put 'em on rails, on your desk, wherever you can get used to seeing that thickness from a few feet away.

Coupled with an angle estimation method, I think it is possible to select the proper aim point within 1-1.5mm on a consistent basis.

 

[CueAndMe]

Very clever, Dead Crab.

 

[CueAndMe]

If I understand you now, I think you must have divided the cut angles between a full hit and a half-ball hit into eighths. In that case, here's a table of cut angles measured three different ways.

On the left, circled in black, are the cut angles (measured from the line between CB/OB centers) from dividing 1/4 of the ball's circumference into 8 equal sections (your "dividing the periphery"?). They range from 0 degrees to 45 degrees.

In the middle, circled in red, are the cut angles (measured from the line between CB/GhostBall centers) from dividing the CB/OB overlaps between a full hit and a half-ball hit into eighths (your "equator fractions"?). They range from 0 degrees to 30 degrees. I believe these are the angles your drawing approximates.

On the right, circled in blue, are the same cut angles as those circled in red, except measured from the line between CB/OB centers. The angles circled in blue are for a CB at a distance of 48 inches from the OB (about what your CueTable diagram shows). At that distance this range of cut angles is compressed by a total of about 2/3 of one degree. At a CB/OB distance of 12 inches (the leftmost blue column) this range of cut angles is compressed by a total of about 2-2/3 degrees.

View attachment 74761

How's that for anal?

pj
chgo

I'm trying to figure out how our angles disagree so much. It's true that I'm doing no math, which can account for some error, but I figure that your "red circle" is the one that should come close to matching up with my numbers, but it doesn't seem to.

I used the overlapping balls on the cuetable aiming table to come up with my angles. Not extremely precise, but shouldn't be so far off. I'm stumped.
And yes, I did come to the same conclusion about the angles closing in towards the edge.

Thanks for the images. Here's your picture edited to show the horizontal midpoints which don't match the perimeter midpoints. Maybe this isn't a bad thing. It just means having more possible reference shots.

 

[chefjeff]

I don't discount "fractional ball" or any other aiming system. I think anything that provides useful references and focus is a good thing.

Regards,
Dave

To me, the biggest advantage of these aiming systems is using them for going into my stance. My aiming system is a lttle different, but having used it for a few years now, I'd say that the best use of it is for accurately setting up my stance. The details of the aim are then within, the now accurate, tweaking range of my bridge, grip, etc., if that makes sense.

Jeff Livingston

 

[Poolplaya9]

I've related this story before.... I got a minor programming job from a friend of mine for his HP calculator back around 1980 or so. He wanted to know the angle of the line joining any two diamonds on adjacent cushions relative to one of those cushions. This is not a trivial formula since it involves how far back from the nose of the cushion the diamonds are.

Anyway, he wanted to know this for his aiming system. He had memorized the cut angles for ball fullnesses down to 64ths. If he saw that the object ball was two balls off the cushion at the third diamond, he knew that the angle of the ball relative to the cushion was 7 degrees. If the line of the cue ball was from the far corner pocket to the third diamond plus a little, he knew that the angle of the cue ball relative to that same cushion was 40 degrees. This makes the cut angle 33 degrees and the required fullness for that cut is 29/64ths. Then all he had to do was hit his usual 29/64th-full shot.

Most people don't have either the attention span or the motivation to go to this amount of effort just to aim. He did. And he played pretty well.

I believe that your friend could fairly accurately determine cut angles on the table. I would have to think though that he would occasionally be off enough with the angle judgement to be outside the margin of error for making longer shots if it could somehow be guarenteed that he would always hit the exact contact point on the object ball that corresponded to the angle as he judged it. In other words, if you were to accurately measure the angle of particular shots that he had judged, you would be able to mathematically demonstrate that the number or degrees he was off on some of them would cause a miss for longer shots.

I do definitely believe that your friend had memorized the corresponding cut angles that went with each 64th of the ball.

I also definitely believe that your friend was a very good player.

What I am having the most trouble with though is believing that he could accurately visualize 64ths of the object ball and then accurately guide the cueball to one of those exact points, say 29/64ths. I'm not sure how you could test that in a fair and accurate way though. My thought would be to give him a 2 1/4 inch perfectly round white piece of paper with some type of flat base at the very edge somewhere to represent the table. Then have him mark where 29/64ths is. I am almost certain that he would be off enough part of the time that you could again mathematically demonstrate that it would cause a miss on a longer shot. I'd have to lose a few bucks letting him prove me wrong in any case.

I'm thinking that although his angle and 64ths judgement were usually close, his mind was actually subconsciously altering his aim based on experience to correct for any errors in his judgements.

I had trouble putting my thoughts into words here, so hopefully you are able to decipher what all I meant. Bob, what are your thoughts about what I suggest in terms of his angle and 64ths judgement errors, and his mind subconsciously adjusting his aim based on experience?

 

[Patrick Johnson]

I'm trying to figure out how our angles disagree so much.

I think I was wrong - none of my calculated angles match your "exponentially spaced" aims (the top circle in my drawing). The ones in the red circle are for "normal" ball fractions (the bottom circle in my drawing). I think that's probably the difference - I only realized that's what you were doing after I posted those calculations.

pj
chgo

Note: In case it's confusing - in my table of calculated angles, the ones in blue on the right are not compressed by being exponentially spaced; they're compressed by measuring the "true" cut angle, taking into account the shifting angle of the CB-GhostBall line.

 

[CueAndMe]

To me, the biggest advantage of these aiming systems is using them for going into my stance. My aiming system is a lttle different, but having used it for a few years now, I'd say that the best use of it is for accurately setting up my stance. The details of the aim are then within, the now accurate, tweaking range of my bridge, grip, etc., if that makes sense.

Jeff Livingston

Can you into your routine in more depth? I'm not fully understanding.
Thanks

 

[CueAndMe]

Poolplaya9, that makes a lot of sense.
Patrick, okay, I'm with ya' now.
Thanks

 

[chefjeff]

Can you into your routine in more depth? I'm not fully understanding.
Thanks

OK. Here's one of my aiming points. If I'm cutting a half-ball aim shot to the left, then I say to myself, center-right, meaning center of the stick to the right edge of the ob. (I have other points of course but I'll leave that for another time)

So, while still standing, I grip normally, put my cuetip where it will be on the back of my backstroke, step my right heel under my grip to begin the proper positioning of my stance.

Then, I let my grip hand/arm extend toward the floor (arm straight)and hold my bridge hand up in the air, about belly-button high. This allows my eyes to see the cuestick, the cb and the ob in relation to each other. I close my non-dominant eye and sight in, for this example, the cuestick so it is going through the center of the cb and the center of the stick is also aligned with the right edge of the ob ball.

Then I tweak my stance to coincide with the above and then I move into my stance, setting bridge and grip etc.

This ensures that my stance is pre-aligned with the aiming point. If off a little, I can easily tweak whatever portion of the whole shebang I need to without getting out of whack.

This shortcut, if you will, makes any aiming system valuable.

Jeff Livingston

 

[CueAndMe]

Jeff, I like what you're saying here. I need to start paying attention to the details of my preshot routine like you do.
Thanks

 

[Patrick Johnson]

OK. Here's one of my aiming points. If I'm cutting a half-ball aim shot to the left, then I say to myself, center-right, meaning center of the stick to the right edge of the ob. (I have other points of course but I'll leave that for another time)

So, while still standing, I grip normally, put my cuetip where it will be on the back of my backstroke, step my right heel under my grip to begin the proper positioning of my stance.

Then, I let my grip hand/arm extend toward the floor (arm straight)and hold my bridge hand up in the air, about belly-button high. This allows my eyes to see the cuestick, the cb and the ob in relation to each other. I close my non-dominant eye and sight in, for this example, the cuestick so it is going through the center of the cb and the center of the stick is also aligned with the right edge of the ob ball.

Then I tweak my stance to coincide with the above and then I move into my stance, setting bridge and grip etc.

This ensures that my stance is pre-aligned with the aiming point. If off a little, I can easily tweak whatever portion of the whole shebang I need to without getting out of whack.

This shortcut, if you will, makes any aiming system valuable.

Jeff Livingston

I think this kind of pre-shot alignment is invaluable. I do almost the same thing, except I actually put my tip on the cloth (right at the cue ball where it will be at the end of my stroke), with my bridge hand completely off the cue. I align my grip hand to aim the stick very carefully through the CB at the OB, including sidespin, then place my back foot under my grip hand and bend (slowly, if I'm doing it right) into my stance, keeping my eyes over the shaft and sliding my bridge hand forward under the shaft.

If I remember (and have the patience) to do all that, and if I remember to be precise about where I hit the cue ball, and if I remember to let gravity work, I usually get into stroke.

pj
chgo

 

[Bob Jewett]

... I'm thinking that although his angle and 64ths judgment were usually close, his mind was actually subconsciously altering his aim based on experience to correct for any errors in his judgments. ...

I'm certain he was adjusting, just as all good players adjust for all the factors that aren't accounted for by whatever system/method/framework/routine they use to aim. How can you tell the foolish system player? He thinks he doesn't adjust. How can you tell the inept system player? He doesn't adjust.

As for the number of angles, if you can handle more angles, I think it will help you because there is less to fill in. The hard part, as has been mentioned, is wrapping your mind around all the little details. Some people can, some can't. There are people who can recite thousands of digits of pi and probably many more people could but few are motivated enough to even try.