Fractional aiming and required accuracy

[Bob Jewett]

One aiming method is to imagine the 2-D overlap of the cue ball as it lands on the object ball and connect the amount of overlap to the cut angle. The common fractions and their approximate degrees of cut are:

full ball -- 0 degrees -- straight shot
3/4 full -- 15 degrees
1/2 full -- 30 degrees
1/4 full -- 45 degrees
1/8 full -- 60 degrees

Except for the half-ball hit which is 1/2 full and a cut of 30 degrees, those numbers are all slightly off, but the errors are not important for this first part of the discussion. Another factor that must eventually be considered is throw which varies with the speed and spin of the cue ball but that gets very complicated and it is better to completely understand the simple fundamental ideas of the situation before we get into all the nasty details. Those details are important and we'll get to them.

In the diagram you see a shot off the spot and five different areas where the five fractional aims will be useful. Let's consider the straight shot or 0 degree cut. How wide is that area? The pocket is two balls wide (more or less) and the two extreme arrival positions of the object ball are shown by the 2 ball and the 3 ball. If you draw straight lines from the centers of those balls back to the 1 ball, you get the angular width of the pocket. It is about 4 degrees. If the object ball is sent more than 2 degrees away from dead center of the pocket, it won't go in. (Again, this is not perfectly accurate. From this approach angle, the pocket is larger for very hard shots, so the pocket size varies with the shot conditions. Pick your own number if you don't like 4 degrees of pocket width.)

Where can the cue ball be in order to pocket a straight shot to that pocket off the spot? It is pretty obviously the red shaded area marked "0°". If the cue ball is anywhere on the bottom/right side of the shaded area, with a perfect, full hit the object ball will pass over the position of the 2 ball. If the cue ball starts on the top/left side of the shaded area the cue ball will pass over the position of the 3 ball. If the cue ball is anywhere outside the red shaded area, a full hit won't pocket the object ball.

The same argument applies to the other standard fractional cuts. It is not hard to see that all the triangular areas for the different cuts are 4 degrees wide. This means that the standard fractional cuts for a shot as hard as a spot shot cover only about 1/4 of the area of the table. The "good" triangles are 4 degrees wide and 15 degrees apart.

But it is a really, really bad idea to wed yourself to exact fractional ball hits. Just consider the straight shot. If the cue ball is on one edge of the red shaded area, and you use a true fractional aim, you will send the 1 ball all the way to the extreme side of the pocket. If your stroke makes a small error in that same direction, you will miss the shot. Since most of us make small errors most of the time (and large errors the rest of the time ), you will end up missing about half of such shots.

The lesson from this is that the "good" triangular areas for the shot are actually considerably smaller. If you are willing to give up half of the allowed error to your aiming system, then the triangles will shrink to 2 degrees wide and the percent of the table that is covered by these fractional aims drops by a factor of two to roughly 1/8th or 12.5% of the table surface.

 

[ChrisinNC]

Common fractions and their approximate degrees of cut change the closer (or the farther) the cue ball is from the object ball, for any given shot, so this fractional aiming system seems flawed to me. For instance, if the cue ball is only 6 inches away from the object ball, a half ball hit is only going to cut the object ball maybe 20° at the most. If the cue ball is 2 inches away from the object ball, a half ball hit is only going to cut the object ball maybe 10° or even less.

Not considering throw in the equation, there will come a point less than 1/4 inch between the two balls that a half ball hit or even a edge to edge hit will not result in any cut on the object ball at all. In fact if they are nearly touching, it will throw the object ball the opposite direction.

 

[Patrick Johnson]

Nice description and illustration, Bob - looking forward to more installments.

So the quick math for shot coverage is:

(number of system angles x angular pocket width) / 90 degrees

...or 25 (or so) percent for this OB>pocket distance (higher from closer, lower from farther).

pj
chgo

 

[Bob Jewett]

Common fractions and their approximate degrees of cut change the closer (or the farther) the cue ball is from the object ball, for any given shot, so this fractional aiming system seems flawed to me. For instance, if the cue ball is only 6 inches away from the object ball, a half ball hit is only going to cut the object ball maybe 20° at the most. If the cue ball is 2 inches away from the object ball, a half ball hit is only going to cut the object ball maybe 10° Or even less.
...

That's not how fractional aim works. A half ball hit always gives a 30-degree cut. The distance from the cue ball to the object ball is irrelevant. The cut angle is measured from the line of the cue stick (and cue ball motion) to the path of the object ball.

You seem to be thinking of the angle between the centers of the balls, CB and OB, and the path of the object ball.

A way to avoid that error is to use the ghost ball to find the correct path of the cue ball, as Pat mentioned. This is kind of circular, since you have get the cue ball path by the ghost ball method.

A different way to get there is to (for example) put your stick down for a half ball hit -- this can always be done -- and then ask yourself what is the angle between your stick and the OB path to the pocket. If that's not 30 degrees, you have to guess again for some other fullness.

 

[Patrick Johnson]

Common fractions and their approximate degrees of cut change the closer (or the farther) the cue ball is from the object ball

You're thinking of the CB moving directly toward the object ball - Bob's diagram shows the line from the CB to the ghost ball.

pj
chgo

 

[Bob Jewett]

Nice description and illustration, Bob - looking forward to more installments.

So the quick math for shot coverage is:

(number of system angles x angular pocket width) / 90 degrees

...or 25 (or so) percent for this OB>pocket distance (higher from closer, lower from farther).

pj
chgo

Yes, that is OK if you are willing to give up all your shot margin when the cue ball is on one side of a "good" triangle.

 

[ChrisinNC]

That's not how fractional aim works. A half ball hit always gives a 30-degree cut. The distance from the cue ball to the object ball is irrelevant. The cut angle is measured from the line of the cue stick (and cue ball motion) to the path of the object ball.

Bob, you’ve lost me on that one and I guess it’s my misunderstanding. When a cue ball and object ball are separated by no more than 1 inch, it seems to me it doesn’t matter how thin you cut it, even edge to edge, you can’t get that object ball to cut more than maybe 10-15 degrees. By comparison, if the balls are 5 feet apart, you can get nearly a 90° cut on an edge to edge contact between the cue ball and the object ball. What am I missing?

 

[Patrick Johnson]

Nice description and illustration, Bob - looking forward to more installments.

So the quick math for shot coverage is:

(number of system angles x angular pocket width) / 90 degrees

...or 25 (or so) percent for this OB>pocket distance (higher from closer, lower from farther).

pj
chgo

Yes, that is OK if you are willing to give up all your shot margin when the cue ball is on one side of a "good" triangle.

Close enough for bashing aiming systems.

pj <- I kid! (kinda)
chgo

 

[Patrick Johnson]

Bob, you’ve lost me on that one and I guess it’s my misunderstanding. When a cue ball and object ball are separated by no more than 1 inch, it seems to me it doesn’t matter how thin you cut it, even edge to edge, you can’t get that object ball to cut more than maybe 10-15 degrees. What am I missing?

The apex of the cut angle is the ghost ball center, not the object ball center.

pj
chgo

 

[Bob Jewett]

Bob, you’ve lost me on that one and I guess it’s my misunderstanding. When a cue ball and object ball are separated by no more than 1 inch, it seems to me it doesn’t matter how thin you cut it, even edge to edge, you can’t get that object ball to cut more than maybe 10-15 degrees. By comparison, if the balls are 5 feet apart, you can get nearly a 90° cut on an edge to edge contact between the cue ball and the object ball. What am I missing?

A half-ball shot is defined by how full you hit the object ball. A half ball gives a 30 degree cut. The cut angle is defined by the line of the stick and the path of the object ball. These are all very, very standard concepts in billiards/pool.

Yes, if the cue ball is very close to the object ball, the range of angles you can send the object ball through is restricted. That does not define the cut angles. Even if the balls are only a quarter-inch apart, if you barely brush the side of the object ball with the cue ball, that is a 90-degree cut because the cue stick -- and the path of the cue ball -- are almost 90 degrees from the direction the object ball takes. Of course cutting left or right on such a close ball is only a small difference in its path. Nearly all the change comes from the direction of the cue stick.

It may help you to draw out a diagram of a close shot and note the angle between the stick and the path of the object ball for very thin hits. That angle is the cut angle.

 

[straightline]

According to these developments. I aim half assed.

 

[BC21]

Bob, you’ve lost me on that one and I guess it’s my misunderstanding. When a cue ball and object ball are separated by no more than 1 inch, it seems to me it doesn’t matter how thin you cut it, even edge to edge, you can’t get that object ball to cut more than maybe 10-15 degrees. By comparison, if the balls are 5 feet apart, you can get nearly a 90° cut on an edge to edge contact between the cue ball and the object ball. What am I missing?

The fractional angles created are always the same, meaning if you aim ccb to ob edge you'll create a 30° cut angle every time. However, if the cb remains on the cb-ob centerline, that 30° angle shifts left or right as the distance between cb and ob increases or decreases.

Let's say the cb is 24" from the ob and the ob is on the foot spot. We are cutting the ball to the right, into the bottom right corner pocket as Bob's diagram shows. Let's say we know the cb-ob relationship is such that a halfball aim (ccb to left edge of ob) will pocket the ball near center pocket. Using Bob's 4° window at the pocket, we have a margin of error of +/- 2°, that's 2° left or right of center pocket.

Here is where the margin of error comes into play... With this particular cb-ob relationship (24" distance between the balls), the difference between aiming ccb to ob center and aiming ccb to ob edge is 2.7°. Let's call this our "perspective angle". It is measured from the triangle created from ccb to the ob left edge then 90° over to the ob center. Naturally this 2.7° angle changes as the distance between the balls changes.

We've already determined that a halfball hit will send the ob toward center pocket. We know we have a tolerance (margin of error) of 2° left or right of center pocket. If we move the cb farther away, along the centerline between the balls (not some imaginary or invisible ghostball line), that 2.7° perspective angle gets smaller.

From 70" away from the ob, the perspective angle (the difference between aiming ccb to ob center and ccb to ob edge) is only 0.9°. With the cb 24" away from the ob this angle is 2.7°, so the difference here is 1.8° (2.7 - 0.9). This means there's a 1.8° difference between aiming for a halfball from 24" away when compared to 70" away. The same 30° shot angle will be created with both shots, but from 24" away the 30° cut will land near center hole, while from 70" away it'll land 1.8° to the right of center hole (thinner, or overcut). But that's still within the +/- 2° window, so if the shot is hit accurately it will go into the pocket.

From the original position (24" distance between the balls), if we move the cb closer to the ob (along the center line between the balls) the perspective angle gets bigger. At a distance of 14" the angle is 4.5°. At 24" it was 2.7°, so the difference in the perspective angle is 1.8° again, only this time the ob will land 1.8° to the left of center pocket (thicker, or undercut), but it still hits the pocket.

If we used the cb to ghostball center line, there is no perspective angle difference because the cb-ob relationship is not relevant. But a ghostball is imaginary, and that's why it involves so much trial and error, guesswork. Using the cb-ob relationship is not imaginary, but one has to work with the fact that the perspective from cb to ob to pocket changes as the distance between cb and ob changes.

 

[BC21]

.....But it is a really, really bad idea to wed yourself to exact fractional ball hits. Just consider the straight shot. If the cue ball is on one edge of the red shaded area, and you use a true fractional aim, you will send the 1 ball all the way to the extreme side of the pocket. If your stroke makes a small error in that same direction, you will miss the shot. Since most of us make small errors most of the time (and large errors the rest of the time ), you will end up missing about half of such shots.

What fractional aim user would be foolish enough to limit shot options to just one of the basic 1/4 aim points? I mean, if the cb and ob are slightly offline from being a zero angle shot, let's say 2 or 3 degrees (just outside the red window in your diagram), very few players would think or be "wed" or committed to using a full ball aim, and certainly no one would think going to the next quarter (3/4 aim) would work.

And of course simply using the basic quarter aim points drastically limits shot options. But it's really not difficult to fine tune fractional aiming to the nearest 1/8, 1/16, or even 1/32 of an aim, or simply aiming a touch thinner or thicker, like aiming 1mm left or right from a perfect halfball aim, which would be about a 1° difference on the shot result.

So you are correct that it's a really bad idea to wed yourself to exact fractional ball hits, but that's only if you're ignorant or foolish enough to only use the basic quarter aim points, or even the 1/8 interval aim points. Some shots fall between these aim points, and that's where some fine tuning needs to be developed. The basic quarters and the eighths can be used to pocket the majority of shots, but for the rest of the shots these aim points are merely references to help determine a more accurate line of aim. As long as the player can deliver the cb accurately, within 2mm of the desired target/aim, then fractional aiming can be a very precise method for most shots.

The width of the ob never changes, which means it can be used as a constant reference for all shots. With some basic spatial skills, anyone can quickly learn to recognize quarter and eighth fractional segments of the ob. So beginning or struggling ghostball users should look passed the estimated ghostball and pay attention to where ccb is headed in reference to the width (the quarters and eighths) of the ob itself. This provides a solid visual reference for your brain, which can help you develop shot recognition much quicker.

 

[Ratta]

What fractional aim user would be foolish enough to limit shot options to just one of the basic 1/4 aim points? I mean, if the cb and ob are slightly offline from being a zero angle shot, let's say 2 or 3 degrees (just outside the red window in your diagram), very few players would think or be "wed" or committed to using a full ball aim, and certainly no one would think going to the next quarter (3/4 aim) would work.

And of course simply using the basic quarter aim points drastically limits shot options. But it's really not difficult to fine tune fractional aiming to the nearest 1/8, 1/16, or even 1/32 of an aim, or simply aiming a touch thinner or thicker, like aiming 1mm left or right from a perfect halfball aim, which would be about a 1° difference on the shot result.

So you are correct that it's a really bad idea to wed yourself to exact fractional ball hits, but that's only if you're ignorant or foolish enough to only use the basic quarter aim points, or even the 1/8 interval aim points. Some shots fall between these aim points, and that's where some fine tuning needs to be developed. The basic quarters and the eighths can be used to pocket the majority of shots, but for the rest of the shots these aim points are merely references to help determine a more accurate line of aim. As long as the player can deliver the cb accurately, within 2mm of the desired target/aim, then fractional aiming can be a very precise method for most shots.

The width of the ob never changes, which means it can be used as a constant reference for all shots. With some basic spatial skills, anyone can quickly learn to recognize quarter and eighth fractional segments of the ob. So beginning or struggling ghostball users should look passed the estimated ghostball and pay attention to where ccb is headed in reference to the width (the quarters and eighths) of the ob itself. This provides a solid visual reference for your brain, which can help you develop shot recognition much quicker.

Very well written posting pal!
Especially the last sentences i really liked how you described it
Many ways can "lead" you to a succesful way to master the game- And if we re talking about quarter system, you ve chosen wise words.
have a nice day and happy thanks giving.

"The width of the ob never changes, which means it can be used as a constant reference for all shots. With some basic spatial skills, anyone can quickly learn to recognize quarter and eighth fractional segments of the ob. So beginning or struggling ghostball users should look passed the estimated ghostball and pay attention to where ccb is headed in reference to the width (the quarters and eighths) of the ob itself. This provides a solid visual reference for your brain, which can help you develop shot recognition much quicker."

 

[duckie]

The thing is this.......a pool ball does not have a width but a diameter which never changes.

What does change is the perceived size of the ball based on distance from CB to OB. Put a OB in front of a corner pocket. Put the CB in front of the opposite corner pocket diagonally from where the OB corner. Go stand behind the pocket where the CB is located.

There is a perceived size difference between the two balls because of distance even though the balls have the same diameter.

Pool is played in 3 dimensions not two.

 

[Patrick Johnson]

The thing is this.......a pool ball does not have a width but a diameter which never changes.

Still having trouble with English, I see...

What does change is the perceived size of the ball based on distance from CB to OB. Put a OB in front of a corner pocket. Put the CB in front of the opposite corner pocket diagonally from where the OB corner. Go stand behind the pocket where the CB is located.

There is a perceived size difference between the two balls because of distance even though the balls have the same diameter.

Pool is played in 3 dimensions not two.

Welcome to reality. So what?

pj
chgo

 

[duckie]

See you are clueless about using the proper terminology.

Well when you draw picture, the circles always appear to be the same size when in reality the balls will appear to be of different sizes. So anyone that using 2d drawings to represent what is happening in reality is talking out their ass.

 

[Patrick Johnson]

...anyone that using 2d drawings to represent what is happening in reality is talking out their ass.

lol

pj
chgo

 

[BC21]

The thing is this.......a pool ball does not have a width but a diameter which never changes.

What does change is the perceived size of the ball based on distance from CB to OB. Put a OB in front of a corner pocket. Put the CB in front of the opposite corner pocket diagonally from where the OB corner. Go stand behind the pocket where the CB is located.

There is a perceived size difference between the two balls because of distance even though the balls have the same diameter.

Pool is played in 3 dimensions not two.

Yes...... the "diameter" is the WIDTH of the ball. And it makes no difference if it looks like the size of a pool ball up close or a golf ball from 8ft away....there is still a simple diameter/width that can easily be used to assist with fractional aiming.

 

[straightline]

Doesn't fractional precision degrade as you get further from center?