... various effects, measures, and techniques related to a pool cut shot.
maintained for the book: The
Illustrated Principles of Pool and Billiards,
the monthly Billiards Digest "Illustrated Principles" instructional articles, and the instructional video series:
Video Encyclopedia of Pool Shots (VEPS), Video Encyclopedia of Pool Practice (VEPP),
How to Aim Pool Shots (HAPS), and the Billiard University (BU)
For more information, see Chapter 3 in The
Illustrated Principles of Pool and Billiards
and Disc I of the Video Encyclopedia of Pool Shots
What is a back cut and why is it tougher than a regular cut?
A back cut is a cut shot where the cue ball is shot well away from the target pocket (e.g., when the cue ball is much closer to the target pocket rail than the object ball). These shots can be more difficult than cut shots looking toward a pocket because the required cut angle can appear larger than it actually is, because you are looking away from the pocket. As a result, most people tend to overcut back cuts (i.e., they are hit too thin). For more info, see shot #6 in VEPS-I. Also, with back cuts, because you are looking away from the pocket and the near rail adjacent to the pocket, the visual cues for the pocket location are not as clear as with non-back-cuts (where you are looking toward both rails adjacent to the pocket, helping to provide better visualization of the pocket location).
A back cut up to (and even more than) 90 degrees is possible with the help of outside english (OE) . Diagram 2 in "Throw - Part VI: inside/outside english" (BD, January, 2007) shows how much OE is necessary for "gearing" OE (resulting in no throw). For a 90-degree cut, 80% english is "gearing," so to throw the ball in the SIT direction with a very thin cut, you need more than 80% english. For more info, see:
HSV B.33 - Outside english gearing, and cut and spin-induced throw
NV B.86 - Cut-induced throw (CIT) and spin-induced throw (SIT), from VEPS IV
HSV A.142 - Vernon Elliott cross-side bank with chalk on the object ball to increase throw and spin transfer
from Patrick Johnson:
When we shoot back cuts we're looking away from some important visual cues, namely the pocket and the rails that point to it. We learned to use these cues to help us see the OB-to-pocket line and find the contact point/cut angle without all the walking around (the usual reason for innovation). But we learned them subliminally, so we don't notice that we're using them and don't know what's wrong when they're gone.
Once we do know what's wrong, the simple solution is obvious: revert to walking around and sighting the OB-to-pocket line as we did before learning to use the visual cues (or resort to the stick-pivot method or any other "mechanical" method to get a fix on the contact point/cut angle).
The main difference between backcuts and other cuts is that there's no nearby rail behind the OB to show you the direction to the pocket. So a useful trick for aiming backcuts is to "replace" the rail by imagining one right behind the OB pointing to the pocket. Sounds a little nutty, but this often helps to see where to hit the OB. It even helps on non-backcuts where the OB is farther from the rail (this is why OBs in the middle of the table can be harder to aim).
The rail behind the OB is an important visual "cue" - I find OBs on or near the rail much easier to aim.
ball-hit fraction vs. cut angle
How is cut angle related to ball-hit fraction?
Illustrations, equations, plots, and numbers on this topic are available here:
TP A.23 - Ball-hit fraction vs. cut angle
Here's a useful illustration from "Aim, Align, Sight - Part I: Introduction and Ghost Ball Systems" (BD, June, 2011) defining the standard ball-hit fractions:
from Bob_Jewett (from AZB post):
Here is a plot of the cut angle you get versus the fullness of hit. For example, a fullness of 0.5 -- an exact half-ball hit -- gives a cut angle of 30 degrees. (This ignores throw which can be several degrees depending on speed, spin, cut angle and ball conditions, but that is mostly a separate issue.) A couple of other fullnesses to note are 3/4 full which gives an angle slightly under 15 degrees and 1/4 full which produces about a 48-degree cut.
estimating cut angle
How can you estimate the cut angle for a shot?
On Disc I of the Video Encyclopedia of Pool Shots, we show how to use your hand to recognize 1/4-ball, 1/2-ball, and 3/4-ball hits. We also show how to calibrate your hand so you can judge these shots (and the corresponding cut angles) fairly accurately. Knowing these three angles well can help you estimate the angle required for any shot. The cut angles for various ball-hit fractions can be found at the end of TP A.23.
A simple way to visualize and estimate cut angles is to imagine an analog clock face (or use one on your wrist). If noon (12) is straight (0 degrees), 11 and 1 are at 30 degrees (1/2-ball hit), 10 and 2 are at 60 degrees (about an 1/8-ball hit), and each minute is 6 degrees. For example, halfway between 12 and 1 ( at 2 1/2 minutes) is 15 degrees (about a 3/4-ball hit), and halfway between 1 and 2 is 45 degrees (about a 1/4-ball hit).
Below is a template posted by oldschool1478 (in AZB post) that can be useful to estimate cut angles and required aim points when practicing. Here's a printable PDF version. If the center of the cutout is placed over the necessary ghost-ball position with the arrow pointed back to the cue ball, sighting to the pocket gives the necessary cut angle, clock position, ghost-ball overlap, and aim point (center of small circle) relative to the object ball. For example, the required aim for a 30 degree cut (assuming no throw) is through the edge of the object ball. The dashed ghost-balls in the small illustrations are useful to get a sense for the amount of ball overlap required on a particular shot.
from Bob Jewett:
The tip of the cue is at the center of the ghost ball. The distance X is the base of an isosceles triangle. If X is measured in quarter inches, it gives the angle, pretty nearly.
Here are x (in) x (in/4) actual angle and error:
1 4 3.82 0.18
2 8 7.65 0.35
3 12 11.48 0.52
4 16 15.32 0.68
5 20 19.19 0.81
6 24 23.07 0.93
7 28 26.99 1.01
8 32 30.93 1.07
9 36 34.92 1.08
10 40 38.94 1.06
11 44 43.02 0.98
12 48 47.16 0.84
13 52 51.36 0.64
14 56 55.64 0.36
15 60 60.00 0.00
16 64 64.46 -0.46
17 68 69.04 -1.04
18 72 73.74 -1.74
19 76 78.59 -2.59
from Dead Crab:
I have a way of estimating cut angles to within a degree. It works for me. Estimating to within 5 degrees would be a cinch.
1. Place a small piece of tape (blue painter's tape is good) on your cue shaft 15" from the tip
2. Place tip of cue on the CB-OB line so that the 15" mark on the cue is over the top of the CB (obviously, not touching it).
3. Leaving the tip stationary, swing the butt of the cue so that the alignment of the cue long axis is parallel to the line of the OB-intended pocket.
4. Estimate the distance (in inches) from the tape mark on the cue to the CB-OB line (i.e. drop a perpendicular to the CB-OB line from the mark on the cue. Multiply this distance by 4. That is your cut angle, in degrees.
With a little practice, the difference between 3.5" and 4" is obvious, and clearly distinguishes a 14 degree from a 16 degree cut angle. For longer shots, you can use the cue joint rather than the 15" mark, and multiply by 2 instead of 4 to get the cut angle.
From a practical viewpoint, it is important to note that the tip of the cue need not be at the GB center. Since the GB center may be 7' away, a more practical approach is to place the 15" mark on your cue over the CB, with the tip on the estimated CB-GB line (as discussed, for long shots the CB-OB line is often adequate for longer shots). Then pivot the cue around the tip until it lies parallel to the OB-pocket line. Estimate the base of the triangle in inches, multiply by 4, and you are done. For really close shots the method can be used by extending the estimated CB-OB line "behind" the CB. This saves a lot of reaching. For intermediate and long shots, the 30" point of the cue is often easiest to use (just 1" above joint), and then the multiplier is 2 instead of 4.
If you know the cut angle, you know where to aim from the CB center. 1mm per degree up to 30 degrees and above that, 0.8mm/degree off ball edge over 30 degrees covers it pretty well. Ball landmarks come in handy. A visible gap becomes apparent between cloth and ball at about 10mm off center (napped), 7-8 mm worsted. A 20 degree cut can be aimed at 7:30 or 4:30 on the clockface, a 25 degree shot at 8:00 or 4:00. A 23 degree cut is 2mm shy of a 25 and 3mm more than a 20.
"impossible" cut shots
Is it possible to make a shot with an effective cut angle greater than 90 degrees?
Yes. Here are several examples:
Here's another extreme cut by Bob Jewett.
HSV A.142 - Vernon Elliott cross-side bank with chalk on the object ball to increase throw and spin transfer
Impossible cuts can also be made by jumping or hopping the CB so it hits the OB while airborne. More info and video demonstrations of this can be found here:
jump shot over cut effects
margin for error
How does the difficulty of a shot vary with cut angle?
The following analysis (which includes several useful graphs) shows how the margin for error varies with both shot distance and cut angle:
TP 3.4 - Margin of error based on distance and cut angle
Also, the effective size of the pocket varies with angle and speed. For more info, see: pocket "size" and "center"
An article that discusses how the angle increases the difficulty of a shot (which is to say, decreases the allowed error), is at: http://www.sfbilliards.com/articles/1994.pdf (April)
The article includes a simple graphical way to see how much the cut angle increases the difficulty over a straight-in shot of the same length.
Why do people overcut cut shots (i.e., hit OB ball too thin)?
Sometimes the aim is just off. When using english (especially outside english), swerve and/or throw might be the culprit. For more info, see:
aim compensation for squirt, swerve, and throw
On firm follow shots and/or jump shots, sometimes the OB is overcut because the CB is airborne when it hits the OB. For more info, see:
jump shot overcut effect
follow shot ball-hop effects
from Bob Jewett:
There is some throw on all shots. That is, the surface of the cue ball is somewhat sticky, and as it passes across the surface of the object ball, it will pull the object ball off the ideal path, which is the line through the centers of the two balls at the instant of contact.
If the cue ball is moving faster, there is not as much friction. This is contrary to the simple explanation of friction which says that the coefficient of friction does not change with the force of the contact. The reduction seems to be over a factor of two as you crank the speed up
If you have stun on the cue ball (no follow or draw), the throw you see on a cut shot is maximized for that speed because all the rubbing is to the side. As you add draw or follow, the effective friction is reduced because part of the rubbing is up or down, and that doesn't contribute to the throw.
Most players have no idea that this stuff is going on, and to some extent it is better for them not to know. They learn subconsciously to make corrections for it, and if they start thinking about it during shots, their brain will get in the way of their arm.
There are fairly simple demonstrations for this. It is discussed on Dr. Dave's web site and in Bob Jewett's May '06 BD article.
The cue ball also jumps on hard shots as mentioned above, but this causes thinner cuts mostly for short distances to the object ball or excess stick elevation.
speed and travel distances for the CB and OB
How do CB and OB speeds and travel distances vary with cut angle?
See "Fundamentals - Part VII: speed control" (BD, March, 2009). It includes distance graphs for both stun and rolling CB shots.
For more information, see the ball speed and travel distance resource page.
Are straight-in shots more difficult than shots at an angle?
No. It just seems that way because there is extra pressure on straight shots, because we expect to make them, even if they are long (especially if we have practiced them specifically). In other words, there is no excuse for missing them. Also, people often compare long, tough, straight-in shots to shorter and easier cut shots. This is not a fair comparison. Straight shots ARE easier than cut shots of the same CB-to-OB distance and the same OB-to-pocket distance. Proof can be found in TP 3.4 - Margin of error based on distance and cut angle. If one does a simple experiment, this fact should become clear. Here it is:
Place an object ball in the center of the table, and place the CB three feet away for a straight-in shot to a corner. Attempt this shot a large number of times and keep track of your make percentage. Then attempt the same number of shots, with the OB is the same place, but with the CB at random angles (maybe up to 30 or 45 degrees) for cuts both to the right and left, still positioning the CB three feet from the OB (along a circular arc) for each shot. Again keep track of the make percentage.
The results of this experiment should shot that the straight shot is easier; in other words, it will have a higher make percentage (unless you have a really serious issue with any of the things below, in which case your results might be somewhat random). The reason is: every straight shot is the same ... it is straight ... no real "aiming" is required (although, you must have your vision and cue aligned accurately). Cut shots at different angles must be aimed (and still require accurate vision and cue alignment). Also, there is less margin for error with a cut shot compared to a straight-in shot (especially with larger cut angles). Even if the same cut angle is used for every non-straight shot in the experiment, the success rate should still be greater for the straight shot (although, after a few attempts, you should no longer need to "aim" the cut-angle shot, because you will have locked in the aim by then).
The most common reasons why people miss straight-in shots, especially long ones, are the following:
- Your "vision center" is not properly aligned. If this is the case, you won't perceive the straight line of the shot and your cue alignment properly. FYI, there are tests and drills for diagnosing and fixing this problem on the vision center resource page.
- You are not hitting the CB on the vertical centerline, creating unintentional sidespin, resulting in squirt, swerve, and spin-induced throw. Tip position is critical on a long, straight shot. The most common causes for having the cue tip off center are a poorly aligned "vision center" and a lack of focus dedicating to checking this during the "set" position of the pre-shot routine. FYI, there are drills for helping with this problem on the "finding the center of the CB" resource page.
- Your cue is not as level as possible. If so, the swerve effect due to any unintentional english becomes significant.
- You are not stroking straight. If so, the stroke "best practices" recommendations might help.
What happens when a straight shot is hit slightly off center by mistake?
This creates "unintentional english." The resulting sidespin, even though it might be a small amount, and the associated squirt, swerve, and throw, can easily cause a straight shot to be missed, especially a long shot with tight pockets.
Interestingly, for some shots with unintentional english, the squirt, swerve, and throw effects can completely cancel. resulting in a perfectly straight shot. For example, for a straight shot with a hit slightly to the left of center, a small amount of left sidespin will be imparted creating squirt to the right and swerve back to the left. With typical cue elevations (near level), the squirt effect will be larger than the swerve effect, especially at faster speeds or with a non-LD shaft, resulting in a net CB deflection to the right. This would result in the OB being cut to the left. However, the left spin will throw the OB to the right. Again, if everything happens to balance, the OB will go straight.
Obviously, you wouldn't want to intentionally apply sidespin (even a small amount) on a long, straight shot because the combination of squirt, swerve, and throw effects can easily cause a miss. It is difficult to get a perfectly centered hit, but the closer to center you are, the smaller all of the effects will be.
The relative amounts of each effect depends on many variables (shot speed, shot distance, cue elevation, cut angle, amount and type of spin, cloth conditions, and ball conditions, etc.). For faster-speed shots, squirt will be the dominant factor for missing a straight shot with unintentional sidespin. If the cue is elevated more than the typical amount, swerve can be the dominant factor. And for slower-speed shots, especially stop shots, throw can be the dominant factor.
A complete list of squirt, swerve, and throw effects, along with explanations and demonstrations of all of the variables can be found here:
squirt, swerve, and throw effects
If you get a well-centered hit on the CB on a straight shot, you don't need to worry about any of this stuff.
Why do some people undercut some cut shots (i.e., hit OB ball too full)?
Some people have trouble visualizing the required ghost-ball center for a cut shot, and get influenced too much by the ball contact point. For more info and illustrations, see "Fundamentals - Part II: aiming" (BD, October, 2008).
Sometimes, cut-induced throw (CIT) is the cause; and when english (especially inside english), swerve and/or throw might be the culprit. For more info, see:
aim compensation for squirt, swerve, and throw
One way to compensate for undercutting the ball is to use outside english, but this isn't the best approach for all people. For more info, see:
outside english resource page
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