... how to use diamond systems to aim kick and bank shots in pool
Dr. Dave's answers to frequently-asked questions (FAQs), mostly from the BD CCB and AZB discussion forums
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)
more information, see Chapter 6 and Sections 7.06-7.08 in The
Illustrated Principles of Pool and Billiards,
Disc III of How to Aim Pool Shots (HAPS), Disc IV of the Video Encyclopedia of Pool Shots (VEPS) ,
and Disc IV of the Video Encyclopedia of Pool Practice (VEPP)
advantages of fast speed
Why do many top bankers use fast speed?
With faster speed, there is much less variation from table to table and from shot to shot. The OB will pick up less roll, and this (combined with the post rebound speed) will minimize how much the OB curves after rebound. As a result the ball will bank in a more consistent direction.
Also, there are many variables that affect how a ball banks (cloth friction, cushion friction and coefficients of restitution, OB spin transfer, and table roll-off). At faster speed, these variables don't change the shot as much with slight changes in speed as they do with similar speed changes at slower speeds. This is another advantage of using faster speed for banks.
At slower speeds, the path and final target of the rebounding ball varies a lot with small changes in speed. The disadvantage of faster speed is the reduced effective "size" of the pocket.
Faster speed can also help reduce the chance for a double kiss at certain approach angles. See:
A good system for aiming fast-speed bank shots can be found here: fast-speed mirror-system adjustment.
contact-point mirror system for aiming shallow-angle, rolling kick shots
How do you aim to kick at balls close to a rail at a shallow angle into the rail?
For shallow angles into the rail, where the OB is fairly close to the rail, the contact-point-mirror-kick method works well. It is described in "VEPS GEMS - Part VII: Contact-Point Mirror Kick" (BD, July, 2010) and "VEPP – Part X: Shallow One-rail Kicks" (BD, January, 2013), and here are video demonstrations with a complete explanations:
from Disc IV of the Video Encyclopedia of Pool Practice (VEPP):
Corner 5 System for aiming two-, three-, and four-rail kicks off a long rail
How does the "Corner 5" System work?
It is illustrated and explained, with examples, in the following articles:
"VEPS GEMS - Part XI: Corner-5 System Intro" (BD, November, 2010).
"VEPS GEMS - Part XII: Corner-5 System Example and Benchmark" (BD, December, 2010).
"VEPS GEMS - Part XIII: Corner-5 System Adjustments" (BD, January, 2011).
Here's a demo starring Donald Duck: "Donald in MathMagic Land" 3-cushioin billiards demo. Here's a complete demonstration and explanation of the Corner-5 system, with lots of examples of how it is applied:
from Patrick Johnson:
[Here's] a simplified way to estimate 3-rail kicks to given targets on the fourth rail. This simplified 3-rail kick system is vaguely similar to the Spot-On-The-Wall system and the Corner-Five system, but instead of off-table visual references (Spot-On-The-Wall) or math (Corner Five), it uses simple diamond-to-diamond alignments.
Three rail kicks that start out parallel to each other (their first legs are parallel) end up hitting the fourth rail very close together - they "converge" on a fourth rail target. It's easy to see parallel lines on the pool table using the diamonds. If we start with a line stretched between one diamond on the near long rail and another diamond on the far long rail, we can simply move each end of the line one diamond to the right to find a parallel line. Move each end another diamond in the same direction (left or right) and there's another parallel line, etc. The angle of these parallel lines between the diamonds is determined by how many diamonds along the rail one diamond is from the other - call this their "separation". For instance, diamonds on opposite long rails with "4 diamonds of separation" make parallel lines at 45 degrees (see third diagram below), while diamonds with "3 diamonds of separation" make parallel lines at 51 degrees (see fourth diagram below).
Using these easy-to-see diamond-to-diamond lines, we get sets of parallel lines to use as reference tracks for 3-rail kicks. Fortunately for us, each set of parallel lines converges near a pocket or diamond on the fourth rail, making both our first legs and our fourth rail targets easy to remember. The correlations are:
- a first leg line with 6 diamonds of separation will come close to the corner pocket on the fourth rail
- a first leg line with 5 diamonds of separation will come close to the 1st diamond on the fourth rail
- a first leg line with 4 diamonds of separation will come close to the 2nd diamond on the fourth rail
- a first leg line with 3 diamonds of separation will come close to the 3rd diamond on the fourth rail
Below are diagrams illustrating these basic reference tracks:
Use a "6-diamond separation" to hit the corner pocket on the 4th rail.
Use a "5-diamond separation" to hit the 1st diamond on the 4th rail.
Use a "4-diamond separation" to hit the 2nd diamond on the 4th rail.
Use a "3-diamond separation" to hit the 3rd diamond on the 4th rail.
I think this will be extremely easy to remember. Notice that for each of the cases you cited, the number of diamonds of separation plus the 4th-rail convergence diamond (counting from the pocket as zero) totals 6. That is, 6+0=6. 5+1=6. 4+2=6. 3+3=6. So we could call it the "Sixes System" for three-rail kicks.
What effect does cut angle have on bank-shot aiming?
The following video from Disc IV of the Video Encyclopedia of Pool Practice (VEPP) covers the important basics concerning how cut-induced-spin (CIS) affects bank shots:
Banks can also be affected by spin-induced-spin (SIS). For more info and examples, see the spin-transfer bank shots resource page.
diamond systems for aiming kick shots
How do diamond systems work?
All of the most common and useful banking and kicking systems (those listed below, and others) are described, illustrated, and demonstrated on Disc IV of the Video Encyclopedia of Pool Shots.
The simplest diamond systems are the equal-distance mirror system and the through-diamond rolling-ball system.
For shallow angles into the rail, where the OB is fairly close to the rail, the contact-point mirror system for shallow-angle, rolling kick shots works well.
The most famous"diamond system" is the Corner 5 System for aiming three-rail kicks off long rail.
Another famous diamond system is the Plus System for two-rail kicks off short rail.
Spot-on-the-wall kicking systems offer an alternative to formula-based systems.
Here's an article on Jimmy Reid's 3-rail systems.
complete "kicking academy" document describing and illustrating many diamond systems for kick shots.
double kiss detection and avoidance with a cross-corner bank shot
How do you know if a bank shot will cause a double-kiss, and how can you avoid it?
The video demonstrates an easy method to use to detect and avoid cross-corner bank double kisses:
This video shows several techniques to avoid a double kiss with a cross-side bank shot.
This video shows how to detect a double kiss when banking a ball frozen or close to the rail.
Here's a good article from Bob Jewett (BD, July '99) covering how to detect and avoid double kisses.
This video shows some examples of how to use a double-kiss bank to your advantage:
Here's another somewhat-unusual example of a double-kiss bank shot:
from freddy the beard:
Determining whether a bank shot lays in the "kiss" zone is often misunderstood, and usually winds up as an educated guess. In the following diagrams I have outlined exactly when a bank cannot normally be made using a rolling with or without english. In diagram #1, I deal with the shorter angle cross-corners. If the straight-in angle of the cueball and object ball is lined up and aiming into the pocket facing, the shot is a certain kiss. Left or right english, follow, center, or draw is not going to help you beat that kiss. With a slight angle adjustment, as per diagram #2, lined up to the middle of the back of the pocket, the bank can now be easily made with rolling or center ball, no english.
Diagram #3 is another variation that must be considered. It involves crossing, or passing-over, the object ball from a much more severe angle. Rather than calculate off of a straight-in angle as per dia.#1 & 2, the kiss/no kiss reference point is determined by lining up the actual cut angle needed to make the bank. If an imaginary line from the center of the cueball, extending thru the cut area on the object ball, continues into the middle of the back of the pocket, the kiss is "on." If the line instead, is aiming at the short/bottom rail, you can go ahead and shoot the shot with impunity. Provided of course you are using a natural rolling ball, center ball, left english in this case, or draw. Right hand english when the bank is "on" could result in a kiss.
effects and factors to consider
What effects does one need to adjust for when aiming bank and kick shots?
First, "VEPS GEMS - Part V: Banks and Kicks" (BD, May, 2010) and the video below illustrate, describe, and demonstrate basic terminology for bank and kick shots:
The basic mirror (angle in equals angle out) systems provide a point of reference only. Your aim with a given shot depends on many effects. The effects that require aim adjustment include:
If one doesn't understand all of these effects, or have great intuition built up from years and years of experience (i.e., lots of mistakes and successes), the mirror systems are not very useful. Here's an excerpt from Disc IV of the Video Encyclopedia of Pool Practice (VEPP) that shows you how to develop a feel for some of the effects during practice:
For kick shots with small approach angles (i.e., almost straight into the rail), it sometimes helps to know how topspin and bottom-spin change off the rebound. For more information and examples, see:
from Patrick Johnson:
For kicks the important thing is what kind of "vertical spin" the CB has on it when it hits the rail:
- CB sliding when it hits the rail will rebound with no curve at the "mirror angle" (minus something for rail friction)
- CB with forward spin (including natural roll) when it hits the rail will curve longer than the mirror angle
- CB with backspin when it hits the rail will curve shorter than the mirror angle
How much longer or shorter the CB rebounds (with forward spin or backspin) depends on how much spin is on the CB* and how much friction there is between the CB and the cloth.
For banks the important thing is how much vertical spin is on the OB when it hits the rail. This can only be controlled by hitting harder or softer (harder = less or no forward spin; softer = more forward spin). This is also why hitting harder shortens bank angles.
*: How much spin is on the CB depends on: - how hard it's hit - how high it's hit - how far it is from the rail when it's hit - how much friction there is between CB/cloth
As this drawing shows, when the CB changes direction off the rail its spin does not change direction. That means that forward or reverse spin which was rotating parallel with the CB's path before hitting the rail is rotating across the CB's path after hitting the rail - this across-the-path rotation is what causes the CB to curve after hitting the rail.
Forward rotation (topspin) can be the result of the CB rolling naturally or of hitting high on the CB. Reverse rotation (backspin) can only be the result of hitting low on the CB.
Concerning HSV B.41, why doesn't speed shorten the rebound angle? Doesn't the ball compress the cushion sideways more at higher speed, and wouldn't that create sideways forces that would shorten the rebound angle?
There are many physical effects that control the immediate rebound angle and the amount of masse curving after rebound. I use the phrase "rail throwback" to refer to the effect you are describing. With more speed the cushion deforms more and can generate more sideways force to shorten the angle; however, the rebound angle is also affected by the efficiency (coefficient of restitution = COR) of the cushion, and this can vary with speed and angle also. Based on the results in HSV B.41, these two effects are balancing each other out. The rail throwback effect tries to shorten the rebound angle and the efficiency effect apparently tries to lengthen the rebound (because the cushion is returning less energy, maybe partly because of the ball shift down the rail). This is all conjecture, but it makes sense physically. There are also friction effects between the ball and cushion and ball and table during impact. These might also vary in complicated ways with speed.
equal-distance mirror system for aiming bank and kick shots
How does the basic mirror system work?
"VEPS GEMS - Part V: Banks and Kicks" (BD, May, 2010) and the video below illustrate, describe and demonstrate basic terminology for bank and kick shots, and explains the basic equal-rail-distance mirror system:
And the following video from Disc III of How to Aim Pool Shots (HAPS) shows how the classic "mirror system" works:
For more information, see HAPS - Part VII: Kick Shots (Billiards Digest, May, 2015).
The basic mirror (angle in equals angle out) systems provide a point of reference only. You must compensate your aim for a given shot based on the many effects and factors to consider.
For shallow angle kicks, where the object ball is close to the rail, the following mirror system works quite well:
Here's another useful video, from Disc III of the Billiard University (BU) Instructional DVD series:
For more information, see: "Billiard University (BU) - Part IX: Kicks," (April, 2014).
from Patrick Johnson:
from Patrick Johnson AZB post:
Here are the reference angles for banking/kicking to the bottom left corner pocket - they connect each 1/2 diamond on the far rail with the whole diamond twice as far along on the near rail:
Of course, I don't visualize all these reference angles for every shot to that corner. For instance, the 2 ball is very near one reference angle, so I'll just compare it to that one:
The 1 ball is midway between two reference angles, so I'll compare it to both of them:
Here's the same technique applied to kicking at a ball that's not on the near rail. Just move the near "rail" (where you measure the whole diamonds) up to be parallel with the target - it doesn't matter if the cue ball is above or below the adjusted "rail".
Here's another way of measuring kick shots, a little different from the "reference angles" method I posted earlier, but using the same 2-to-1 principle. It should be self explanatory...
Like the "reference angles" this measures the "equal angle" kick, so of course you need to adjust for cloth stickiness & ball speed/spin.
fast-speed bank aiming system
How do adjust your aim for a fast-speed bank?
The bank shot aiming system described in the following articles works well for fast-speed banks: "Fast Speed Banks" (BD, July, 2013) and "HAPS - Part VIII: Bank Shots" (BD, June, 2015). It also works well for banks of any speed if the OB is close to the banking cushion (where it doesn't have time or distance to develop forward roll). Here's a diagram from the article illustrating how it works:
And here's a video demonstration from Disc III of How to Aim Pool Shots (HAPS):
The aim always originates 1/3 of a diamond above the standard 2-to-1 mirror system (measured across from the diamonds in the rail groove). It can be referred to as the "(2x + 1/3) to x" or "1/3-more-than-twice system. See the article and the video above for examples of how it is applied. The system is also described and demonstrated in "VEPS GEMS - Part V: Banks and Kicks" (BD, May, 2010). Here's the diagram from the article that illustrates how the adjustment works. The exact amount of adjustment needed will vary with conditions and the angle of the bank, but 1/3 of a diamond is a good general benchmark reference. The diagram also shows another useful reference for fast-speed banks: the 3-to-1 through-diamond reference. On most tables, shooting through 1 from 3 with very fast speed pockets the ball.
An alternative to the "(2x + 1/3) to x" system described above is a through-diamond system described in the following video: Eckert's bank shot reference lines. It can be described concisely as the "2x-to-3/4x through-diamond system" as opposed to the "(2x+1/3)-to-x rail-groove system." Both this system and the system above are described and illustrated in detail in: "Fast Speed Banks"(BD, July, 2013). They actually agree fairly well in the resulting aim, except for very-large-angle banks. Another way to interpret the Eckert system, is the "8/3x to x" or "x to 3/8x" system (by dividing the "2x to 3/4x" numbers by 2). This implies that the aim point on the banking rail (3/8x) is between 25% (1/4) and 50% (1/2) of the distance from the target pocket as the distance on the adjacent rail (x). This provides an easy way to visualize fast-speed banks. When the aim is correct, the aim point on the banking rail is exactly between 50% (1/2) and 25% (1/4) of the distance from the pocket on the opposite rail, which is very easy to visualize without any diamond counting or math.
The following illustration compares the two systems. The systems provide very close to the same lines of aim for small-to-medium-angle banks. At larger bank angles, above the (5+1/3)-to-2.5 line, the "1/3-more than twice" system aim will tend to make the ball bank a little short of target (in which case you can make a small adjustment).
In addition to being able to use the aiming systems above, there are advantages to using fast speed with bank shots. For more info, see: advantages of fast speed.
from John Gaynor (via e-mail):
I found a way to simplify the calculations for the Ralph Eckert system for banking with speed. First, I use 10 as the distance between diamonds. So the 3 to 1 track becomes 30 to 10. Then every point on the target rail that is a multiple of 3 leads to a convenient reference track since the crossing point on the near rail is 8/3 times the point on the target rail. So reference tracks are 8 to 3, 16 to 6, 24 to 9, 32 to 12, 40 to 15, 48 to 18, etc. Calculating between the reference tracks is easy. For example, if you're between the 24 to 9 track and the 32 to 12 track, the tracks are 26&2/3 to 10 and 29&1/3 to 11, or with slight rounding 27 to 10 and 29 to 11.
magic spot three-rail mirror-image kick shot aiming system
How do you find and use the "magic spot" for three-rail kick shots?
See the following document from Marcel Elfers: Pool Magic Spot.
Plus System for aiming two-rail kicks off a short rail
How does the Plus System (AKA Plus Two System, AKA "Plus 2 System") work?
It is described and illustrated in detail in the following instructional articles:
"VEPS GEMS - Part VIII: Plus System Intro" (BD, August, 2010).
"VEPS GEMS - Part IX: Plus System Adjustments" (BD, September, 2010).
"VEPS GEMS - Part X: Plus System Examples" (BD, October, 2010).
Here's a video demonstration and explanation:
shallow-angle contact-point-mirror-image kick-shot aiming system
How do you aim shallow-angle kick shots where the object ball is close to the rail?
When the object ball is close to a ball away from the rail, the following mirror system, from Disc IV of the Video Encyclopedia of Pool Shots (VEPS) is very effective:
The following video, from Disc IV of the Video Encycopedia of Pool Practice (VEPP), demonstrates a good way to practice these shots:
For more information, see: "VEPS GEMS - Part VII: Contact-Point Mirror Kick" (BD, July, 2010) and "VEPP - Part X: Shallow One-rail Kicks," (BD, January, 2013).
Sid System for aiming steep two-rail kicks off a short rail
What is the "Sid System" and how does it work?
from Bob Jewett (from AZB post):
For those who are wondering what "System Sid" is, here is the diagram from Walt Harris's book, "Billiard Atlas". To hit a spot on the second cushion, multiply the number for the spot by how many diamonds the cue ball is from point X. In the example, the target is 2.5 and the cue ball (Q) is 3 diamonds from X so the target is 7.5 on the short rail. Note that the short rail (M) is numbered 10 to the diamond, the second rail has a variable numbering that you have to memorize, and the rail you are shooting from (O) is numbered in units to multiply with. Harris recommends renumbering the O rail according to the second rail number, so in the example it would be numbered 0, 2.5, 5.0 and 7.5 starting from X.
If you work out the geometry in detail, the numbers on the second rail are off a little but as listed they are easy to remember.
spin-transfer bank shots
Is spin transfer required to make certain bank shots?
Yes. See NV B.20 for two important examples. For more information, and another example, see "Throw - Part VIII: spin transfer" (BD, March, 2007). Many more examples of spin-transfer shots can be found here:
spot-on-the-wall kick shot aiming system
How do "spot-on-the-wall" kicking systems work?
The three-rail Corner-5, two-rail Plus-2, and one-rail kick "spot-on-the-wall" systems are described and demonstrated here:
More information, including guidelines on how far the spot should be from the table, can be found in "VEPS GEMS - Part XIV: 'Spot-on-the-Wall' System" (BD, February, 2011).
There are different "rules of thumb" for estimating the best distance to the spot on the wall, but they don't always match the results in the article very well. Here's a common rule that does a decent job (although, it predicts a distance longer than recommended for a 3-rail shot and a distance shorter than recommended for a 1-rail shot):
from Monte Ohrt:
For any given spot-on-the-wall kick shot, the exact optimal distance from the first rail to the spot is the distance the cueball travels after it hits the first rail to the target. For a one-rail kick, this is simply the distance from rail 1 to the target. For a two-rail kick, it is the distance between rail 1 and 2, and also add the distance between rail 2 and the target point. For a three rail kick, it is the distance between rails 1 and 2, 2 and 3, and 3 to the target point ... and so on for 4 rails, 5 rails, etc. After about 3 rails the point of convergence is so narrow that it normally doesn't make any difference, just pick a spot at least 3 tables away.
through-diamond rolling-cue-ball 2-to-1 one-rail kick and bank shot aiming system
How does the through-diamond rolling-cue-ball one-rail kick system work?
It is described in "VEPS GEMS - Part VI: One-Rail Kicks" (BD, June, 2010). Here's a video demonstration, from Disc IV of the Video Encyclopedia of Pool Shots (VEPS), with a complete explanation:
Here's another useful video, from Disc III of the Billiard University (BU) Instructional DVD series:
two-rail bank shot aiming system
Is there an aiming system for two-rail bank shots off the short rail?
You can use the Plus System for aiming two-rail banks off the short rail, but it will require practice to learn how to adjust for the lack of running english and forward roll on the OB into the first cushion which varies with distance and shot speed.
If the OB is fairly close to or frozen to the short rail, the systems below from Freddy Bentivegna work fairly well.
from freddy the beard AZB post:
two-rail parallel-line kick shot aiming system
Dave, I have been practicing the 2-rail parallel line kick shots you show in your
book on pages 229 & 230 and demonstrated in NV
7.9. It works fine if I set up the balls similar to what you show in your
book but I am having difficulty envisioning the same shot from other set ups.
I don't think I fully understand how to determine the center line between the
2 parallel lines. Can you elaborate on this idea?
The following video, from Disc III of the Billiard University (BU) Instructional DVD series, demonstrates the system:
Unfortunately, the action of this shot depends on english, shot speed, and table (especially cushion) conditions. Obviously, when practicing, you need to try to use consistent english and speed on a given table to see how the cue ball responds at different angles.
For more information and demonstrations, see Shots 514 and 515 on Disc IV of the Video Encyclopedia of Pool Shots.
from Patrick Johnson:
You have to aim a little closer to the corner than the measurement suggests - experience will tell you how much, depending on the angle to the first rail and the cleanliness of the table/balls.
In this drawing the blue line is the measured track, but the actual track will look more like the red line:
... the "Amazing Double-mirror Image Method" or ADIM for short ... is explained on the second page of http://www.sfbilliards.com/articles/2004.pdf (July). Mostly, it gives you a very easy way to put up a target ball exactly where the real ball would appear for a perfect mirror system. ... This lets you see immediately how pitifully awful the two-rail mirror system is, but it also allows you to try to find out where it does work and maybe how to modify it so it works for more cases.
two-times-across and three-times across bank shots
What are "two-times" and "three-times" across bank shots, and how do they work?
from Patrick Johnson:
It's a series of spin events:
1. The CB colliding with the OB puts some "holdup" spin on the OB, which shortens the angle off the first rail.
2. The OB colliding with the first rail at an angle reverses the spin that was put on by the CB (just like any ball picks up "running" spin when it hits the rail).
3. The reversed spin throws the OB toward the side pocket off the second rail.
two-times-across Z-kick aiming system
How does Jimmy Reid's two-times-across Z-kick system work?
from Patrick Johnson:
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