# Aiming in Pool and Billiards

## ... how different aiming systems are used to aim pool shots.

for more information, see Section 3.02 in The Illustrated Principles of Pool and Billiards,
Disc I and Disc II of How to Aim Pool Shots (HAPS),
and Disc I, Disc II, and Disc IV of the Video Encyclopedia of Pool Shots

aiming systems

How do different people aim?

"Fundamentals - Part II: aiming" (BD, October, 2008) and "Aim, Align, Sight - Part I: Introduction and Ghost Ball Systems" (BD, June, 2011) articles have some good illustrations and explanations related to aiming. See also: DAM aiming system. Aiming requires good visualization skills, precise body and cue alignment, accurate and consistent sighting, and an accurate and consistent stroke. And most importantly, it requires a lot of focus, and a lot of practice. There are no quick-fix solutions; although, "aiming systems" can help some people (for many reasons).

I personally use a combination of straight intuition (just "seeing the angle"), ghost-ball aiming, and contact point visualization (see DAM for more info). Bottom line: I just visualize the aim without using any kind of fractional-ball or fixed-reference compensation system. I certainly don't use any kind of math or numbers when I aim, like some people have suggested.

I think (but don't know) that if a scientific survey were done with all of the pro players, many (maybe even most) of them would say that aiming comes naturally (i.e., its "intuitive" or they just "see the angle"), because they have played so much. Some people might find the How the Pros Aim article interesting; although, it is not the result of a rigorous scientific study.

Here's a good introduction to aiming from Jerry Briesath.

from TAR Podcast #24 with Corey Deuel and John Schmidt:

John Schmidt:
Well, don’t get me started on aiming systems. I’ll tell you ... Maybe they work ... but nobody’s telling me the ones that work. Because if they work, first of all you’re not factoring in swerve and deflection. OK, now what if a guy comes up with a delivery system, that’s different. But, aiming’s adorable -- but you still have to deliver -- so you could aim perfect. If those aiming systems worked, well there would just be like four million people who played like Corey. But it’s year after year and it’s still Corey.

So these aiming systems are overrated, they’re a way to sell videos and books and make people pontificate about their own greatness and believe me if it worked, then they’d be out there winning tournaments, but they’re not.

What Stevie Moore doesn’t get is -- Stevie Moore -- you could put a bag over his head and he’d run out. He’s a great player. So he’s playing great in spite of his aiming system, not because of it. I mean, think about it: he’s already a great player. He could aim at the wall and he’s still going to make the ball. And it’s a way to give him comfort and confidence. He’s kind of like tricked himself into thinking ‘this aiming system works.’

(John sets up to demonstrate a shot.) I just can’t see how I’m going to use english here and I’m going to aim bottom right english. So I’m aiming out here -- it’s going to squirt. Well, what aiming system is going to work for that?! It’s only going to work with center ball. And you know, all these guys with their aiming systems can get like weight from me. And I don’t use an aiming system.

Corey Duel:
Yeah the one that he’s talking about I haven’t been able to comprehend it yet. It’s something about pivoting the back foot and... I don’t know.

John Schmidt:
My piece of advice, if anybody cares to the viewers at home: forget all the aiming systems. Just like when you throw a baseball to first, you just do it. Right? There’s no aiming, you do it, you feel it. It’s same with pool. You get a mental picture and you do it. Aiming systems are the most ridiculous, overrated thing...The pros scoff at that stuff, they’re like, ‘aiming systems, really?!’...

If they would quit spending so much time on line and learning about aiming systems and go hit more balls they’d become better players. There’s no short cut to it. Sitting on AZBilliards looking for aiming systems isn’t going to get it. It’s like the golf swing guys. They got a thousand videos. But the guy that goes to the driving range till his hands bleed, that’s the good golfer. You can’t watch it online and go, ‘oh, there’s got to be a system for hitting a four iron two hundred yards on the green.’ It’s the same with pool. We’ve hit a million pool balls -- that’s our system. I mean, you’re not going to get good at anything using a system.

I could be wrong, I don’t know if I’m right. I just think aiming systems are crazy. Deflection and swerve is what makes this game so tough. If there was no such thing as that, you know you just hit whatever english, but this thing goes sideways off of your stick. That’s why the game’s so impossible.

from Patrick Johnson:

Many, maybe most, players learn to aim with no conscious technique, just by practice and repetition. Aiming techniques might make aiming easier for you, or you might be one of the many who use no technique. It isn't necessary to use them in order to play well. None of these techniques are better or worse than others, and it's not better or worse to use a technique or not. It's a personal choice.

Two general categories of aiming techniques are:

1. "Exact" techniques produce exact aim in theory, but are limited by our imperfect ability to visualize and execute them. They include:

An advantage of Exact techniques is that they call your attention to the correct cueball/object ball alignment and contact point.

2. "Align & Adjust" techniques begin by aiming at the same part of the object ball each time (center, contact point or edge) and adjust from there "by feel" to the actual aim for the shot. Common beginning alignments are ("CB" = cue ball; "OB" = object ball):

1. CB Center to OB Center
2. CB Center to OB Edge
3. CB Center to OB Contact Point
4. Stick Edge to OB Contact Point

An advantage of Align & Adjust techniques is that they call your attention to stick alignment. It's good practice to "aim with your stick."

from Spiderman:

You are correct, that is a fine article. But, as even that author concludes, it will never be "put to rest". Luckily, it doesn't really matter. The numerous pros interviewed used a vast and disparate array of aiming techniques. "Ghost Ball" seemed to be the only somewhat-recurring assertion, but not to a dominant extent. There were even one or two who claimed to aim by "feel".

Personally I use the "ghost ball" technique most often, but not to exclusion of others. I learned to play with no coaching, and "ghost ball" was something I thought I invented . I didn't learn what everyone else called it until I read "99 Critical Shots". Now on some simple shots I just let the subconscious handle aiming - all I visualize is the desired result, and it happens, right down to how much the CB path distorts from the draw, and how far it rolls after the second rail. On very thin cuts I may visualize actual ball-to-ball contact points. But on ALL caroms I fall back to an augmented ghost-ball alignment. Most players will hit caroms too thick if they rely on feel.

What I would like to stress from that article is the one thing that everyone interviewed DID have in common - "the balls went in" for them.

The fact that so many different methods will work, and work well, ensures that some will die convinced that "their" way is "the only" way. Clearly all brains are not wired alike, and no one technique is ever going to be a panacea. Use what works for you, as long as it makes sense.

from Bob_Jewett:

You may find one of the following articles useful. I included the article about finding the center of the pocket because if you don't know where that is, it's pretty hard to aim well.

http://www.sfbilliards.com/articles/1993.pdf (June) -- close ball aiming
http://www.sfbilliards.com/articles/1996.pdf (February) -- frozen ball aiming
http://www.sfbilliards.com/articles/1997.pdf (April) -- finding the center of the pocket
http://www.sfbilliards.com/articles/1999.pdf (November) -- a smorgasbord of systems
http://www.sfbilliards.com/articles/2000.pdf (June) -- analysis of three systems
http://www.sfbilliards.com/articles/2004.pdf (June) -- ferrule system, lights system, overlap system
http://www.sfbilliards.com/articles/2004.pdf (December) -- aiming devices
http://www.sfbilliards.com/articles/2005.pdf (January) -- some more devices
http://www.sfbilliards.com/articles/2005.pdf (June) -- a history of parallel aiming

Why are some basic cut shot "aiming systems" helpful and effective?

Any "system" that forces a person to focus on aim, alignment, and sighting consistently and with concentration will be beneficial to many people, especially people who currently don't focus well or long enough. It also helps to have a consistent and purposeful pre-shot routine, which the systems can help foster. The DAM advice page summarizes many of the best practices used by top players when aiming, aligning, and sighting. The How to Aim Pool Shots (HAPS) DVD series covers a wide variety of aiming techniques and systems, and shows how to apply them effectively at the table.

Concerning CTE, using the edge of the OB as a visual reference, and doing so consistently in setting up for every shot (e.g., by initially aligning with the CTE line), might help some people judge and visually learn/reinforce the amount of cut needed from one shot to the next. Also, focusing on the center of the CB (after the pivot) will help avoid unintentional sidespin, which can cause squirt, swerve, and spin-induced throw, which can reduce accuracy and consistency. Also, placing the bridge hand down with the cue off angle (before the pivot) might allow some people to place their bridge hand more accurately because the pre-pivot cue might not disrupt the aiming line visual as much as when it is brought straight into the aiming line direction with the bridge.

Concerning shot-making success, a consistent and purposeful pre-shot routine can help, and having your vision center aligned properly and consistently is key, and having a reliable and repeatable stroke are all important. But if you can't accurately visualize and perceive the required angle of the shot or the required line to the necessary ghost-ball position or ball contact point, you won't be a good shot maker. I think these skills can come only with dedicated practice and successful experience. They can't come from an "aiming system" alone; although, the systems can help some people be more methodical and maybe arrive at the necessary skills more quickly than they would otherwise. Therefore, an "aiming system" can be a good thing.

from Colin Colenso (concerning 90/90 and CTE pivot-based systems):

I wanted to make a post listing what I perceive to be the strongest advantages of these systems.

I think these advantages are the main reason players often find great success aiming and shooting this way.

PLAUSIBLE CONTRIBUTING FACTORS:

1. Sighting point to point helps one to perceive an exact line and to take in the positions of the two balls relative to this line. In other words, they use a repeatable fixed method to visualize the ball positions.

2. These systems put you either right on line to begin with or in the ball park when used for appropriate shots.

3. In the pivot phase they move from this fixed line to another visual line that they perceive through the center of the CB. This finding of an aim line forces the mind to be decisive and exact. I believe forcing this decisiveness trains the mind not to wander and to make better decisions than just feeling around back and forth hoping to feel a ghost ball or contact point angle.

4. I suspect this one is the most powerful factor in these aiming methods. They force a player to commit to a pot line and then strike the cue dead straight through that line, rather than to swoop sideways on the shot as almost all beginners do. Because they focus hard on their pre-stroke alignment, they trust this line and stroke straight. If they do miss certain shots they will soon compensate with their aim until they learn to see the correct line. The normal player very often aims thick on their cut angles and swoops a little to make the cuts. When they try to bring speed or english into those shots they meet with many difficulties. So using any system that forces a player to adopt strict and accurate pre-alignment, followed by a straight stroke, should meet with considerable success and consistency after intensive practice.

5. Because players learn to trust their pre-alignment they begin to be able to relax during the actual stroke. This takes tension out of their arms and body and they can begin to execute with better speed and a more satisfactory feeling during execution. This may explain the feeling that they feel like they just pivot, bang and the ball goes in.

6. A system that requires a focus on the positioning of the cue may cause the player to be more highly aware of the line of cue. In standard aiming, some players may glance a little at the tip and CB but be mainly focused at the OB and therefore not getting much visual feedback from their cue, which is a straight line guide waiting to be used. Also, this cue position awareness may lead to a more constant positioning of the eyes over the cue. This is quite different to the normal play experience where there is a tendency to ride the ball into the hole. This occurs when players don't trust their alignment and tend to swoop a little to ride the cue ball to the correct point. This method of playing tends to make one have to work physically and mentally during the stroke. When pre-aligned well, the stroke is simply a matter of swinging the cue.

7. Using these systems may represent the most organized approach they have attempted for aiming. Several aspects have been compartmentalized so that each of these aspects can be focused on more clearly and developed individually. This organization may also assist in allowing the player to relax through the early implementation stage and then put their entire focus into the final alignment stage.

8. While sliding or shifting the cue into the final line of the shot, players may be incorporating a method that helps them to sight the required line of aim. This may be due to coming across the line, from left to right or vice versa, such that the sighter gets a feel for how the line of aim is moving relative to the position of the OB.

The only thing I don't agree with regarding these systems is that the systems find the aim line. I think it is the players that align themselves (via slight intuitive adjustments) to the correct aim line when need be. It will take them a little while to develop this ability for a wide range of shots.

from Mike Page (concerning pivot-based systems like CTE):

Various people report immediate improvement upon adopting a fractional ball approach. Others report immediate improvement upon adopting a "pivot" approach. Here's why. There are five independent "things" involved with aiming.

(1) the pocket
(2) the object ball
(3) the cue ball
(4) the stick
(5) the cyclopean eye

All 5 are necessary to get the job done. But the essence of determining the AIM LINE involves just three of these: the cyclopean eye, the cueball, and the object ball. The pocket should be considered BEFORE determining the AIM LINE The stick should be considered AFTER determining the aim line.

Many aiming perception problems involve, imo, either

(1) keeping the POCKET in the process too long
or
(2) entering the STICK into the process too early

Those with problem (1) are helped by fractional ball approaches. Those with problem (2) are helped by pivot-style approaches.

A player MUST consider the pocket before determining the aim line. But once the pocket is considered to determine an object ball contact point or a ghost ball location or (along with the cueball) a fullness of hit, there is no more information needed about the pocket. Many players suffer from being biased by the pocket when they're down on the shot. For those players, focusing on a ball overlap or on a cueball aim point can help a lot.

Here's the other problem. When you are ready to pull the trigger, the STICK LINE and the AIM LINE are one and the same, and they need to be on the CORRECT AIM LINE. But before you are ready to pull the trigger, while you are just starting to get into position, all three are different. Imagine a red laser beam that is fixed on the CORRECT AIM LINE, and a green laser beam that is wherever you are looking, and a blue laser beam that goes through the center of the stick.

The CORRECT way to aim, imo, is first to get the green laser beam on the red one, and THEN to bring the blue one on board. If you don't do that, then you are biased by the stick line coming into view. The "almost right" stick line holds no value, but just like the fun-house almost straight walls and floors, we are drawn to them more than we should be.

So try aiming the shot by getting down into position with the stick off to the side and then with the ball-ball aim in view, bring the stick in from the side. Some people are helped a lot by this. It's a matter of not letting the tail wag the dog. So no, HOW you pivot doesn't matter. There are no magic rotating airpivoting receding hyperspheres. The emperor is naked.

from Mike Page:

If something seems to work or to help some people it IS important to many of us to understand WHY it helps. Part of this--most of us are here for fun when it comes down to it--is intellectual curiosity, but a big part of it is understanding what specific problems are solved by a particular approach to be able to incorporate and communicate those things directly and extend them to new situations.

There are reasons why beginning every shot the same way--looking full on or looking at the half-ball hit for instance--might be useful. The "SEEing it (from manual repetition)" you described above benefits from approaching the same shots the same way every time.

There are other reasons some of these approaches--whether it's one of Hal's methods or S.A.M. or whatever is being discussed here--help people. Get ready, because there's a big secret coming... These approaches cause people to do something they don't usually do. It's such an important thing that we have a name for it. It's called AIM. That's right.

If you look at the QUIET EYE studies, you will find one bit of consistency about the studies of pool, of putting, of basketball free throws, and of other aims involving stationary targets. Consistently a group of experts is compared to a group of wannabes. Consistently the group of experts GAZE at they target on average for a notably longer period of time in the "set" position. I'm talking maybe 2.5 seconds versus 1.5 seconds. It has become increasingly clear that this slightly longer gaze time--locking on your target for enough time-- is crucial for processing the information necessary to aim successfully.

Let's suppose many people suffer from inadequate GAZE time. IF true, then showing them a new method that forces them to lock in on the target (while following whatever the prescription is) will increase their success rate. Like the poop-on-the-swingset, the method might just be a mechanism to bring out the real solution (water/quiet-eye gaze time).

I point out in one of my aiming videos that I think another reason for any success people find with fractional ball aiming techniques is it causes them to sight parallel to the line the stick is moving. Many people don't. Many people sight from above the stick to the object ball contact point. This line is not parallel to the line of the stick or the cueball motion.

Please understand that when someone suggests a method that SEEMS to not have the gaps filled in, that SEEMS to have shots that require two different angles to receive the same aim, that SEEMS to request the exact same aim for two sticks that we know squirt differently, it is like a giant bell going off for many of us.

Then if rather than taking off the system's clothes so that we can examine it honestly, the proponent points out that you really have to learn it in person or that such and such a world-class player uses it, it's like another giant bell going off.

... focusing on center-to-edge or edge-to-wherever gets your site line parallel to your stick. This could be a key for you to unlock the aim you really already have.

Or perhaps focusing on a shot from the edge of the cueball and pivoting toward the center--like being discussed here--locks a person into an eye dominance that is different from what he would have done going straight down into the shot and gives him a perspective that works better for him.

My point is if these sorts of advice help certain people under certain circumstances pocket balls, then that's great. But it is very different from the aiming system "working." These people are actually finding their own aim; they're just approaching their own aim from a different angle.

from JoeW:

I suspect that aiming systems give people a reference point from which to think about the shot. Some players may or may not be aware of the idea that for some shots their subconscious makes adjustments.

On the one side aiming systems provide a zone of comfort for the player because they work in some (many) situations. This in turn leads to confidence when shooting and the player, over time, learns to compensate as needed.

On the other side it can be demonstrated that some aspects of these systems can not work as described. Proponents of the system seem to indicate that these systems take several weeks (?) to learn. However, the concepts are basically straightforward and could be briefly described and learned in a few hours. Weeks of training are required because the systems involve the development of "feel" though the user may not be aware of this aspect and therefore does not have to trust their natural sighting ability which is being developed within the system. For the present they have a system that can be relied upon.

In a sense, a player could be taught any of several systems and they all would work equally well if the player is willing to trust the system.

The conclusion is that one may seek the limits of the aiming system to learn what is useful for some particular shots from a physical basis and this may contribute to the development of a new, more advanced, system.

Why is aiming so difficult for some people?

Aiming is tough because it involves 3D visualization, visual perception, physical and visual alignment, and compensation for CIT (with no sidespin) and/or squirt/swerve/throw with sidespin.

from Patrick Johnson:

Aiming isn't a science, despite what some system [people] think. It involves many kinds of estimation:

- estimating where the OB contact point is by aligning it with the pocket, from a distance and an angle

- estimating how to adjust the OB contact point for throw

- estimating where the CB contact point is by imagining where it is on the "dark side" of the CB (this is part 1 of the subject of aiming systems)

- estimating how to align the CB and OB so the two contact points come together (this is part 2 of the subject of aiming systems)

- estimating how to position your head and eyes so all the above things are visualized correctly (this is part 2A of the subject of aiming systems)

This is only a partial list of the estimations required just for aiming (not stroking), and only for shots without sidespin (don't get me started).

Even with a perfect stroke aiming isn't a simple, mechanically repeatable process.

from Colin Colenso:

I think that the biggest error that most players make when trying to become more accurate players is when they presume that their missed shots are caused by poor Stroke Mechanics, while they overlook the most common and significant cause which is poor Initial Alignment.

By Initial Alignment, I basically mean the positioning of the bridge point.

If you do not get your bridge to a point + or - a millimeter or less from the required line, then you are going to have to play an off center or sweeping stroke to pocket the OB as hoped.

In fact, it is common for players to subconsciously make this stroke adjustment when they feel that the shot is not going on line. This creates tension in their swing...their brain is fighting their heart is one way to describe it. So after they miss, they recall the sense of tension in the stroke, so confusedly start practicing their stroke, blaming their wrist action or some other aspect of stroke mechanics which is usually just a symptom of their poor Initial Alignment.

So to establish some proof for my contention, I set up a test.

A mechanical bridge was wedged into position. A piece of chalk sat under the rail as a firm point to keep the bridge from moving. CB and OB were put into positions that lined up for pocketing to the corner. Once established, I tapped the balls into place marked by a cross on the cloth. Hence I could replace the balls to almost identical positions each shot.

Using the bridge, fixed in place, my stroking did not feel very stable, yet I was able to pocket this shot 20 times in a row with very little variation in the pocketing accuracy. Not a single time did the OB hit the jaw.

Now I could make this shot miss by striking deliberately with english, but the point is, that it's not hard to hit the CB center ball accurately enough to provide satisfactory accuracy for most shots on the table.

The hard part is getting the bridge hand in perfect position for the shot...that is, to align perfectly.

from Patrick Johnson:

You'll always aim by feel; no system will change that. Even with the "systems" that show you exactly where to hit the OB ("ghost ball", "double overlap", "paralleling") you need to "feel" when you're lined up exactly right and "feel" how much adjustment to make for OB throw and CB squirt/swerve.

And most systems don't show you exactly where to hit the OB; they give you an approximate aim point (which you have to line up correctly by feel) and from that you have to adjust to the real aim point by feel. "Approximating" systems include all the systems that are not the well-known "exact" systems I named above.

"Approximating" systems include those taught by Hal Houle, Cue-Tech, RonV, Stan Shuffett, Joe Tucker and others, going by such names as "fractional aiming", "3-angles", "S.A.M.", "center-to-edge", "Pro 1", etc., etc. Some users and teachers of these systems will tell you that they are "exact" systems that need no adjustments, but they're wrong. All of them are approximation systems and all of them require you to adjust your aim by feel. The only one that I'm aware of that actually admits this fact openly is Joe Tucker's system.

Confidence is essential to increasing your "feel" for aiming, with or without an aiming system, and one of the main benefits of using a system is that it can help boost your confidence by narrowing down the range of choices you have to make by feel. Even players who don't think they use any system often use one (or more) unconsciously - for instance, when faced with a tough shot they might get a "second opinion" on their aim by imagining how "ghost ball" or "double overlap" aim would look. Many players use different systems for different kinds of shots - for instance, the "double overlap" system is especially useful for long thin cut shots.

Whether or not you use a system(s) and which one(s) you use are personal choices. Hopefully understanding exactly what aiming systems are and are not before you make those decisions will help you make the right ones for you.

aim compensation when using sidespin

Is there a style of play (e.g., using aim-and-pivot aiming methods) that can compensate for all of the effects of squirt, swerve, and throw when using sidespin?

Background information on important related topics can be found here:

There is no sliver-bullet "style of play" that can magically solve all of the "challenges" associate with compensating one's aim for squirt (CB deflection), swerve, and throw when using sidespin. The BHE and FHE aim-and-pivot methods can be used to adjust for squirt (and in some cases the combination of squirt, swerve and/or throw, using an "effective pivot length" for each shot), but swerve and throw vary too much with shot speed, shot distance, cue elevation, type and amount of english, amount of forward roll, ball and cloth conditions, etc. The best you can do is be knowledgeable of all of the effects (e.g., see "Squirt - Part VIII: squerve effects" - BD, March, 2008 summarizing squirt and swerve effects, and "Throw - Part XI: everything you ever wanted to know about throw" - BD, June, 2007 summarizing throw effects) and/or have solid intuition based on many years of successful practice and play. There is no magical "style of play" that can solve all of the world's problems ... playing pool at a high level is simply not easy.

and here are some other more-detailed videos on the topic:

The BHE method can be used to adjust for both squirt and swerve if you adjust your bridge length based on the distance and speed of the shot. Basically, at slower speeds and greater distances between the CB and the OB, a longer bridge length is required because the "effective squirt" (or squerve) is reduced due to swerve. This will only work with a near level cue, because with an elevated cue, swerve becomes a larger factor and can make "effective squirt" negative. Also, with a follow shot, swerve happens sooner than with a draw shot (of the same cue elevation), giving less effective squirt (squerve), so again a longer pivot length would be necessary. Colin Colenso has come up with some experiments and formulas to help methodically determine the required effective pivot length (i.e., required bridge length) for any shot (see below).

An alternative to using BHE with a variable bridge length is to use a fixed bridge length and appropriate combinations of BHE and FHE as described briefly on the BHE/FHE resource page and in detail on Disc I of How to Aim Pool Shots (HAPS).

What squirt (cue ball deflection), swerve, and throw effects do I need to be aware of?

A complete summary of all squirt (cue ball deflection), swerve, and throw effects and rules of thumb can be found below in the numbered list beneath the videos and illustrations.

As background, here are some pertinent video demonstrations from the Video Encyclopedia of Pool Shots (VEPS):

The following diagram from Jeremiah Gage (courtesy of BullseyeBilliards) nicely illustrates the numerous interactions that occur in the execution of a shot, especially when english (sidespin) is used.

The numbered list below is a quick summary of important squirt (cue ball deflection), swerve, and throw effects, along with links to supporting resources. Let's start with a short glossary of definitions and an illustration of some of the terminology used in the effects list. More definitions can be found in the online glossary, and additional info and examples can be found in the linked resources.

 BHE: back-hand english CB: cue ball CIT: cut-induced throw FHE: front-hand english gearing OE: the amount of outside english that results in no throw IE: inside english OB: object ball OE: outside english SIT: spin-induced throw squerve: combination of squirt and swerve

Squirt (cue ball deflection), Swerve, and Throw Effects:
(everything you ever wanted to know about squirt, swerve, and throw)

1. Squirt increases with the amount of sidespin.
2. Squirt does not depend on shot speed (see squirt speed effects for more info).
3. Squirt increases with the amount of shaft endmass (e.g., a low-squirt cue has less endmass and results in less squirt).
4. Squirt is slightly less with a heavier CB (see CB weight effects).
5. Squerve (net effect of squirt and swerve = net CB deflection) can be zero with certain speeds and cue elevations for a given shot distance, amount of sidespin, and cue.
6. Squerve is less for follow vs. draw shots (see squirt tip-contact-height effects).
7. Squirt or squerve can be canceled using back-hand english (BHE) and/or front-hand english (FHE) aim-and-pivot methods.
8. Swerve increases with cue elevation and the amount of sidespin.
9. Swerve occurs with practically all sidespin shots because the cue must be elevated to clear the rails.
10. Swerve is delayed with faster shot speed.
11. Swerve occurs only while the CB is sliding; once rolling begins, the CB heads in a straight line.
12. Swerve occurs earlier with sticky cloth and later on slick cloth.
13. Swerve occurs earlier with a follow shot than with a draw shot (see "Squirt - Part VIII: squerve effects" - BD, March, 2008).
14. Swerve angle is larger with a draw shot than with a follow shot (see "Squirt - Part VIII: squerve effects" - BD, March, 2008).
15. Swerve angle can be predicted and visualized using the Coriolis masse-shot aiming method.
16. For small cut angle shots (i.e., fuller hits), the amount of CIT does not vary with shot speed, but increases with cut angle (see NV B.86 and "Throw - Part II: results" - BD, September, 2006).
17. For larger cut angle shots (i.e., thinner hits), the amount of CIT is significantly larger for slower speed shots as compared to faster speed shots (see "Throw - Part II: results" - BD, September, 2006, and Ball Motion Properties in Stun and Follow Shots).
18. The amount of CIT decreases some with larger cut angles, but not by much (especially for slower speed shots) (see "Throw - Part II: results" - BD, September, 2006).
19. Maximum CIT occurs at close to a half-ball hit (30-degree cut angle) (see "Throw - Part II: results" - BD, September, 2006).
20. In general, throw is larger at slower speeds, and for stun shots.
21. Maximum throw, under typical conditions, is about 1 inch per foot of CB travel, which is about 5 degrees.
22. Both follow and draw reduce throw, and they do so by the same amount (see "Throw - Part III: follow and draw effects" - BD, October, 2006).
23. The largest discrepancy between throw values for stun and follow/draw shots occurs close to a half-ball hit (30-degree cut angle) (see "Throw - Part III: follow and draw effects" - BD, October, 2006).
24. The difference between the throw of stun and follow/draw shots is not as great at larger cut angles (see "Throw - Part III: follow and draw effects" - BD, October, 2006).
25. More sidespin gives you more SIT only up to a point. Additional sidespin beyond that point actually reduces the amount of SIT (i.e., more sidespin doesn't always give you more throw) (see "Throw - Part V: SIT speed effects" - BD, December, 2006).
26. SIT is largest for a slow stun shot with about 50% of maximum sidespin (see see NV B.86 and "Throw - Part V: SIT speed effects" - BD, December, 2006).
27. The amount of throw can increase significantly as a small amount of sidespin is added, especially for a stun shot (see "Throw - Part IV: spin-induced throw" - BD, November, 2006).
28. SIT is independent of speed (i.e., the throw is the same at all speeds) for small amounts of sidespin (see "Throw - Part V: SIT speed effects" - BD, December, 2006).
29. "Gearing" OE results in absolutely no throw. The amount of sidespin required for "gearing" increases with cut angle. At a half-ball hit, the amount of sidespin required is about 50% (see gearing outside english).
30. At very small cut angles, IE and OE create similar amounts of throw (although, in opposite directions) (see "Throw - Part VII: CIT/SIT combo" - BD, February, 2007).
31. For large cut angles, a small amount of OE can result in more throw than shots with no sidespin (see see "Throw - Part VII: CIT/SIT combo" - BD, February, 2007).
32. For large cut angles, IE results in less throw than shots with no sidespin (see see "Throw - Part VII: CIT/SIT combo" - BD, February, 2007).
33. IE increases throw at small cut angles, but actually reduces the amount of throw at larger cut angles (see see "Throw - Part VII: CIT/SIT combo" - BD, February, 2007).
34. OE can cause throw in either direction depending on the amount of sidespin and the cut angle (see "Throw - Part VI: inside/outside english" - BD, January, 2007).
35. Even for large cut angle shots (thin hits), excess OE (more than the "gearing" amount) can be applied to throw the OB in the SIT direction (see gearing outside english).
36. The amount of throw with IE can be much more consistent than with OE if the amount of sidespin varies a little. In other words, the amount of throw varies more with tip placement for OE vs. IE. This might explain why some people prefer using IE on cut shots ... because they can better anticipate and adjust for the amount of throw.
37. The least amount of throw, and the most throw consistency, occurs with fast IE shots.

In support of the last two inside english items above, see the 2nd plot on page 3 of TP A.28, which corresponds to 30-degree cut-angle stun shots at different speeds and varying amount of both outside english (positive in the plots) and inside english (negative in the plots). In the plot, notice how consistent and small the amount of throw is for fast-speed inside-english shots over a wide range of sidespin amounts (see the left side of the green curve, which is very low and level).

A good analysis and presentation of squirt effects can be found in Ron Shepard's "Everything you Always Wanted to Know About Cue Ball Squirt, but Were Afraid to Ask." Here's a good summary of squirt effects from that document.

from Colin Colenso:

It's little wonder that pros are adept at, and usually rely almost solely upon simply estimating how to align to any shot they want to make using english.

There really has been no other way to learn how to execute english for a wide range of shots. So they learn a huge range of shots by repetition and this gives them the intuitive feel to make, or get close to almost any shot they attempt with varying degrees of cut angle, speed and tip offset.

When I first learned about BHE a few years ago I thought it was some instant quick fix. But I soon learned that there were variables that affected the success on many shots quite significantly. These are:

1. The effective pivot point changes according to speed and distance traveled. (Swerve is the culprit).

2. The actual contact point required to make shots varies considerably with CB speed, cut angle and type and rate of spin on the CB.

So without knowing how much to adjust for all of these variables, BHE is only useful for a limited range of shots.

[Here is a method, with formulas, that can be used to select a bridge length to compensate for both squirt and swerve, assuming you have already adjusted your aim for any throw effects.]

PPe = PPi + DVK

PPe = required effective pivot point for any shot based on distance and shot speed.
D = Distance from CB to OB (or target) in feet.
V = Velocity Factor where 0 is maximum speed and 4 is slow, or one table length roll including bouncing off one rail (see below).
K = correction factor to account for cloth slickness given by:

K = (PPe* - PPi) / 15

PPi = The Intrinsic Pivot Point. Estimated by finding the effective pivot point for a shot over 5 feet hitting at maximum velocity, such that swerve has insignificant influence on the shot. My cue's PPi is 9.5 inches. Low squirt cues are 12 to 14 inches.

PPe* = the pivot point required for a 5 foot shot at speed factor 3, which is medium slow, enough to bounce 2 rails back to the original position. This figure will be different for each cue on each table. It brings the slickness variable into the formula.

My preferred cue on my table has PPe* = 13.7 inches. (This could change with humidity changes). It's PPi is 9.5 inches, so my K value for my cue on my table at the moment is (13.7 - 9.5)/15 = approx 0.28. 0.28 is the adjustment needed at distance 1 foot and speed factor 1. The number 15 is derived from the PPe* being at 5 foot at speed factor 3. 5x3 = 15. PPe* could use any shot as a basis with a different numerator, but 5 foot is a good number because it is about the length of the cue, it can be played with little elevation and it is long and slow enough to provide a decent difference with PPi, hence giving it a reasonable margin of error. PPe* can vary by around 2 inches depending on cloth slickness. It is a number that can be derived pretty accurately within half a dozen hits on a new table.

So for any shot my PPe = 9.5 + D x V x 0.28

So if I have a shot at speed factor 2 over 4 feet my PPe = 9.5 + 2.24 = approx 11.7 inches.

Below is a chart with PPe's for the full range of speeds and distances for my cue. You should be able to plug data into this formula and get PPe's that correspond to those in the chart. Note: The key to making this formula simple was creating the methodology of the speed factor. In the chart below, the speeds are divided into 6 markings, rather than the 5 for speed factors 0-4.

General Speed Factor (V) Rules are:

0 = Max speed, would bounce about 5 rails.
1 = Firm speed, would bounce 4 rails and back to starting position.
2 = Medium speed, would bounce 3 rails and back to starting position.
3 = Slow-Medium speed, would bounce 2 rails and back to starting position.
4 = Slow speed, would bounce 1 rail and back to starting position at center table.

[To compensate for how squerve changes for draw vs. follow shots (for more info, see "Squirt - Part VIII: squerve effects" - BD, March, 2008), we can also make an adjustment to the pivot point based on the height of the cue:]

Based on the above observation I was able, via some testing to establish a pivot point adjustment key depending on the height the cue ball is struck with english.

Strangely enough it seems to work pretty well independent of distance, speed or cue offset. Though this hasn't been tested comprehensively.

So the total PPe Effective Pivot Point formula, as it has been refined is:

PPe = PPi + DVK + H

H = Height of hit on CB using the numbers given below in the diagram.
(Note: In most practical cases we don't need to hit higher than the 1 range. Most draw shots fit into the -1 range.

For a low squirt cue, such as a Predator Z, I would increase the numbers in the below chart by about 33%. So they might range from 4 to -1.3. Current information suggests the Predator Z has a natural or intrinsic pivot point of between 12 and 13 inches, compared to a normal shaft which is in the 9 to 9.5 inch range.

bank and kick shot aiming systems

How do you use diamond systems to aim kick and bank shots in pool?

bisect-pivot-and-shift aiming system

How does the "bisect-pivot-and-shift" aiming system work?

It is described an demonstrated in detail, along with other common aiming systems, in How to Aim Pool Shots (HAPS). A brief summary is below, along with an illustration showing how the contact points, bisect midpoint, and cue pivot angle are related.

from bluepepper:

1. Sighting for a straight in shot from behind the cueball, place tip of cue on table midway between cue ball and object ball.
2. Then locate contact point on object ball.
3. Keeping tip in same spot on table move to the right or left until the cue is pointing directly at the contact point.
4. From there, roll the cue, staying parallel to that line, until the center of the cue is hovering directly above the center of the cueball. That's your aim line. Pick a spot along this line to aim at in order to pocket the shot.

from Patrick Johnson:

bottom-of-the-ball aiming

How does the "bottom-of-the-ball aiming" aiming system work?

"Bottom-of-the-ball" aiming is a way to visualize the required contact point on the object ball (assuming no throw). First visualize the required cut angle for the shot as shown in "a" in the diagram below. Then visualize this same angle on the face of the object ball, as shown in "b" below. If the vertex of the angle is on the edge of the ball, and one leg of the angle goes through the center of the ball with the other leg vertical, the necessary contact point (CP) is where the vertical leg crosses the ball's equator.

Below is an example for a 1/2-ball hit, 30-degree cut shot.

from Patrick Johnson:

combination shot aiming

How do you aim combination shots?

contact-point-to-contact-point and parallel-lines systems

How does the "contact-point-to-contact-point" or "parallel-lines" aiming system work?

It is described an demonstrated in detail, along with other common aiming systems, in How to Aim Pool Shots (HAPS). Also see: "Aim, Align, Sight - Part I: Introduction and Ghost Ball Systems" (BD, June, 2011). Here's a useful illustration from the article:

and here's how it works:

1. Visualize a line through the center of the OB in the target direction. This locates the CP (red dot) on the OB.
2. Shift this line to the CB, keeping it parallel to the line in step one (see the blue lines). This defines the CP on the CB.
3. Visualize a line through the CB CP and the OB CP (see the red line).
4. Parallel shift this line to the center of the CB. The result is the required aiming direction (neglecting CIT, of course).

Other parallel lines relative to edges of the ghost ball (GB) can also be useful in visualizing proper aiming, per the diagram below. The inner and/or outer GB-OB edge lines (orange) parallel to the desired OB target direction can be visualized to help clearly see where the OB needs to head, and the inner and/or outer CB-GB edge lines (yellow) parallel to the necessary CB aiming-line direction can be visualized to help with final aiming.

One way to help visualize the outer GB-OB edge line is to imagine that the OB is frozen to an imaginary rail leading to the pocket. This can help some people visualize the angle of the shot and be more effective.

from Patrick Johnson:

CTE aiming system

How does the Center-to-Edge (CTE) aiming system work?

CTE (Center-To-Edge) is an "align-and-pivot" pre-shot routine and "aiming system" that uses a line through the center of the CB and outside edge of the OB as a reference. There are several different versions and interpretations of CTE, but they are all based on establishing an initial "alignment" and then "pivoting" to the final aiming-line direction.

CTE Version 1 (an early and simplified "version" of CTE) - 3 pre-pivot alignments:

Here is a description of a version of the CTE, based on a video demonstration posted (and later removed) by eezbank, that he claimed was the version of CTE originally taught to him by Hal Houle:

For a "thick hit" (a small cut angle, less than about 15 degrees) to the left:

1. Align the cue 1 tip to the right of the CB center through the right edge of the OB.
2. Place the bridge hand down with the cue along this line.
3. Pivot the cue until the cue is pointed directly through the center of the CB.
4. Stroke perfectly straight along this line.

For a "half-ball hit" (close to 30 degrees) to the left:

1. Align the cue through the center of the CB and through the right edge of the OB.
2. Place the bridge hand down with the cue along this line.
3. Stroke perfectly straight along this center-to-edge (CTE) line.

For a "thin hit " (a large cut angle, more than about 45 degrees) to the left:

1. Align the cue 1 tip to the left of the CB center through the right edge of the OB.
2. Place the bridge hand down with the cue along this line.
3. Pivot the cue until the cue is pointed directly through the center of the CB.
4. Stroke perfectly straight along this line.

Here's a more-recent clarification from eezbank:

The way Hal teaches the system you pivot on every shot. So, the halfball info is wrong. Also, where I use the one tip reference Hal says it doesn't matter how many tips you use. You can start all the way to one side of the CB if that's what works with your pivot length.

CTE Version 2 (posted by Shawn Armstrong, as taught to him my Hal Houle) - 4 pre-pivot alignments:

The direction of the pivot, and the starting point, are determined by the angle of the cut. This is why you need to know the half ball hit angle. The alignment point on the object ball is always the outer edge. The starting point on the cueball is always the edge. However, it can be the inside or outside edge. That is determined by the cut angle.

For shots less than 30 degrees, line up the center of the cueball with the edge of the object ball. Start with the outside edge of your cue tip lined up with the outside edge of the cueball. Pivot towards center. Your pivot should be leading you towards the center of the object ball.

For cuts greater than 30 degrees, but less than 65, the pivot comes from the inside edge of the cueball. When you pivot to center, you should be going towards the outside edge of the object ball, away from the center.

For thin cuts, the pivots are edge to edge. For cuts between 65-80 degrees (thicker than 80), the pivot is towards center from the outside edge of the cueball. For cuts thinner than 80, the pivot is from the inside edge of the cueball.

Thinner than 80, pivot from outside edge to center on the cueball, with the starting alignment being cutting edge of cueball to the cutting edge of the object ball. For razor cuts, line up outside edge to outside edge, and pivot away from the edge.

CTE Version 3 (posted by Dave Segal on Spidey's blog) - 2 pre-pivot alignments:

An excellent explanation and illustration of this approach, from mohrt, can be found here.

Note: CTEL = Center-to-Edge Line = line through CB center and perceived OB outer edge.

BASIC CTE PIVOTS (as taught by Hal Houle):

For thick cuts: Your cue is parallel to the CTEL with your tip pointing at the outside edge of the CB (the edge of the CB that’s farthest from the pocket). You then pivot your tip towards the pocket until it reaches CB center.

For thin cuts: Your cue is parallel to the CTEL with your tip pointing at the inside edge of the CB (the side of the CB that’s closest to the pocket). You then pivot your tip away from the pocket until it reaches CB center.

If you’re not sure which side to pivot from, only one will work. One will look right – the other will not.

For straight-ins: It doesn’t matter which side of the CB you address, just make sure you perform a thick-cut pivot.

Here's a more recent clarification from Spidey (based on a phone conversation):

What qualifies as a "thick cut" or "thin cut" isn't strictly based on the cut angle needed for a shot. It also depends on the distance between the CB and OB. You develop a sense for this as you work with the system.

CTE Version 4 (as interpreted by dr_dave from the description and examples on Stan Shuffett's Pro One DVD) - 6 pre-pivot alignments:

While standing, sight through the center of the CB and the outside edge of the OB (i.e., sight along the CTE line). Then, based on the type of cut (see the table below), shift your sighting to visualize a line through the inside edge of the CB to a given alignment point on the OB (see the table and figure below), while also maintaining the CTE visual. Then drop and slide into your stance straight toward the CB, placing your bridge to align the cue 1/2 tip off the CB's center (per the table and figure below). Now pivot the cue to the center of the CB with a fixed-bridge pivot. Here is a summary of the OB alignment points and pre-pivot tip positions for each type of cut:

cut type
OB alignment
cue tip alignment
straight-in
inside 1/4*
outside
very thick cut
inside 1/4*
inside
medium thick
center
outside
medium
center
inside
medium thin**
outside 1/8
outside
very thin**
outside 1/8
inside

inside: on the side of the ball toward the cut (i.e., the left side for a cut to the left, the right side for a cut to the right)
outside: on the side of the ball away from the cut (i.e., the right side for a cut to the left, the left side for a cut to the right)
*: If the CB-OB distance is less than about 1', sight to "inside 1/8" instead of "inside 1/4."
**: For thin cuts, you ignore the CTE visual and just sight for the 1/8-ball overlap.

You also need to adjust your bridge length for different CB-OB distances, based on the following table:

 CB-OB distance bridge length > 2' about 2' about 1' < 1' very close 8-9" 7-8" 6-7" 5-6" very short

Note - Stan uses the "A," "B," and "C" notation (see the illustration above) to refer to the inside, center, or outside of the OB. With a cut to the left, the inside is "A" and the outside is "C." With a cut to the right, the inside is "C" and the outside is "A." "B" is always the center. For example, with a "very thick" cut to the right, you align the right (inside) edge of the CB with point "C" (inside 1/4). With a "very thick" cut to the left, you align the left (inside) edge of the CB with point "A" (inside 1/4). Also, Stan indicates the pre-pivot cue alignment based on whether the cue tip is "left" or "right" of center. For example, with a cut to the left, if the pre-pivot cue tip alignment is to the right (outside) of the CB center, Stan calls this a "right pivot." If the pre-pivot tip alignment is instead to the left of center ("inside" for a cut to the left, or "outside" for a cut to the right), Stan calls this a "left pivot."

You develop a feel for the alignments and pivots required for different shots based on practice and experience (i.e., there is no direct guidance on how to judge and choose the proper cut category for a given shot). You can also vary the cut angle created with a given CB-OB distance and a given alignment choice by varying your eye position some, also based on practice and experience.

Here are some example shot layouts and alignments (from Stan's first CTE/Pro-One DVD), originally posted by mohrt on AZB.

Here's a demonstration of how the pivots work.

from Stan Shuffett (from AZB post):

Previously, I added A and C as thin cut OB aimpoints. That was my first adjustment in 2 years to CTE PRO ONE.

After much study and consideration a FINAL adjustment in my CTE PRO ONE system is being implemented.

For shots at or near a zero angle and with CB and OB further apart than 1 diamond's distance, please note this change to your visuals.

Instead of using OBA or OBC as an aimpoint for the near zero angle shots, use CBE to OBE with a center to edge perception. All pivot information remains the same. Near zero angle shots can have slight left or right cuts.

This is my FINAL adjustment for any major system aspect of CTE PRO ONE.

from AtLarge (from AZB post):

After DVD1, Stan adjusted the visuals to include C (without a coupled CTE visual) for left cuts and A for right cuts, both with left or right pivots. So it would now be 8 instead of 6 in each direction.

[Although, ] A-left and B-right are now considered to produce the same result for left cuts.

CTE Evaluation and Analysis:

If you are good at judging the type of cut, version 4 above will generally work better than the others (without conscious or subconscious "adjustment") because it involves a larger number of pre-pivot alignments, which will offer better coverage over a wide range of cut angles (with a consistent pivot). Also, because there is less pivot than with the other versions, there will be less variation in results with different bridge lengths and CB-OB distances (see more info below).

If you follow any of the procedures above literally and exactly (without conscious or subconscious "adjustment" and with a consistent and non-variable pivot), you will make shots within certain limited ranges of cut angles and CB-OB distances for each resulting line of aim (see limited lines or alignments of aim).  However, if you don't vary the alignment or pivot (see more below), you will miss shots outside of and between these ranges, unless the OB is close to the pocket or the pockets are large (providing a large margin for error).  However, even if a person is not good at judging or "adjusting" between the alignments or by using a variable pivot, CTE still might be beneficial for any of the many possible reasons summarized here.

Many "challenges" relating to "aiming systems" are described and illustrated in "Fundamentals - Part III: DAM aiming system" (BD, November, 2008) and "Fundamentals - Part IV: bridge length" (BD, December, 2008). These difficulties certainly apply to CTE. Here's a good experiment you can use to test whether or not you understand how to apply CTE (or any pivot-based aiming method) effectively:

Shot "A" is about a 10-degree cut, shot "B" is about a 15-degree cut, and shot "C" is about a 20-degree cut. All three shots fit into the "thick cut" category of some versions of CTE. Also, the CB-to-OB distance is the same for all three shots. If the bridge length and pivot amount is the same for all three shots, a pertinent question is: What do you do differently with the alignment and/or pivot steps of CTE to pocket each of the three shots? There are several possible answers. You can:

1.) Change the initial alignment slightly (e.g., by shifting your eye alignment so the perceived cue alignment and/or parallel shift is different)
or
2.) Change the amount of the parallel shift (before the pivot) so you don't quite go all of the way to the perceived CB edge (e.g., shift a given number of "tips" instead)
or
3.) Pivot a slightly different amount (e.g., not quite to center, or just past center).
or
4.) Change the "effective pivot length" slightly (e.g., by adjusting your bridge length or by shifting/tilting your bridge during the pivot).

Options 1 and 4 are probably the most common approaches. The diagram below (from "Fundamentals - Part IV: bridge length" - BD, December, 2008) shows how a change in "effective pivot length" changes the amount of cut. The diagram shows two different bridge positions, but it could also represent two different "effective cue-pivot-points" created by a non-rigid-bridge pivot method (see more below).

If using a "mechanical pivot" (i.e., pivoting after placing the bridge hand down), one way to vary the "effective pivot length" is to vary the bridge length (as implied by the diagram). Another is to shift, rotate, tilt, or deform your bridge hand during the pivot as you shift your body (AKA "hip pivot"). Here are examples of this, posted by Colin Colenso, where the "effective pivot length" is changed with a bridge shift:

Another way is to use an "air pivot," where you pivot the cue and/or entire body before placing the bridge hand down. In this case, you can easily create any "effective pivot length" over an extremely wide range. Sometimes, the "effective pivot length" is referred to as the "shot arc." Here is a demonstration of how some forms of pivoting are used in conjunction with CTE and other pivot-based aiming methods: CTE pivot demonstration. For more info concerning pivoting, "air pivot," and "shot arc," see Spidey's blog.

The difficulty is in judging how much to change the initial alignment or "effective pivot length" to pocket balls requiring similar, but slightly different, amounts of cut. Many of the CTE proponents will say you don't need to know where the pocket is, or take into consideration the necessary amount of cut (other than to judge a "thin hit" vs. a "thick hit"), but this obviously cannot be the case. Maybe people who seem to use CTE effectively must at least sense where the pocket is (even if they don't look at it), or maybe they just have a feel for how much cut they need to pocket the ball. This sense or feel could influence their alignment or "pivot" in intangible ways that are difficult to describe or illustrate.

With all pivot-based aiming methods, the choice for "effective pivot length" must vary with the distance between the CB and OB, as illustrated by the following diagram from "Fundamentals - Part III: DAM aiming system" (BD, November, 2008). Note - the purpose for this diagram is simply to illustrate a general principle pertinent to all align-and-pivot systems like CTE and 90/90. The diagram is not meant to show a specific aiming example for any particular system or shot. The pre-pivot alignment shown is actually a 90/90 edge-to-edge (ETE) alignment, but again, this choice is not important for the point being made. With a fixed alignment (whatever alignment that might be) and a fixed "effective pivot length," the distance between the CB and OB has a huge effect on the resulting cut angle of the shot:

Interestingly, with the exact same initial alignment and pivot, two of the three balls can be potted if the pocket happens to be at points "a," "b," or "c." This would actually be a good proposition shot. Approach somebody who doubts pivot-based aiming systems and bet him or her you can make two radically different shots (e.g., shots "A" and "B" in the diagram) with the exact same initial alignment and the exact same pivot. You can even have the doubter shoot the shots for you, as long as his alignment and stroke skills are reasonably good. If the balls are lined up to take advantage of the effect shown in the diagram (i.e., if the balls are lined up so the corner pocket is at point "a" relative to the balls), both shots will go and you will win the bet.

The diagram above begs the following question: Is there a pivot length that would allow all three balls to be sent to the same position (e.g., where a pocket is located)? Unfortunately, this is not possible in this case. With a shorter pivot, the ball-hit fraction on shot "C" reaches 0 before all of the lines can meet:

and with a longer pivot, the CB aiming line will be closer to parallel to the the original alignment line, creating smaller cut angles, but the lines still can't all meet at one point:

and with a true parallel shift (infinite pivot length), all of the cut angles would be identical and the OB lines would be exactly parallel (i.e., they wouldn't intersect at all).

Here's another way to explain the impact of the limited lines of aim created by a limited number of initial alignments and pivot directions, applied again to the following three shots:

Instead of just the three shots (A, B, and C), consider 15 shots equally spaced between shots A and C. Let's use Stan's version of CTE for this example. According to the system procedure, alignment and pivot choices change with shot cut angle. As the cut angle changes in small increments between shots A and C, the choices for alignment and pivot change at certain points in the range. For example, on Stan's DVD, he suggests an inside 1/8 OB alignment with with an inside cue tip position (for a left-to-right pivot) for shot "A," an inside 1/4 OB alignment (point A) with an inside cue tip position (for a 1/2-tip left-to-right pivot) for Shot "B," and a center OB alignment (point B) with an inside cue tip position (for a 1/2-tip left-to-right pivot) for Shot "C." At each point in the range of 15 shots where the alignment and/or pivots change, because neighboring shots of the group of 15 are so close together, different alignments and pivots would need to produce the same cut angle (e.g., to pocket the ball with an angle in between both choices). Also, the alignment and pivot will not change for certain ranges of shots within the 15. Therefore, a single alignment and pivot would need to create a range of cut angles. However, if you follow the procedure accurately and consistently for a selected alignment and pivot, with a given CB-OB distance and bridge length, assuming a rigid and fixed bridge, the procedure would result in the exact same cut angle every time (without conscious or subconscious "adjustments"). Obviously, this particular cut angle will work for some of the shots in the indicated range, and it won't work for others (depending on the distance to and size of the pocket), because every shot in the indicated range requires a different cut angle (assuming center-pocket aiming).

Now, does that mean you can't make CTE work for all shots at a table? Absolutely not. Four ways to make it work are summarized above. This is where "visual intelligence," "adjustment," "experience-based intuition," and "feel" come into play. And with enough practice, a person might be able to learn to apply one or more of the four techniques suggested, and do so naturally and even subconsciously ... to where they might not even know they are doing them.

Here's another useful experiment and drill related to Version 4 of CTE above:

1.) Place the CB on the head spot, and place the OB 2 feet in front of the CB on the table centerline.

2.) Ignoring the rails and pockets for now, cut the OB to the left using each of the alignments and pivots suggested by Stan's manual-pivot version of CTE, placing the CB and OB is the same positions for every shot. The six possible align/pivot choices for a cut to the left are:

i.) A-right
ii.) A-left
iii.) B-right
iv.) B-left
v.) 1/8-right
vi.) 1/8-left

from AtLarge (in AZB post): After DVD1, Stan adjusted the visuals to include C (without a coupled CTE visual) for left cuts and A for right cuts, both with left or right pivots. So it would now be 8 instead of 6 in each direction. But A-left and B-right are now considered to produce the same result for left cuts.

After each alignment and pivot, shoot the CB into the OB and note or mark the direction the OB heads on the table (maybe by marking where the OB hits the nearest cushion). Even though different people might see and execute the visuals, alignments, and pivots differently, a single person (if careful and consistent) should send the OB in a repeatable direction for each of the 6 choices (with a different angle resulting from each of the 6 shots). One can try these 6 shots multiple times to test and verify their consistency. This actually might be a good drill for dedicated CTE users out there.

3.) Now shoot the same shot again multiple times, this time sending the OB in a wide range of directions at and in between each of the 6 directions from step 2. If you desire, place a spare ball on the target cushion, and move it from one shot to the next, to simulate different pocket positions.

Alternatively, move the CB and OB together into different positions with the OB along an arc a fixed-distance from the corner pocket, always placing the CB 2 feet above the OB with the line through the ball centers parallel to the table centerline (and side rails). At each position, attempt to pot the OB in the corner pocket. Each of these shots will have the exact same CB-OB relationship and the exact same distance to the pocket. The only thing different will be the cut angle required to pocket the ball in the corner. Vary this angle, moving along the arc in both directions to cover the widest possible range of cut angles (from close to straight-in along the side rail adjacent to the corner, to the thinnest cut you can get with the balls close to the side rail across from the corner).

4.) For each angle or range of angles in step 3 (using either approach), explain the method used to decide which of the 6 align/pivot choices is used in each case. Also, for the directions that are between the 6 angles determined in step 2, clearly explain what is done differently during your pre-shot routine to create angles different from the original 6 directions.

This experiment is the easiest way to fully understand how CTE can actually work for the people who use it effectively over a wide range of shots.

BOTTOM LINE OF THE ANALYSIS : Any align-and-pivot system like CTE requires changes in alignment and/or effective pivot length as the cut angle and shot distance change.

DAM is still a much simpler approach to basic center-ball aiming than any pivot-based system; although, like anything, it does requires practice. Regardless of which "aiming system" you use (even if you just "see the angle"), you still need to practice to develop and improve your "visual intelligence" and consistency, and you need to actually focus on aiming the shot. It also helps to have an effective and consistent pre-shot routine. Many aiming systems can help some people do this (for more info, see benefits of "aiming systems"). Also, when you use sidespin, you need to compensate your aim to account for squirt, swerve, and throw.

insightful CTE-related quotes from others:

from mohrt (in AZB post), concerning step 4 of the final experiment suggested above:

mohrt: What you are doing "different" for every single shot is acquiring a unique visual for the given shot (which means a unique physical eye position for the given perception.) Many shots share the same alignment and pivot. But the perception is always unique. This is what leads to a unique connection for each and every shot line. As for determining when an alignment changes from one to the next, that comes from experience.

dr_dave: Based on your explanation, I would describe how CTE/Pro-One "actually works" like this: The pre-shot routine fostered by CTE/Pro-One creates a methodical framework that allows one to visualize and aim each shot more consistently and effectively. The alignments and pivots don't do the aiming for you. You still need to "acquire a unique visual" for a given shot and "perceive" the necessary line of aim on which you must place the fulcrum of your bridge (so the pivot brings you to the necessary line of aim for the shot).

from AtLarge (concerning Version 4 above):

If performed robotically, Stan's CTE is a discrete aiming method ("x-angle system" in pj's terms) rather than a continuous aiming method. That means, on paper, that it offers only a limited number of cut angles for any given distance between the CB and OB. If the CB-OB distance changes, you get another set of cut angles.

In use, however, I believe many players actually convert it into something more flexible (more cut angles) by slightly modifying something either before or after the pivot, based upon their knowledge of where the pocket is. I think those "feel" adjustments can become so routine and ingrained that the method starts to seem like a continuous method (unlimited cut angles at any CB-OB distance).

I'll say again what has been said many times about why it is an "x-angle" system. Let's say we're talking about cuts to the left. Stan's method calls for sighting the CB center to the OB right edge. That's the CTEL. Now, we have a secondary alignment line and a pivot direction to choose. But the menu offers only 6 choices for these: A with right pivot, A with left pivot, B with right pivot, B with left pivot, 1/8 to 1/8 with right pivot, and 1/8 to 1/8 with left pivot.

Assume the CB and OB are 3 feet apart. Place them anywhere on a flat surface. Forget about any pocket for now. Stan's method, if performed robotically for the two balls 3 feet apart, offers just 6 ways to align yourself, i.e., 6 ways to determine the final direction of aim of the cue stick. You could run through the entire menu of 6 ways to cut the OB to the left, replacing the two balls identically each time. You'll get 6 different lines of travel for the OB, i.e., 6 actual cut angles. Repeat the drill as many times as you want to with a 3-foot separation between the balls. You have only 6 menu items or 6 sets of instructions. If you do each of them the same way each time, you'll get the same cut angle each time for each of the 6 alignment-menu selections.

Now transfer the two balls to a pool table, but keep them 3 feet apart. You have the same 6 menu items or sets of instructions. If you perform them the same way, you should get the same 6 cut angles. But now, you have an intended pocket for the OB. This, at last, means you must choose just one of the 6 menu items for alignment. If you choose the best of the 6, and perform your alignment exactly as you did on the flat surface with no pockets, you should get the same cut angle that you did on the flat surface with no pockets. That actual cut angle may or may not be the cut angle necessary to pocket the shot. What increases the likelihood that the shot will be pocketed is that the player now knows precisely where the pocket is. His "visual intelligence," as some have called it, allows him to slightly modify something in his visuals, or in his stance, or in his approach to the table, or in his offset, or in his pivot, or ... in something. And that adjustment, be it conscious or subconscious, converts the 6-angle system into a more continuous system (far more cut angles for that 3-foot CB-OB distance).

from AtLarge (concerning Version 4 above):

dr_dave: For a given CB-OB relationship and cut direction, there is only one vertical plane or line through both the center of the CB and the outer edge of the OB (i.e., the CTEL), in 2D or 3D. If you are able to visualize more than one, that might explain how you are able to create a wide range of cut angles for a given CB-OB relationship (i.e., with the CB and OB a fixed distance apart).

AtLarge: Exactly, Dave. When users talk about the outermost edge or rotating edges, they must just be referring to viewing that plane, or a line in that plane, from a slightly different angle (i.e., the "vision center" isn't in that plane).

stan shuffett: If a player's eyes were positioned exactly the same for each shot, A and B, the results would be identical. ...[but]...The eyes are in different positions for each shot. ...Just because a CB and an OB share a common distance and the same visuals does not mean the eyes will be positioned the same way for each shot. Perception is altered with varied eye positions. ...

AtLarge: What is it, then, that guides the positioning of the eyes other than the CTEL and the secondary alignment line. I was under the impression that those two lines force an eye placement that "locks in" the two relevant edges of the CB and, therefore, control the pre-pivot cue alignment. The answer must have something to do with the actual pocket (target), right? Would you not call that something "visual intelligence" or "feel"?

stan shuffett: I would call it experience. Experience is our major teacher. ... I use the word experience as a reference to knowledge. ...

AtLarge:

I take this input from Stan as revelatory. He is acknowledging that the basic set of prescriptions, if executed precisely the same way every time, would create only a small number of cut angles for a given CB-OB distance. So that issue should be settled. What, then, creates the additional cut angles; what turns a discrete method into a continuous method -- one with enough cut angles to pocket all shots? Where is the "feel" being introduced? Stan has now answered that question -- it is different eye positions for the same set of visuals. In other words, for any particular shot and alignment-menu choice, such as this:

CB-OB distance = 3 feet
cut to left
secondary alignment line to "B"
bridge length = 8"
cue offset = 1/2 tip
pivot from left to right
multiple cut angles can be achieved by viewing the CTEL and secondary alignment line from different eye positions.

How does one know where to put his eyes? It is knowledge gained from experience. Stan did not acknowledge that this is "feel," but I'm sure many of us would view it that way, as feel in any aiming method is developed from experience in using the method.

So there we have it. Stan's manual CTE depends upon utilizing multiple eye positions within each of the basic 6 alignments. The feel or additional knowledge is not introduced by varying the offset, or by varying the bridge length (beyond what Stan prescribes), or by fudging the pivot -- it comes from knowing where to place the eyes while still somehow holding to the underlying pair of visuals for each of the prescriptions.

I hope this really puts an end to the squabbles. Manual CTE is not some voodoo hocus pocus. It is not geometric magic. There are no supernatural powers to align-&-pivot methods. It doesn't work because of numerology -- the table being 1x2 or 90 being the sum of 45, 30, and 15. It works by utilizing a small number of reference alignments that the player has learned to fine tune based on his explicit knowledge of where the pocket is and the appearance of the cut angle needed for the shot, i.e., his experience-based knowledge of the shot needed.

dr_dave: I would add to your synopsis that CTE can also provide many other potential benefits to some of its users.

from Patrick Johnson (concerning Version 3 above):

First, what I think it is: I think CTE is a "reference" aiming system (very similar in concept to, and in fact an outgrowth of, Hal Houle's old "3-angle" system), that divides all the possible shots into two categories (thinner or fuller than half ball), leaving the final aim adjustment up to you to learn "by feel". I think it adds some suggested "systematic" adjustments, but nobody can seem to describe those, which makes me think they're probably mostly learned by feel too.

How it works/what it offers: I think CTE offers its users the following things:

1. A specific and easy-to-see starting place (the half-ball alignment) that's in the middle of all the possible alignments. Each shot can be "measured" in relation to the half-ball alignment, giving some structure to an otherwise wide-open (and maybe daunting) narrowing-down process. (This is also the way the old 3-angle system worked, but with three reference angles rather than just one.)

2. A specific and easy-to-see starting alignment of the stick, CB and OB (again, the half-ball alignment) that brings your focused attention to how those three things are aligned, something very helpful in learning to aim (and in executing aim once you've learned it) but often overlooked.

3. Because of its structured approach to aiming, a confidence boost that helps your mind make focused "recordings" of successful shot alignments which can be more readily recalled for future similar shots ("learning by feel").

These might not be all the benefits (see Dr. Dave's website for a list that may go beyond these). I don't believe any of these benefits are only available from CTE, but CTE may be the best way to get them for some players.

The controversy surrounding CTE is about whether or not it's an "exact" system that doesn't rely on the player's ability to finish the aiming process "by feel". Since nobody can seem to describe the whole process (actually, nobody can seem to clearly describe any of it past the initial half-ball alignment), it seems obvious to some (including me) that it therefore can't really be an "exact" system and must include some (maybe a lot of) feel. For some reason, CTE users can't stand this idea and argue vehemently against it (this may be part of the confidence thing), but their arguments always boil down to the same thing: it works for them.

I take CTE users' word for the fact that "it works for them" and only take issue with the claim that it doesn't involve any "feel", but the arguments usually become unfocused very quickly and devolve to "it works" vs. "it can't work", giving us all lots of opportunities for playing the dozens (trading clever insults), but shedding no light whatsoever.

from SpiderWebComm (Dave Segal) (concerning Version 3 above):

- You should never sight directly down the CTEL (center to edge line). Your head should always be on one side or the other. I like pretending the CTEL is a vertical plane ... my body leans against it, one side or the other.

- The bridge position is not really correct in the diagram... it's never on the CTEL. I did it this way just for simplicity in making the diagram. My only intent is to show how the shot circle works - not the other details of CTE.

Consider the following:

What you see here applies to any shot until the distance between the OB and CB is less than the bridge length. I always shorten my bridge to a distance short than that between the CB and OB when this happens. Technically, a "pivot" isn't required at all - that's another story... you can step into the top of the shot circle from one side of the CTEL.

If you were to rotate the cue in the bridge as a true pivot (once again, pretend a nail is driven through the point where the cue touches the skin and into the slate), the cue would turn around the bridge circle radius. This is why people miss shots completely. You would technically only turn the cue like this on a short shot.

For the "mechanical pivoters" out there, you always place your bridge first. Once you're set in your bridge, the cue is turned along the shot circle arc, in relation to the OB - not "rotated/pivoted" from the bridge (bridge circle arc).

This is just a helpful way to describe what is really happening. This is not a functional way of playing....i.e. no one has to "see" a circle on the table in order to make any shot. This is really a "classroom" style of learning how to pivot (um, turn your cue).

OK - practical application when at the table: You should see the OB as a two-dimensional object on a vertical plane (think of the OB as a sticker on a window when down on your shot). Imagine your cue extending to the window and scrape your tip along it until you hit center ball. That's what I do. I only "see a shot circle" on very close shots - within, say, a foot or so.

Notice the longer the shot is, the bigger the circle--- the flatter the arc (think of the Earth - when you look at the horizon, it's nearly flat). The shorter the shot, the smaller the circle--- the curvier the arc (think of a basketball).

I think the reason why so many people say this is a visual system is because they "pivot to the OB" and make the shot and don't know why.

In conclusion, the "correct" center of the CB is determined by the position of the OB, always.... not by the bridge position/bridge length.

from Colin Colenso (concerning Version 3 above):

Any cue that moves or turns from one position to another can be described as having been pivoted at some distinct point. On CTE shots this pivot point must be behind the CB and usually it is behind the bridge hand so the shape of an arc, projected to the front of the shot circle would always be flatter than the actual shot circle arc.

Hence, it seems more like the shot circle is an approximate visualization method, like, as you've said, scraping your tip along a distant window. This is fine, but it's not very quantifiable or systematic, other than it would seem to indicate that you can intuitively sense the nature of the turn and that the turn pivots noticeably closer to the CB with closer distance shots.

Regarding edges of the OB, technically there is only one edge each side that is on the CTE line, but I understand that one's perception of variations in this edge change if one sights the various angled shots from different positions relative to the CTE line.

from Jal (concerning Version 3 above):

[The dependence on pivot length] is why it's not an exact system and why a majority of shots will be missed unless some intuitive adjustment is made. However you have the stick aligned prior to pivoting, the correct pivot point is on a line from the center of the ghostball through the center of the cueball. Where that line crosses the long axis of the cue, is the place to pivot.

Of course, if you can picture where the ghostball is located with sufficient accuracy to make the shot, on the face of it, there seems to be little point in doing the pre-alignment/pivoting procedure. That's related to the main bone of contention between those who are critical of these types of systems, and those who support them: unless you can come up with some procedure for determining the pivot distance that's not tied to shot geometry (impossible), the system(s) are not exact and rely on the experience and judgment of the player to make the final crucial adjustment, consciously or subconsciously.

That's not to deny that many have found them useful.

Dr. Dave's Aiming Method (DAM) aiming system

How does Dr. Dave's Aiming Method (DAM) work?

I first came up with Dr. Dave's Aiming Method (DAM) as a joke to mock some people who try to promote "aiming systems" with outrageous claims and snake-oil-salesman type statements, but I also have some serious and useful recommendations below.

First, let's start with a satirical list of outrageous claims, many of which are direct quotes or paraphrases from statements posted by "aiming system" proponents on pool Internet forums over the years ...

I have invented an amazing and new aiming system called DAM that will revolutionize pool playing all around the world. You won't find DAM in any books, because it has just been recently invented.  But rest assured ... all future pool books will present DAM in its full glory. DAM is the best and most complete aiming system, that also contributes to correct body alignment, that has ever been devised. Most of the pros use it, especially the Filipino players ... that's why they are so good. DAM works on every shot, regardless of the distance between the balls, or the angle and distance to the pocket. The best thing about DAM is you don't even need to know or see where the pocket is. Just align and pivot, and the ball goes in the hole. When a good player uses the system, it is impossible to tell ... it will just look like they are naturally pocketing balls.  That's when you know they are using DAM!

Try to prove that DAM doesn't work ... you can't, because it does work.  If you can't make it work, it is either because you really don't understand it or you don't have an open mind. If you ask a pro if he or she uses DAM, and he or she says he or she doesn't, it is because he or she doesn't want you to know his or her secrets. The DAM system will radically improve the shot-making abilities of those who spend the time to learn it. DAM will eventually become the "aiming standard" and will significantly accelerate your learning curve. There are those who will eventually learn the system, and there are those who will not, and be beaten by those who do. If you don't think DAM works, it is because you haven't had personalized lessons with somebody who truly understands it. I make almost every shot with this system ... I rarely miss. Isn't that proof of how good it is? Don't you want to be as good as me? If you want to master the DAM system, you must visit me in person and pay outrageous sums of money to learn all of the required intricacies.

It only takes two days to learn DAM, and if you practice it for two months, you will start winning tournaments. If you can't make it work, it is because you don't have enough "visual intelligence," in which case you are hopeless. Don't ask me to describe the system in words or with diagrams, because this can't be done; although, I do have lots of fancy words and phrases to describe various parts of the system ... aren't you impressed? If you don't believe in my system or if you doubt the validity of my approach, you will be banished by all of my followers.

Probably the most amazing fact about DAM is that it works for all types of shots, not just cut shots. It also gives you the correct line of aim for combos, caroms, and banks. And you don't need to adjust for speed, sidespin, throw, or spin-transfer effects. All of the adjustment happen automatically with DAM.

If you want to learn the magic of DAM, I am currently offering exclusive private lessons. I know this might sound ridiculous, but I must be clear on this matter: My students are not allowed to share with anybody anything they learn. They are required to sign a special nondisclosure agreement that binds them for life. People are willing to openly discuss and share everything they learn from my currently-available instructional DVDs; but if and when I ever release a DAM DVD, the information must not be disclosed by any viewers; otherwise, they risk exposing themselves to extreme wrath and persecution.

Now for a somewhat more serious, realistic, and useful description of what Dr. Dave's Aiming Method (DAM) actually is ...

The basics of the DAM system are: with a consistent pre-shot routine, visualize the required "angle of the shot" and required "line of aim" while standing, then align your vision center with the line of aim as you move your bridge hand and cue forward into your stance while keeping your focus on the object ball (or ghost-ball resting point, or contact point, or ball overlap, or whatever else defines your target), then follow all of the recommended stroke "best practices." Be sure to maintain "quiet eyes" both at the "set" aiming position, checking both the CB tip contact point and your aiming line, and when focusing on the object ball (or whatever target you have identified) during the final forward stroke. If you are a good shooter and maintain focus and don't do anything wrong during the entire DAM process, you will make every shot.

The key to aiming is placing the bridge hand in the exact required position so the bridge guides the cue along the necessary line of aim for the shot. Sometimes you might need to adjust your bridge position a little as you get down and settle into your stance, because you are not likely to place your hand down perfectly every time. Good shooters can see the required angle of the shot and make the necessary fine adjustments to bring the cue (with the bridge) into alignment with the necessary line. Good shooters can also make adjustments where necessary for squirt, swerve, and throw based on shot distance, shot speed, cue elevation, ball and cloth conditions, bridge length, amount and type of spin, etc.

Good shooters use all visual information available to them to help see the required angle of the shot and the necessary line of aim. They might use any or all of: ghost-ball visualization, ball-to-ball contact-point visualization, impact-line (or "target line" or "line of centers") visualization, required ball-hit fraction (CB-OB overlap) visualization, center-to-edge (CTE) 1/2-ball-hit line visualization, visualizing the angular "relationship" between the balls and the rails, etc. Regardless, a good shooter doesn't need a procedural "aiming system" to do this. For not-so-good shooters, there are drills and techniques they can use to help develop their visualization skills so they can improve their ability to "see" the shot. For example, see:

For more information, see "Fundamentals - Part II: aiming" (BD, October, 2008) and "Fundamentals - Part III: DAM aiming system" (BD, November, 2008).

For seeing the required line of aim of a shot, I personally use a combination of straight intuition and feel (just "seeing the angle") and ghost-ball aiming. I visualize the necessary CB-OB contact point (to account for throw when appropriate), the necessary line-of-centers for the shot, and the entire ghost-ball. I do this before and while I am moving my bridge hand forward into my stance, maintaining focus at the OB. I sometimes also visualize the amount of "ball overlap" (between the GB and OB) required during this process. This seems to help me focus better and maintain my aiming line when I'm down low in my stance.

Here's a video demonstration from Disc II of the Billiard University (BU) Instructional DVD series that illustrates a version of DAM:

When the CB is really close to the OB, I sometimes use the double-the-distance method. And when the cut angle is close to 30 degrees (which I can judge very well with the help of my peace sign), I sometimes use the CTE (center-to-edge) line as a visual reference. And when I use sidespin, I sometimes use BHE (especially for short, fast shots), FHE (for slow, long shots), and a combo for shots in between. For more information dealing with these and other techniques for aiming all types of pool shots, see the How to Aim Pool Shots (HAPS) DVD series.

Regardless of what I or anybody else says, the most important components for success with any aiming system are:

PRACTICE ... PRACTICE ... PRACTICE!!!

and

FOCUS ... FOCUS ... FOCUS!!!

Don't forget to actually aim (while standing), and keep your eyes "quiet" during cue alignment and aim checks. Also, maintain full concentration only on stroke execution during the final stroke. During the stroke, you should not be second-guessing anything about the shot. Everything should be decided and figured out before you settle into your stance.

double-the-distance or double-the-overlap aiming method

How does the double-the-distance aiming method work?

It is described an demonstrated in detail, along with other common aiming systems, in How to Aim Pool Shots (HAPS). See also: in "Aim, Align, Sight - Part I: Introduction and Ghost Ball Systems" (BD, June, 2011). Here's a useful illustration from the article:

Here's how it works:

1. Visualize the distance "d" from the center of the OB to the desired CP on the OB.
2. Double this distance by adding it to the other side of the CP. This locates the required line of aim through the center of the GB.

For thinner cuts, it can be easier to visualize the smaller distance "x" from the CP to the outside edge of the OB, which is doubled to locate the inner edge of the GB relative to the CP.

Here's a document from Don Smith showing the results of sighting through the center of the CB (or any other point), instead of along parallel lines. With non parallel sighting, the system doesn't work well when the CB is close to the OB (see error "E" in the diagram below), but it works fine when the balls are farther apart, for all cut angles. See the document for more info and examples.

It does take a little practice estimating the distances, but you can use your cue tip to help. See the document for more info and examples.

Jal has also done an analysis of the error with plots.

from Patrick Johnson:

Variously called "double-the-distance", "double-the-overlap", etc. It came up often in discussions of aiming systems because it's one of the few "geometrically correct" systems (like ghostball). It's OLD.

It's so well known that it's illustrated on CueTable.com's Aiming Calculator. Here's a snapshot from it. Notice the red X in the center of the CB/OB overlap

I've noticed on AzB some discussion of the sighting error inherent in Double-the-Distance aiming, and I think people are making a common conceptual error about it. The conceptual error is to assume that the distance between the CB and OB determine the magnitude of the sighting error, when in fact it's the distance between the eyes and the OB that determine it.

The reason for this is that, when the player sights the OB center and contact point and estimates the aim point from those, he doesn't move his head back and forth to sight each of those through the CB's center; he simply moves his eyes from one to the other. So the sighting "pivot point" is at the eyes, not at the CB, which means it is always a couple of feet farther from the OB than the CB is, and the magnitude of sighting error is never more than that distance dictates.

from Slide Rule:

Double the Distance
Construct a triangle between the centers of Object Ball, Cue Ball and the Image Cue Ball in contact with the Object Ball. See a line 90° from the Object Ball to the contact point (side distance as viewed from the Cue Ball). They make up two triangles that appear to be congruent (equal sides, equal angles). In order to be congruent the red and green triangles need to be equal.

A small gray triangle represents the error. For the red and green triangles to be equal the lines drawn from the cue ball to the centers of the object ball and virtual cue ball at contact would have to be parallel (which they are not). There is a small error inherent to the method. The method may be a good enough as first order approximation for distances sufficiently far from the object ball (about 1 diamond) or for cases where the cut angle is sufficiently small. Note that the following diagram shows a relatively severe cut shot. The error may be sufficient to cause a missed shot due to hitting the object ball slightly too full.

Of Significance is the Error at Extreme Cut
The relatively small dark triangle is the error. The significant part is in noting that as the cut becomes thinner, the error increases. If you are using double the distance here, I think some sort of correction is required.

from heater451 (via e-mail):

fractional-ball aiming

Are fixed-line of aim, fractional-ball aiming systems useful?

Fractional ball aiming is illustrated and described in the following video from Disc I of How to Aim Pool Shots (HAPS):

and in part 2 of NV B.3 - Mike Page's aiming video (part 1, part 2). For more info, see: "HAPS - Part I: Fractional-Ball Aiming" (BD, November, 2014).

Also, 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:

And here are ball layouts one can use to set up the standard ball-hit fractions at a table (from "HAPS - Part I: Fractional-Ball Aiming" - BD, November, 2014, and "Aim, Align, Sight - Part I: Introduction and Ghost Ball Systems" - BD, June, 2011):

The illustration below (from Patrick Johnson) shows the approximate cut angles for all standard ball-hit fractions. TP A.23 - Ball-hit fraction vs. cut angle shows equations and plots for all ball-hit fractions and cut angles. See estimating cut angles and below for other methods to visualize fractional-ball cut angles.

Various aiming methods (even though they are not perfect) do help some people aim, concentrate, focus on the OB, stay down, and shoot better. I don't think anybody (even me) would say that is a bad thing. On the other hand, people should realize that fixed-point aiming systems with a limited number of aiming lines are not perfect and will cause you to miss shots if you don't compensate (consciously or subconsciously).

The common fractional-ball aiming system, sometimes referred to as Hal Houle's 3-angle system. Basically, the claim is there are only three different aims for all cut shots: a "15-degree cut," a "30-degree cut," and a "45-degree cut." In TP A.11, I show that these aims are equivalent to 3/4-, 1/2-, and 1/4-ball-hits and the 15- and 45-degree angles are not exact. Also, I show an example shot "in between" two of the aim references to show a deficiency of the method. The method provides easy visual aiming, and it helps a player establish good reference aims for different ranges of cut shots; but for "in-between" cut angles, one must adjust or compensate between the aim references.

Fractional-ball aiming references (1/4, 1/2, and 3/4), on either the CB or OB, can be useful to help some people aim because the references are easy to visualize. However any system that offers only a limited number of lines of aim from which to choose can be limiting if the user isn't good at adjusting for the many shots that fall between these references. For more info, see: limited lines or alignments of aim. Also, any "aiming system" can offer a person benefits, especially a person that doesn't aim accurately or consistently.

from Patrick Johnson (in AZB post and via e-mail):

To use Fractions for aiming you need to get familiar with (learn to visualize at the table) the cut angles formed by the three common fractional overlaps: 3/4, 1/2 and 1/4 ball. To help with that, here's a practice setup diagram of the fractional cut angles (left and right) for shots parallel with the short and long rails.

Your hand can be a useful guide for estimating the cut angles made by fractional CB/OB overlaps. Just spread your fingers as far as possible so the thumb and little finger form a 90-degree angle, and your other three fingers space themselves more of less naturally on the three major fractional cut angles (roughly 15, 30, and 45 degrees - actual fractional cut angles shown below).

To cover the rest of the 90-degree "aiming field," cut angles for two more (less frequently used) fractional overlaps are shown in black.

Use your other hand to estimate cuts in the other direction.

from Spiderman:

Like all "discrete", "fractional-ball", and similar aiming systems, it gets you in the ballpark for most shots and depends upon subconscious correction to make the fine adjustments. In other words, you have to use it as a guide, "take it on faith", and shoot the shots.

For a beginner, it will get them in the ballpark and they'll accidentally pocket more balls than by winging it. For an intermediate, they may have enough experience that they will subconsciously correct, and the system might work well for them. The expert doesn't need a system to get them in the ballpark.

All discrete systems have the same failing - they are not geometrically correct for all setups. If you claim that there are only a (small) discrete number of aim points required to hit any pocket from any setup, and disallow the subconscious correction factor, all such systems may be easily disproven. In practice, your ability to compensate overcomes the built-in flaws of the system.

from Hal Houle:

When cutting to the left for 15 degrees, aim the cue ball's left edge at the object ball's left quarter. When cutting to the left for 30 degrees, aim the cue ball's left edge at the object ball's center. When you cut to the left for 45 degrees, aim the cue ball's left edge at the object ball's right quarter. When you cut to the right for 15 degrees, you aim the cue ball right edge at the object ball's right quarter. When you cut to the right for 30 degrees, you aim the cue ball's right edge at the object ball's center spot. When you cut to the right for 45 degrees, you aim the cue ball's right edge to the object ball's left quarter.

frozen-ball shots

Is it a foul to hit "into" a cue ball frozen to an object ball?

When the cue ball is frozen to the object ball, you are allowed to hit into the cue ball toward the frozen ball with a normal stroke. In fact there are aiming systems devised just for this type of shot. High-speed video footage clear shows that hitting into a CB frozen to an OB, with a normal stroke, results in a non-pushing, clean hit, just like any other legal shot. Examples can be found in HSV A.96 and HSV A.97. These shots might "feel" like "push" shots, but they are not. Examples of true push shots can be found on the push shot foul resource page.

Now, if there is a miscue during a frozen CB shot, it could be ruled a foul if there are obviously multiple hits or if the miscue is intentional. HSV 7.5 is an example that is tough to call, even with high-speed video.

For many example calls along with explanations, see the following videos:

How do you aim frozen-ball carom shots (e.g., a frozen carom/billiard shot or a frozen spot shot in one-pocket)?

See:

ghost-ball aiming

How does ghost-ball aiming work?

The ghost ball (GB) is the imaginary position the CB must be, at contact with the OB, to make a shot. It is easy to practice visualization of the GB target by having a helper place a real ball in the desired GB location (adjusted for throw or not) and pull it away when the person shoots. I demonstrate this technique in NV 3.1; although, I didn't have a helper to remove the ball for me. Also, striped balls are useful to help the shooter visualize both the "aiming line" (from the CB to the GB center) and the "impact line" between the GB and OB centers. To me, that's the most useful advice in the video.

Here's a video demonstration of how you can use the cue to help you aim, from Disc II of the Billiard University (BU) Instructional DVD series:

And here are some additional videos and drills to help improve your ghost-ball visualization skills:

"Fundamentals - Part II: aiming" (BD, October, 2008)
"Fundamentals - Part III: DAM aiming system" (BD, November, 2008)
"Aim, Align, Sight - Part I: Introduction and Ghost Ball Systems" (BD, June, 2011)

There are many possible aiming-system variations based on ghost-ball aiming, including:

In the "beginner's version" of ghost-ball (GB) aiming, throw is not considered. In more advanced GB aiming, the GB position is the exact position the CB must be at contact with the OB (adjusted for cut- or spin-induced throw) that will send the OB into the heart of the desired pocket.

There are several suggested methods to help one adjust for squirt, swerve, and throw. The required GB position is affected only by throw. The path of the CB to the GB is affected by both squirt and swerve. I suspect many top players can compensate for all of this stuff mostly intuitively (i.e., by "feel") because they have had lots of "successful experience" and lots of quality "table time." For people not so good at compensating for these factors, I and others have some suggestions and useful info here:

aim compensation for squirt, swerve, and throw

from CreeDo:

1. Eyeball the line between the OB and pocket to get your contact point. I mean physically walk near the OB to make this easy.
2. Put your tip on that line exactly half a ball width behind the OB CP. It helps to physically lean over it and get a bird's eye view.
3. With your tip resting there, walk back around to your shot so that your cue is on a new line between the tip's resting place and the middle of the CB.

from Patrick Johnson:

Hal Houle's 3-angle system

How does Hal Houle's three-angle system work?

Hal Houles' 3-angle system is a type of fractional-ball aiming system.

from Hal Houle:

There are only 3 angles for any shot, on any size table. This includes; caroms, single rail banks, double rail banks, 1, 2, 3, and 4 rail banks, and double kiss banks. Any table has a 2 to 1 ratio; 3 1/2 x 7, 4 x 8, 4 x 9, 5 x 10, 6 x 12. It is always twice as long as it is wide. The table corners are 90 degree angles. When you lay a cue from the side pocket to the corner pocket, you are forming an angle of 45 degrees. When you lay a cue from the side pocket to the middle diamond on the same end rail, you are forming an angle of 30 degrees.  When you lay a cue from the side pocket to the first diamond on the same end rail, you are forming an angle of 15 degrees. When you add up these 3 angles, they total 90 degrees, which is the same angle formed by the table corners. The cue ball relation to object ball relation shot angle is always 15, 30, or 45 degrees. The solution is very simple. There are only 2 edges on the cue ball to aim with, and they are always exactly in the same place on the cue ball. There are only 3 exact spots on the object ball to aim to, and they are always exactly in the same place on the object ball. So, 2 edges on the cue ball, and 3 spots on the object ball; 2 x 3 = 6 which is the total number of table pockets. This means that, depending upon how the cue ball and object ball lie in relation to one another, you may either pocket the object ball directly into a pocket or bank it into any one of the remaining 5 pockets. Of course, the reverse is true. If the relationship of cue ball to object ball can only be a bank, so be it. There is never a need to look at a pocket or cushion while lining up the edge on the cue ball to the spot on the object ball. You have only those 3 angles Your only requirement is to recognize whether your shot is a 15, 30, or 45 degree angle. Recognizing those 3 angles can be accomplished in an instant by aiming the edge of the cue ball to one of the spots on the object ball. It will be obvious which object ball spot is correct. There will be no doubt. Any time either one of the 2 edges on the cue ball is aimed at any one of the 3 spots on the object ball, that object ball must go to a pocket. Choose the correct spot and the object ball will most certainly go to the chosen pocket. The top professional players in the game have always known about this professional aiming system, but they are a closed fraternity, and you are the enemy. Interested in where those spots are located?

The 2 places on the cue ball are the left edge of the cue ball when you are cutting the object ball to the left; and the right edge of the cue ball when you are cutting the object ball to the right. The 3 spots on the object ball are the quarters, and the center. The quarters and center of the object ball face straight at the edges of your cue ball, not facing toward the pocket. In other words, if you were on a work-bench at home, there would be no pocket, so you would just line up the edge of the cue ball straight to your target on the object ball. When you cut to the left for 15 degrees, aim the left cue ball edge at the object ball left quarter. When you cut to the left for 30 degrees, aim the cue ball left edge at the object ball center. When you cut to the left for 45 degrees, aim the cue ball left edge at the object ball right quarter. When you cut to the right for 15 degrees, you aim the cue ball right edge at the object ball right quarter. When you cut to the right for 30 degrees, you aim the cue ball right edge at the object center. When you cut to the right for 45 degrees, you aim the right cue ball edge to the object ball left quarter. If you'll just get down and aim your old way, you'll be close to where you should be aiming. Look to see (without changing your head or eye position) just where the cue ball edge is aiming at the object ball. You'll see that on every shot that the cue ball edge is always aiming at the same targets on the object ball. Remember, this system is for any shot on the table; banks, caroms, combinations, and so forth. The only shot remaining is the extreme cut  for any shot over 45 degrees. Aim the cue ball edge to the eighth of the object ball (which is half of the quarter).  Don't let the pocket influence you. Have a friend hold the ball tray between the object ball and the pocket, so you cannot see the pocket, and you'll see that those 3 angles will handle just about anything. Of course, you would have chosen the 15, 30, or 45 degree angle before your friend put the ball tray in place. It also makes it much more interesting if you don't tell your friend how you are pocketing the ball without seeing the pocket. Have some fun. For any questions, call me. Regards, POOL HAL.

Hit-A-Million-Balls (HAMB) aiming system

What is HAMB?

The "Hit A Million Balls" (HAMB) "system" refers to what some people think is required to get good at aiming (i.e., "HAMB" is the only reliable "aiming system").

How to Aim Pool Shots (HAPS)

What is HAPS?

How to Aim Pool Shots (HAPS) is a three-disc instructional-DVD set created Billiards Digest columnists Dr. Dave Alciatore and Bob Jewett. HAPS covers cut-shot aiming systems, how to adjust for cut-induced throw, how to aim without guessing when using sidespin (english), and how to aim specialty shots including caroms, kisses, combos, rail cut shots, and elevated-cue shots. Also included are numerous simplified and effective systems for aiming kick and bank shots. An outline of the entire HAPS series along with video excerpts from each DVD can be viewed online at: DrDaveBilliards.com/aiming.

limited lines or alignments of aim

How many lines of aim are required to pocket a typical range of shots?

Many "aiming systems" use a limited set of alignments or lines of aim that can get you close to the right aim for a wide range of shots. However, a limited number of aims is not sufficient for a typical range of shots, unless aiming adjustments are made relative to these fixed references.

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 make-able with one of the selected aiming lines.

Even with english effects (squirt, curve, and 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:

• To be able to pocket an object ball into a "large" 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 fixed-reference aiming systems can still be very useful, based on the benefits listed here. The systems can provide a good "framework" from which to work, especially for people that have difficulty aiming accurately and consistently.

from Patrick Johnson:

[The diagram below] shows that to make a spot shot from anywhere on the table into a 4.5" pocket takes ~25 discrete cut angles per quarter ball (per cut direction), each ~3.6 degrees wide (contact area ~1/16" on OB's surface).

What does this mean?

If the OB is left in place and the CB is moved around it in an arc, the cut angle needed to make the shot changes. If the pocket was exactly as wide as a ball, then the cut angle would have to change with every infinitesimal movement of the CB and it would take an infinite number of cut angles to make shots from all possible CB positions. But with a 2.25" margin of error in the pocket, the cut angle only needs to change with every 3.6-degree movement of the CB (25 times as the CB moves through a 90-degree arc for all the cuts in one direction).

This is why it is often said that any system must define more than a handful of cut angles in order to work "without adjustment". For example, if a system defines only 6 cut angles for each cut direction, then the system by itself can only make 6/25 (~1/4) of all possible spot shots into a 4.5" pocket, and the other 3/4 of all possible cut angles are in the gaps between the 6 system-defined cut angles.

from Patrick Johnson:

It takes 15 aim points to make any shot on the long string near the pocket (ignoring some space at the top of the string to put a cue ball) - more on strings farther away. The drawing below shows how this is true, but it may take some staring and scratching to understand.

Each two contiguous balls (and any ball between them) can be made in the upper right corner pocket (5" wide) with the same cut angle. Each ball can be made with the cut angle of both balls contiguous to it. So they show when the angle must change and the maximum it can change without leaving any OBs that can't be made.

For illustration, the common cut angle for each of the first two pairs of balls is shown by parallel lines of matched color (red or white) - these lines show that both balls will fit between the pocket points using the same cut angle. By cheating the pocket the maximum amount one way or the other, the second ball can be made using either cut angle #1 (cheating the pocket to the right) or cut angle #2 (cheating the pocket to the left) - this dictates the change in cut angle from #1 to #2, ensuring there are no gaps between OBs that can be made.

from Patrick Johnson:

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 about 4 feet from the pocket. So your estimate that "any typical shot" works is overstated, but not ridiculous. With a real aiming system, we have to double the number of aim points - an aiming system would have to have a minimum of 30 total aim points per side (left or right cut) for half of them to cover most "typical" shots.

90/90 pivot-based aiming system

What are the basics of the 90/90 pivot-based aiming system?

90/90 is an align-and-pivot aiming system developed by Ron Vitello.

and here's a related document from Andrew Cleary containing some good illustrations.

from cleary:

If you break the ball up into 10% increments, you want to line your cue up so that you are aligning the last 10% of the cue ball and object ball... or as Ron V calls, 90/90.

90/90 (pocketing without side spin/english)

Pivot your HIPS to the center of the cue ball. You should now be lined up to make the shot. If you pivot past center ball, don't try to fix it while your down, just get up and start over.

from dr_dave:

The key to pivot-based systems appears to be the "pivot" and the effective center of the pivot. If you shift the bridge hand a small but critical amount during the pivot, then the resulting "line of aim" can be tweaked quite a bit. Assuming your initial alignment is consistent (for different but similar shots), and if you don't adjust your bridge during the pivot, and if you don't adjust by the exact right amount, you will miss many of the different, but similar, shots. As the diagrams in my articles show, the pivot-based systems will not work for a wide range of shots if the bridge is fixed during the "pivot" step (i.e., if the cue "pivots" about the bridge point), or if you don't use different bridge lengths for different shots. In "Fundamentals - Part III: DAM aiming system" (BD, November, 2008), Diagram 1 shows how angle to the pocket matters, and Diagram 2 shows how distance to the OB matters. In "Fundamentals - Part IV: bridge length" (BD, December, 2008), Diagram 4 shows how bridge length matters with pivot-based systems. If a "basic cut-shot aiming system" does not account for the effects in these diagrams, then the aiming system will have limited use (without intuitive compensation). After numerous conversations over the years with many of the aiming system proponents out there, and after trying everything all of the proponents have suggested to me, it is not clear to me how the aiming systems account for the effects in the diagrams. If the systems work (and they seem to for many people), they must involve adjustments that account for these effects.

For more info, see the background information for the CTE aiming system, which is also an align-and-pivot system.

Perfect Aim

What is Perfect Aim?

Perfect Aim is a method of sighting recommended by Gene Albrecht. It is about getting the eyes in the right place for different types of shots.

from Gene Albrecht (in AZB post):

This is what Perfect aim is all about: Making sure the dominant eye is in the most dominant position making sure the other eye is not being dominant at all. This allows your eyes to work together in the most efficient way to envision the shot as Perfectly as possible.

from Gene Albrecht (in AZB post):

Cutting to the right and the left.

One is a dominant eye and the other is non dominant.

When we cut to the right it is the right eye and when we cut to the left it is the left eye.

from Gene Albrecht (in AZB post):

The head position will always be the same for every shot.

The hard part is knowing how to get there and keep it there for all shots.

from Patrick Johnson (in AZB post):

[In Gene's Perfect Aim DVD, he suggests] that we should sight all pool shots by aligning the "inside" edge of the CB with the place on the OB where it should overlap for the cut angle we want, and that we should position the eye nearest that side of the CB directly over this line to get the truest picture of it. For instance:

- for a 30-degree cut to the left (a 1/2 ball hit), sight from the CB’s left edge to the exact center of the OB by positioning the left eye over that line

- for a 49-degree cut to the right (a 1/4 ball hit), sight from the CB’s right edge to the point 1/2 radius in from the OB’s left edge by positioning the right eye over that line

- for a straight shot, sight from the CB’s edge to the OB’s edge by positioning the dominant eye over that line (obviously, using the edges on the dominant eye side)

... Gene is a very good player with many high-level tournament notches on his belt ...

Pro One

What is the "Pro One" aiming system?

Pro One is based on a version of Center-To-Edge (CTE) aiming taught by Stan Shuffett, which is described here.

Pro One is really not so much an "aiming system" as it is a "level of ability" that one can develop through lots of practice with CTE, where bridge hand placement and accurate center-ball alignment come naturally without a mechanical fixed-bridge pivot. Pro One is also a pre-shot routine, which can help create consistency with alignment and focus.

A summary of the example shots from Stan's DVD can be found here: www.ohrt.com/billiards/ProOnePractice.pdf

shaft-edge aiming system

How does the shaft-edge (or edge-of-ferrule) aiming system work?

And here's an explanation of a variation by Shane VanBoening: shaft-edge-to-object-ball-edge system.

from 3andstop:

It's pretty self explanatory. If I'm cutting my shot to the left, I use the left edge of my shaft, if my shot is straight with no angle, I use the center of my tip, and if I'm cutting to the right, I use the right edge of my shaft. No matter, I stroke that part of the shaft directly into the contact point on the object ball. If I must apply any english (sidespin) I merely move my stick parallel to my original aim and I still shoot that part of the stick into the contact point on the object ball. No twisting or pivoting or anything else.

from coloartist:

from Patrick Johnson:

Because of its fixed width, the edge of a centered shaft points directly at the OB contact point for only one cut angle. For a 12.7mm shaft like the one in the pictures below this "Stick Aiming cut angle" is 13 degrees. The "Stick Aiming cut angle" for smaller shafts is a smaller angle and for larger shafts it's a larger angle.

Stick Aiming is done by learning how the edge of your stick lines up compared to the OB contact point for different cut angles and recreating the correct alignment from memory for each shot that comes up. The edge of the stick almost never (except for the shaft's one Stick Aiming cut angle) lines up exactly with the OB contact point, but using it as a fixed comparison for any cut angle can be a helpful memory aid.

Like other "reference" systems, Stick Aiming can be used with varying degrees of awareness of how it functions:

- "consciously", with real time awareness of estimations being made

- "subconsciously", with abstract understanding that estimations are made

- "unconsciously", with no awareness that estimations are made (believing the method is "exact" for all shots)

from dr_dave:

By aligning your vision center with the inner edge of the shaft (instead of the through the center of the shaft), you're perception of the line through the contact point might indirectly cause you to align your cue to aim slightly outside of the contact point (which is required to make a cut shot). If you don't aim the center of the cue outside of the desired contact point, you will undercut the shot:

Squirt actually makes the situation worse by deflecting the CB away from the necessary ghost-ball position, but swerve helps counteract this. Also, outside english helps limit CIT, and with small cut angles, it could even create a small amount of SIT to help.

This method will obviously work only for shots at certain angles, speeds, distances, and cue elevations; and the cue's squirt also has an effect. However, "aiming systems" like this can still be helpful and effective for some people, because they offer many potential benefits (see aiming system benefits).

from AtLarge:

First, I'll state what I heard Mr. Mullen say to define the method:

1. Find the intended contact point on the object ball (OB).
2.a. For a cut shot to the left with no english, point the cue stick through the center of the cue ball (CB) with the left edge of the ferrule aimed at the contact point.
2.b. For a cut shot to the right with no english, point the cue stick through the center of the CB with the right edge of the ferrule aimed at the contact point.
3. Stroke straight back and through on this aiming line.

What follows are eight pictures. I used a half-black/half-red ball to represent the OB. It has a clear line separating the two colors. I aligned this separation line vertically and pointing at a corner pocket. I placed this OB frozen to a CB that is on the head spot. So the necessary contact point (ignoring cut-induced throw) is on the equator of the OB on that vertical line where red meets black. The eight pictures below are the following (all cut shots are to the left):

Picture #1. The CB on the spot and the OB frozen to it, with the line of centers pointed at a corner pocket.

Picture #2. The CB removed and the OB left in place. To make the shot without english and ignoring throw, the CB must pass over the center of the white dot in the middle of the black spot (i.e., through the center of the ghost ball).

Pictures #3 through #8. The cue stick placed across the center of the spot, i.e., on the proper line of aim, to make shots at 15-degree intervals: 0, 15, 30, 45, 60, and 75 degrees.

Here is what one can observe from the pictures:

1. For a straight shot, the edge of the cue stick needs to point to one side or the other of the contact point, not at it. So the Mullen Method is not accurate for straight shots. [But if the shot is a real short one, pocket slop may be sufficient to absorb the angled hit that would result from using the Mullen Method.]

2. For a 15-degree cut, using the cue stick in the pictures, the shot is pretty much "right on," i.e., the left edge of the ferrule is in the same vertical plane as the contact point, and the shot would undoubtedly be pocketed.

3. For a 30-degree cut (half-ball shot), the left edge of the ferrule in the picture is pointing to some point on the OB, but it is to the right (outside) of the contact point. So, using the Mullen Method, if you aimed the left side of the ferrule at the contact point, you would under-cut the shot. [The shot might still "go" if the OB is close enough to the pocket, but probably not if it is a long distance from the pocket.]

4. For properly aimed cut shots of 45, 60, and 75 degrees, the cue stick points entirely outside the right edge of the OB. Using the Mullen Method on these angles would drastically under-cut the OB.

My conclusion, then, is that the Mullen Method, if followed literally and exactly, is really "right on" (to the center of the pocket) for just one cut angle. For the stick I was using (13mm ferrule), that angle was approximately 15 degrees. However, it is approximately "on" for some small range of angles (somewhere greater than zero and less than 30 with my stick), and may pocket many of these shots because of pocket slop. The method may serve as a good approximation method within that range of shots. It may also serve as a good starting point for the player to make further refinements of the aim.

from Bob Jewett:

In the video, the system is described as always aiming the edge of the shaft at the contact point on the object ball. According to the system, if the edge of the shaft were aimed at the edge of the object ball, you would get a 90-degree cut. That's clearly very, very wrong. The system has large errors for nearly all cut angles, but the errors for thin cuts are enormous. This is pretty simple geometry.

But the system is not based on geometry. The system gets you to pay attention to the contact point -- which is good -- and makes you pay attention to stick alignment -- which is good. With practice, the system will give you some kind of aiming framework. The system might be described as a perceptual or psychological system, but it is not a geometrically accurate system.

Whether the system will be helpful to any particular person depends on that person and how they apply it. Personally, because I can see the gross geometric errors in the system, I could never trust it.

Supplemental Aiming Method (SAM)

What is SAM?

The Supplemental Aiming Method (SAM) (AKA "Stick Aiming Method") is a fractional-ball aiming method taught by some BCA instructors.

from caedos:

using lights and ball reflections

Can lights and ball reflections be useful in aiming?

The value of this is debatable, but some people do claim it is useful. Bob Jewett's June '04 BD article describes a possible approach for using reflections of lights in balls.

why people miss shots

What are the main and most common reasons why people miss shots?

1.) not enough care and focus given to actually visualizing and aiming the shot.

2.) not enough care and focus given to accurately aligning the cue and tip for the shot.

3.) inaccurate or inconsistent visual alignment (see vision center).

4.) poor or inconsistent pre-shot routine.

5.) lack of understanding or intuition for how to adjust aim for squirt, swerve, and throw (see aim compensation for squirt, swerve, and throw)

6.) inconsistent and inaccurate stroke resulting in poor speed control and inaccurate tip contact point, resulting in the next shot being missed (even if you pocket the current shot).

Most people miss shots because their aim is off; although, 6 is a huge factor, so the stroke is also very important. To win, you need to make the current shot, but you also need to make the next shot; so if your speed and position control are inaccurate or inconsistent, you won't be a good player.

from Colin Colenso (in AZB post):

On near straight in shots, applying unintended side english throws the OB offline. On slow shots the throw effect increases, as does swerve on the CB, further messing up the shot. On firm shots, throw is less, swerve is far less (unless the CB is hit high) and depending on one's bridge position relative to the cue's pivot point, deflection could counteract or add to the error. Bridging a little longer than one's pivot point can reduce and even cancel out the effects of such stroking errors.

On cut shots, applying unintended outside english can throw the OB significantly off the intended path. Conversely, unintended inside english often has negligible effect on the OB path. So being careful to hit center or slightly inside can be a way to avoid the stroking errors that result from unintended outside english.

from Matt (in AZB post):

1) If all you are concerned with is making the object ball and you are bridging at the effective pivot point and swerve and throw are insignificant, alignment is far more important than stroke accuracy.

2) If all you are concerned with is making the object ball and are attempting a shot where you are compensating for swerve or throw, stroke accuracy is more important than it is in the first case.

3) If you are trying to make a shot while controlling the cue ball, compensating for swerve or throw, bridging somewhere other than the pivot point, shooting down on the cue ball, and pretty much any other situation besides just trying to make a ball using BHE, I would say that the accuracy of the stroke is at least as important as the alignment. That said, you can have a laser-straight stroke and still miss the object ball if you haven't lined up correctly in the first place, including any necessary compensations.

from 12squared (in AZB post):

I agree that poor alignment maybe the cause of a miss, but there are several instances where a bad stroke would cause a miss, most of which is when using side spin. Here are a couple of examples I would consider reasons for a miss that was stroke related:

1) on your final stroke, you twist your wrist or do something to change the direction.
2) If you decelerate during your final stroke using sidespin causing the swerve to increase over the plan. (I call this finishing my stroke before I hit the ball).
3) you stroke slower or faster then planned (still accelerating through the stroke unlike #2) while using sidespin that changes how much swerve was planned. This could be because of pressure or whatever.