# Category Archives: Theory

## The Seven Day Miracle: Part 7 of 7

Pulling it together

Figure 1

This is the final post of my seven part series to improve your game.  Today I will pull together all the pieces we have studied and show you how to apply what we learned to play the perfect game of pool.  As a review, here are the individual components that we worked on:

1.  Aiming shots with the Ghost Ball method

2.  Calibrating our arm to control the speed of a shot

3.  Predicting the cue ball deflection angle after collision with an object ball

4.  Predicting the cue ball rebound angle after it hits a rail cushion

5.  Adjusting the speed of a shot to compensate for energy lost in the cue ball / object ball collision.

Figure 2

Now, let’s get down to business!  Take a look at the table layout in Figure 1.   This is a game of eight ball, we are stripes, and we have only one stripe ball left to pocket.  What we want to do is pocket the fifteen ball, then make the cue ball travel around the table to get into position for the final shot, which is the eight ball.  That looks like a pretty hard shot doesn’t it?  How do we make it happen?  Should we just hit it hard and hope for the best?  Heck no!  With the knowledge that you now have, and with the countless hours you spent calibrating your arm in part 3 of this series, you should be confident and totally in control!

Let’s analyze the shot.    First, we need to figure out how to make the fifteen ball go into the pocket.  We will use the Ghost Ball aiming method.  See Figure 2, where we have imagined the Ghost Ball, and determined the aiming point.  Notice the aiming line that extends through the ghost ball.  The aiming line just barely touches the edge of the object ball.  If you refer to the Angle of Deflection chart in part 4 of this series, you will see that this is a half ball hit.  According to the Deflection chart, the Angle of Deflection will be about 30 degrees, so in your mind’s eye, see the “Peace Sign” to determine the initial direction of the cue ball after collision.

Figure 3

In Figure 3, we utilize the Angle of Reflection from part 5 of this series to estimate the path of the cue ball after collision with the first rail and subsequent rails.  Based on the extension of this “natural” path, we should check to see if any of the solid balls are going to get in the way.  Fortunately, in this case, none of the balls are in our way.  Yippeee!  This means there’s no need for us to use extra cue ball spin to avoid unwanted collisions!  Now we can just hit the ball and try to make it land it somewhere near the spot marked “X”.  But wait a minute.  Do we really need to be that exact?  Take a look at Figure 4, and notice the position of the eight ball and the blue line that I drew on the table which outlines a “safe” zone highlighted in yellow?  As long as the cue ball lands anywhere in this yellow zone, you should be able to make the final shot and win the game fairly easily; therefore, there’s actually a pretty large margin for error on this shot.

Figure 4

Now the question is: “How hard do I need to hit the cue ball in order to make sure it stops in the yellow zone?” If we extend the cue ball path through the yellow zone, we can put limits on how soft and how hard you can hit the cue ball.  See Figure 5.  The point marked “A” is the softest you can hit, and point B is the hardest you can hit.   But wait, we get a bonus!  If the cue ball makes it all the way to point B, it will collide with the green ball and come to a stop.  The green ball will act as a stopper to keep the cue ball safely within the yellow zone.  As such, we can actually hit the cue ball even harder, and still be able to keep the cue ball in the yellow zone.  We could probably hit the cue ball hard enough to theoretically make it to point “C” (if the green ball were not in the way).  Now, let’s calculate the distances the cue ball would have to travel to get from its starting point to points “A” and “C”.  The distance to point “A” is ~10 diamonds.  The distance to point “C” is ~16 diamonds.  If you refer back to the exercise from part 3 of this series, this translates into an arm stroke with a speed between 3 and 6.

Figure 5

So we want to hit the cue ball with an arm speed between 3 and 6, but remember, today we are also hitting an object ball with a ½ ball hit.  As such, the object ball will be ‘stealing’ some energy from us, so we need to make an adjustment for that.  According to the “Speed after Collision” chart from part 6 of this series, the object ball will take 4 parts of the cue ball’s energy, and the cue ball will retain about 3 parts of its energy.  Just to make the math easy, let’s assume the energy split is 50/50, even though it’s really about 57/43.  This means that the cue ball will only retain about half its energy after it hits the object ball.  In order for the cue ball to end up with enough speed to get into the yellow zone, we will need to multiply our calculated speed range by two, since object ball will steal about half of the cue ball’s energy.  So the modified distances are 20 diamonds for point “A” (10 x 2) and 32 diamonds for point “C” (16 x 2).   This translates into newly calculated arm speeds of 8 (minimum) and 14 (maximum).

After you’ve done all the thinking and calculating, let’s review the final answer:  In order to hit the perfect shot, you will need to do the following:

1. Use a half ball hit on the object ball
2. Hit the cue ball with normal ‘running’ English
3. Hit the cue ball with an arm speed between 8 and 14.

That’s it!  At this point, there’s nothing else to worry about.  Just get into your stance, use proper fundamentals, and execute the shot with the proper speed.  If you take your time and go through this type of analysis on every single shot, you should be running tables in no time.  Nothing to it!

## The Seven Day Miracle: Part 6 of 7

Speed after collision

Remember in part 3 of this series we discussed the importance of being able to control the speed of your shooting arm?  In today’s post we take what you learned in part 3 and add a slight complicating factor to the equation: the object ball.  Remember, the ultimate goal in this game is to be able to control the final resting spot of the cue ball, and parts 3 and 6 of this series both deal with the speed of the cue ball.

For today’s post, I will first present some theory about energy transfer between cue ball and object ball.  Next, I will tell you how to make adjustments to your arm speed to compensate for the energy loss that occurs when the cue ball collides with the object ball.  Armed with this new information, you will have all the information necessary to make the object ball in a pocket, and subsequently move the cue ball around the table for a specific distance.

Okay, here’s the theory part.  When the cue ball strikes an object ball, a certain amount of the energy contained in the cue ball is transferred to the object ball.  For the purposes of this discussion, we will assume the cue ball is a naturally rolling ball with no English.  Depending on the angle of the collision, the amount of energy transferred between the two balls changes.  Pool players often have limited control over the angle of the shot they are taking (i.e. they have to play what the table gives them or their opponent gives them); therefore, it is important to know for a variety of angles (or ball hit fractions) how much energy will be contained in the two balls after impact.  Once again, thanks to our mechanical engineering friends at Colorado State University, we don’t have to derive any of the math; we can just review the answer and implement the information learned.  See the graph in Figure 1.

Figure 1

Here’s how you read the graph.  The bottom row of numbers is the ball hit fraction, which tells you how “Full” the cue ball hits the object ball.  The top row of numbers tells you the ratio of energy contained in each ball after the collision.  All of these calculations assume a normally rolling cue ball (no English).  Let me walk you through a few examples:

(1) If you aim the cue ball directly at the center of the object ball (a full hit), the ball hit fraction will be “1” and after collision the object ball (OB) will travel seven times further than the cue ball (CB)

(2) If you aim the cue ball directly at the outer edge of the object ball (a half ball hit), the ball hit fraction will be ½ and the object ball (OB) will travel 4 units of distance for every 3 units traveled by the cue ball (CB)

(3) If you aim the cue ball directly at the ¼ fraction hit mark, the cue ball (CB) will travel twice as far as the object ball (OB).

How is this information useful to us?  By knowing how much energy is lost in the collision, we can make adjustments to our arm speed (increase it) to compensate for the loss of energy, and still be able to place the cue ball exactly where we want it after the shot.  If you remember back to part 3 of this series, we were hitting the cue ball directly up and down the table without any interfering balls, and we were able to make the cue ball stop within certain zones of the table.  In my final post of this series, we will repeat the exercise from post 3, but add an object ball to make it a little more interesting.  In order to control the cue ball and make it come to rest in the appropriate zone of the table, we will be forced to make adjustments for the energy lost in collision.  In the next post, I’ll pull together all that we’ve learned in this series, and show you how to make a shot, then control the final resting spot of the cue ball.

﻿

## The Seven Day Miracle: Part 5 of 7

The Angle of Reflection

Hello World!  Sorry for the tardy post, I’ve been in bed for two days sick, but hey baby, I’m back!  Since I’m a day behind, I’ll do two posts today.  I’ll start with the Angle of Reflection, then later today when hopefully I feel a little better, I’ll write about the next topic, Speed after Collision.

So here we go…the Angle of Reflection.  When a cue ball rolls toward a cushion, hits the cushion and rebounds back, how do we predict the angle the cue ball will take when it leaves the cushion?  That seems like an easy thing to predict, huh?  Well, in some ways it is.  The generally accepted rule of thumb for predicting the angle of rebound goes something like this: “The angle of incidence equals the angle of reflection.”  This is a concept borrowed from classical physics.  Although this approach is very accurate when applied to light waves or other forms of electromagnetic radiation (with little or no mass), this rule of thumb can be highly influenced by other forces when applied to a real world setting that is filled with rolling and spinning spheres of significant mass.

Figure 1

Let’s start simple.  In figure 1, I show the classic concept from physics, where the angle of incidence equals the angle of reflection.  This is actually a very accurate guideline for predicting the path of a cue ball bouncing off a rail under the following three conditions: (1) if the cue ball is rolling naturally (not over spinning, sliding, or rotating backwards), (2) if the cue ball has a very slight horizontal rotation to it (in this case, a slight right spin, also known as “Running English”), and (3) if the cue ball is hit with normal speed (between 3 and 7 on the Arm Calibration scale from my November 10, 2009 post).  Under these three conditions, the angle of reflection will almost exactly equal the angle of incidence.  However, if you vary any of these three factors, the angle of reflection will be modified from the theoretical value.  How much will it be modified?  Unfortunately, you have to go to the table and experiment with these factors to get a feel for how much they influence the rebound angle.

Here are the general rules for determining the influence of these factors:

1.  For very large angles of incidence (the cue ball is approaching the rail at a shallow angle), the angle of rebound will be even shallower than the theoretical value (more oblique).  Conversely, for shots into the rail that are nearly perpendicular, the rebound will be even more perpendicular (more acute) than theory suggests.

2. If you hit the cue ball hard, the angle of rebound will be sharper (more acute).  For cue balls hit really soft, the angle will be fatter (more oblique).

3. Cue ball rotational at the time of impact has a MASSIVE affect on rebound angle.  This motion can be present in two forms: (1) Forward/Backward rotation, and (2) Side Spin (commonly referred to as Spin or English).  As an example, in Figure 1 above, if the cue ball was rolling forward and had a hard right spin, the cue ball would come off the rail at an angle much more oblique (more parallel to the rail) than expected.  Conversely, on the same shot if the ball had backward rotation and/or hard left spin, the angle of rebound would be modified to be much more perpendicular to the rail than theory would suggest.

OK, sounds interesting (or maybe not), but how much do I really need to worry about this?  If you want to be able to predict the path of the cue ball, you need to develop a good feel for how much influence these factors have.  What’s the worst that can happen?  Just for fun, I’ve included some graphs below that demonstrate some of the most extreme examples of shots that I’ve seen that deviate from the “angle of incidence = angle of reflection” rule of thumb.  All of these shots are possible, given changes in the three factors that I mentioned above: the angle of incidence, speed of the shot, and rotational spin.  Don’t believe it?  Yes, these are extreme examples, but they are possible.  Maybe in a future post I’ll go into a little more detail on how these shots are performed.

Examples of deviant Angles of Reflection

Later today, I’ll post the final technical installment called Speed after Collision.  Then Saturday I’ll wrap up the series and show you how to apply these concepts in a real game.

## The Seven Day Miracle: Part 4 of 7

The Angle of Deflection

Today we are going to address one of the greatest mysteries, and provide one of the most valuable pieces of information, from the world of pool.  I am often asked, “How do you know where the cue ball is going to go after it hits the object ball?” Before I explain the answer, let’s first define a couple of terms:

Angle of Deflection – When the cue ball strikes an object ball, the cue ball will be deflected from its original path by a very predictable angle.  That angle is called the angle of deflection.  Why is it important to know this angle?  Because knowledge of this angle will allow you to predict with great accuracy the path the cue ball will take after it collides with an object ball.

Ball hit fraction – From the shooter’s point of view, ball hit fraction is defined as the point that you are aiming your cue stick at when you shoot the cue ball into the object ball.  It’s easier to explain with the help of a simple diagram, like the one shown in Figure 1 below.  Let me help clarify by walking you though three examples: (1) If you aim the cue ball directly at the center of the object ball, your ball hit fraction will be one; (2) If you aim the cue ball directly at the center of the ghost ball, the ball hit fraction will be zero.  In other words, the cue ball will just barely miss the object ball; (3) If you aim the cue ball directly at the outer edge of the object ball, the ball hit fraction will be 1/2.  In pool parlance, this is often referred to as a “Half Ball” hit.

Figure 1

Figure 2

For the purposes of our discussion today, let’s assume the cue ball is rolling naturally down the table with no side spin.  How do you determine the angle of deflection?  The folks at the Colorado State University Mechanical Engineering department have taken on the arduous task of calculating the math for us, so there’s no need for us to get into the details.  The graph in Figure 2 that tells you exactly what the angle of deflection will be for any ball hit fraction.

Figure 3

Hummm…that’s not a very friendly graph is it?  I don’t know about you, but there’s no way I will be able to remember that when I’m shooting!  Let’s get away from the exact theoretical numbers, and simplify the graph so we can remember it and apply it in a practical setting.  You will notice in Figure 3 I’ve greatly simplified the graph by drawing two vertical lines at the  ¼ and ¾ ball fraction points and inserting a flat red line between these vertical lines.  This of course is an approximation of the original chart, but it is very useful information nonetheless.  The reason is because in most situations when you are moving the cue ball around the table to get into position for your next shot, you will want the cue ball to approach the next object ball at an angle that falls between these two lines.  Why?  Because the angle of deflection is relatively flat and predictable between these two lines: approximately 30 degrees.  For ball hit fractions between 0 and ¼, and between ¾ and 1, the angle of deflection is roughly linear and proportional.  Huh?  Don’t worry about the language; just take a look at the simplified graph in Figure 3.

Figure 4

As discussed earlier, we want most of our shots to have ball hit fractions to be between ¼ and ¾.  If we do, the angle of deflection will be relatively robust and predictable, at around 30 degrees.  Why is this so special? Because if you have to deal with the same angle of deflection on every shot, you will get much better at predicting the path of the cue ball, and the key to winning pool is being able to control the cue ball.  The next logical question is:  “How do I know what 30 degrees looks like when I’m at the table shooting?” Good question!  Here’s a very easy way to estimate a 30 degree angle.  Just make relaxed a peace sign with your fingers.  Guess what?  The angle is approximately 30 degrees!  (Figure 4)

Enough info for one day?  Yes, my brain hurts also.  How are you going to use this information to improve your game?  Heck if I know.   Why don’t we both take a break and come back tomorrow, where we will be discussing a much simpler topic, the Angle of Reflection.

## The Seven Day Miracle: Part 3 of 7

Today we will work on calibrating your shooting arm.  First, I would like to make a prediction:  I bet I can improve your game without ever seeing you shoot.  Here’s some free advice that will immediately improve your game:  Stop hitting the balls so hard!  Almost all players hit the balls too hard for the same reason; when we are insecure about a shot, we tend to overcompensate by hitting the balls too hard.

In this part of the series, we will lay the foundation for improving what I believe to be the most neglected pool playing skill: the ability to control the distance the cue ball travels after pocketing the object ball.  I must be honest with you, the drill that I’m sharing with you today could be the most boring drill you’ll ever perform; hence, the reason so few people ever practice it.  Although it takes some mental firmness to execute it for more than a few minutes at a time, I PROMISE YOU that every minute you invest in this drill will be repaid a thousand-fold!!

Figure 1

Take a look at Figure 1.  This is your standard pool table.  Let’s divide it into five zones.  The first zone starts at the top end of the table, and is one diamond wide; the second, third, and fourth zones are two diamonds wide, and the fifth zone at the bottom is one diamond wide.  For the purpose of this practice drill, all we are going to do is simply hit the cue ball up and down the table.  We don’t have to hit any object balls and we don’t have to make any balls in any pockets.  Wow!  What could be easier?!  Sounds really simple huh?

The objective is to hit the cue ball at different speeds, and by doing so make the cue ball come to rest in different zones of the table.  In Figure 2, I’ve plotted the theoretical path of the cue ball as it moves through 15 consecutive zones.  When doing this drill, always start with the cue ball in the position as shown in Figure 2.  Why do I start numbering shots at the top rail?  Because you will almost never hit a shot softer than that.  Why do I stop with shot number 15?  Because you will almost never need to hit the cue ball hard enough to make it travel more than 15 zones.  The reason is that it’s nearly impossible to hit the cue ball any harder and still maintain any semblance of control.  The only shot that you could possibly hit harder is the break shot.  For this drill we will keep it simple and only attempt five different shots; shots 1, 3, 5, 7, and 9.

Figure 2

Let’s get started.  First, place the cue ball near the position indicated in Figure 2.  Get into your shooting stance, and hit the cue ball very gently towards the top rail so that it rolls to a stop in zone 1.  It doesn’t matter if the cue ball stops short of the rail or bounces off the rail, as long as it stops within the zone labeled “1”.  It may take you a few attempts before you successfully complete the shot because I know you have been conditioned to hit the ball much harder, but fear not, you can do it!

After you successfully complete shot number 1, next try shot number 3.  Place the cue ball at the starting position again, and hit the cue ball a little bit harder, bounce it off the top rail, and have it roll to a stop somewhere within zone 3.  Repeat this shot until you can do it a couple times in a row, then move on to the next shot.  Try shots 5, 7, and 9.  After completing each of these successfully, now comes the really fun part:  randomly pick a number in your head between 1 and 9, place the cue ball at the starting point, and then execute the shot so that the cue ball stops within the zone that you picked.  Repeat this process again, and again, and again.

Did you think that was tough?  Don’t worry, it will take some time to master this.  Here’s the good news:  In 98% of all pool shots that you will take, the proper speed of the cue ball will be somewhere between 1 and 9.  If you can teach your arm/brain system to consistently perform shots 1, 3, 5, 7, and 9, and you can do it on demand, you are on your way to mastering this game!   If you have the discipline to practice this drill a couple times a week, the time you invest will pay off big time with improvements to your game.  In the sixth part of this series, we will revisit the skills you are learning here, and apply it to a real world game.  Tomorrow, I will discuss the angle of deflection, a concept that will allow us to predict the initial path the cue ball takes after it collides with an object ball.

## The Seven Day Miracle: Part 2 of 7

The Ghost Ball

Figure 1

In today’s post, I introduce a method of aiming commonly referred to as the Ghost Ball method.  Suppose you are faced with the shot illustrated in Figure 1.  The question is, “Where do I need to aim the cue ball in order hit the object ball into the pocket?” The exercise I share with you below will help you determine the precise aiming point.

The first step is to locate the correct contact point on the object ball.  The contact point is the point where the cue ball will come into contact with the object ball.  In order to locate this point, take a look at Figure 2.  To find the contact point, you will first need to locate the “pocket aiming point”, which is identified as a red dot located right in front of the pocket.  From this red dot, draw a line through the center of the object ball.  The place where this line exits the object ball is the contact point.  In essence, the contact point is the point on the object ball exactly opposite from the mouth of the pocket.

Figure 2

The second step, for visualization purposes, is to place an extra ball up against the object ball so that it touches the object ball at the contact point.  (See Figure 3) This is exactly where the cue ball needs to be in order to strike the object ball at the contact point.  Get into your shooting stance behind the cue ball and take look at this extra ball.  Remember, this is where the cue ball needs to end up.

Figure 3

The third step is to remove the extra ball.  Now get down into your shooting stance again, and pretend the extra ball is still there.  (See Figure 4)  In your mind, the extra ball has now become the “Ghost Ball.”  The objective is to aim through the center of the cue ball and shoot directly at the center of the ghost ball.  If you shoot the cue ball directly at the center of the ghost ball, the object ball will go into the pocket.

Figure 4

Now you need to perform this exercise several times.  (See Figure 5)  As with any skill, it will take many repetitions before you get really good at it.  As you practice, you will get better and better at seeing the ghost ball, and your shot making percentages will go up.  To enhance your shooting skills, you can also change the angle of the shot, just keep in mind that the same steps above always apply.  Does the ghost ball aiming method always give the correct aiming point?  No, it is not.  In certain situations, such as shots that require extremely thin cuts, adjustments will need to be made to the aiming point; however, for the majority of shots that you take, this is a very good aiming method.

Figure 5

If you’d like to see a ‘live’ demonstration of the ghost ball aiming method, I’ve located a video clip from the Colorado State Mechanical Engineering Department that illustrates the method .  If you are interested, take a look. Tomorrow, I will share a drill with you that will pave the foundation for improving the most neglected pool playing skill, to ability to control the distance the cue ball travels after a shot.  Until then, practice the ghost ball aiming method, and happy shooting!

## The Seven Day Miracle: Part 1 of 7

Mr. Miyagi

Do you remember the movie The Karate Kid?  In it, a teenager named Daniel is trying to learn Karate from Mr. Miyagi.  Mr. Miyagi takes an unconventional approach to training: instead of teaching Karate directly to Daniel, he breaks it down into a few critical skills, then focuses on each until it is mastered.  In one scene, Mr. Miyagi hands Daniel a set of wooden sanding blocks and tells Daniel to sand his entire deck.  He tells Daniel to use a circular motion: “Wax on, Wax off.”  At first, Daniel thought that Mr. Miyagi was just using him to get work done around the house.  In actuality, Mr. Miyagi was utilizing Daniel’s focused efforts to build Myelin and reinforce the proper techniques that would allow him to excel in competition.  This approach is very similar to the approach discussed by Daniel Coyle in his book The Talent Code.  Now, for the first time, I will apply the same approach to the game of pool.  Over the next few days I will present to you the few critical skills of pool that, if mastered, are guaranteed to take your game to the next level.

Tomorrow I will start with part two of this series titled The Ghost Ball, in which I discuss the Ghost Ball aiming method.  This is one of the simplest methods for determining the precise place to aim in order to hit an object ball into a pocket.  In part 3, Calibrating Your Arm, I will describe the process you need to follow in order to develop the ability to precisely control the distance a cue ball travels after you make a shot.  This is a skill that very few players practice, which is fascinating to me because it plays such a crucial role in your ability to run the table.  More than any other, mastering this one simple skill will lead to huge improvements in your game.  On Wednesday we will cover part 4, The Angle of Deflection.  In this part I reveal to you the answer to one of pools greatest mysteries:  How does a player determine the exact angle at which the cue ball will deflect after it collides with an object ball?  In part 5, The Angle of Reflection, I will share with you a concept borrowed from classical physics that allows you to predict the path a cue ball will take after it hits a rail and rolls around the table.  On Friday I’ll cover part 6, Speed after Collision. In this part I will show you how to apply the concepts presented in Part 3 of this series, and we will determine the exact speed you need to give the cue ball in order to move it around the table and stop it exactly where you want it to stop.  Next Saturday I will present the final part of this series, Putting it together. In this part I will review all the concepts presented, and then I’ll show you how to bring it all together and take your game to the next level.

So there it is dear reader.  Over the next week, I’m going to ask you to step up to the proverbial fire hydrant and open your mouth as wide as you can.  Once you are in position, I’ll turn the lever and then LOOK OUT!  Even if you only catch 10% of the information I’m going to share, it should be enough to take your game up a notch or two.  So batten down the hatches, sit back, and prepare for one heck of a ride!