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:
- Use a half ball hit on the object ball
- Hit the cue ball with normal ‘running’ English
- 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!
Angle of Reflection 
This is a truly excellent post. I’ve read lots of books and articles on pool, but I don’t ever remember anyone laying it all out so well in a single place. You put it all together perfectly. Bravo.
Thanks John, I appreciate your feedback. I’m glad you are enjoying the blog. Let me know if you have any suggestions.
It’s a lot to think about when approaching even this simple shot example you give. Math is not my strong suit. I have a feeling that either 1) I’d screw up the math calculations 2) or take way to long to figure it all out and my opponent will be screaming ‘delay of game’ at me as I try to calculate all the variables.
Given the method, have you found that making it work for you becomes easier (i.e. you can calculate all the variables fairly quickly) with continued use? Seems to me it would have to become close to second nature to be really useful, particularly under pressure of competition.
You are correct…that’s a lot to think about. The approach I outlined in the post, although technically correct, is not usually necessary in practice. Well, let me qualify my response. If you are a complete beginner (i.e. have never picked up a cue stick), and you LIKE math and geometry, then this approach will work for you. Most people would rather have their fingernails pried off with a pair of pliers than to face a math problem. Professional players included. So, fear not, you actually don’t have to do the math. I’m an odd bird in that I like math, but it gives me no advantage over my opponents. I’m certainly no professional, nor am I a beginner. Here’s what I actually do on shots like this: (1) Recognize that I have to make the stripe in the corner pocket and somehome get to the other end of the table [pretty obvious]. (2) Recognize that the most predictable shot is the half ball hit and I know from experience what the cue ball path looks like from a half ball hit (this YOU need to drill into your head! Remember the “peace” sign to “see” the angle the cueball takes after collision with the object ball). (3) Recognize that I got very lucky with this particular layout, because the natural extension of the half ball hit naturally goes down the table with no interfering balls. [I can assess this almost instantly based on my experience. It may take you a little longer to “see” the extended path in your head, but you can do it. There’s no math involved.] (4) Now I just hit the shot with the correct speed. [I know, I know, based on my experience, my “brain arm system” just knows what to do.] This can only be learned with experience. You know not to hit it too soft or it won’t get down table, but also you don’t want to hit it too hard or it will go down table and come back up. Distance control is the toughest skill to master because it’s based on “feel”. The reason pros are so good, and they make everything look so easy, is because they have excellent distance control. Hope this helps!
BTW, I will be posting some distance control drills later this week. Stay tuned.
One thing I’m not quite sure why you say the distance to A is ~10 diamonds. I am new so maybe I’m conting wrong but I count 9 at the most. does hitting a rail count as a diamond?
Hi Dave, very good question; the confusion was my fault. When I said that point ‘A’ was 10 diamonds away, I was thinking more in terms of the actual distance traveled by the cue ball. I wasn’t actually counting the diamonds around the edge of the table. I guess I should have explained this better. On a nine foot table, the distance between diamonds is a little bit more than a foot (it’s about 13 inches). I was looking at the actual travel distance of the cue ball and estimating it would travel about 13 feet to point A since it’s traveling both horizontally and vertically down the table. What I was trying to do is then compare this distance back to the ‘arm calibration’ exercise, so in essence you would need to hit the cue ball with the speed necessary to make it travel 10 diamonds. I hope this clarifies.