Sports Situations - Physics Analysis

Aspects of Physics are EVERYWHERE in sports and games!

Pool or Pocket Billiards

During my College days, I happened to learn to play pool at virtually the same time that a Professor of mine was regularly using billiard balls in his many examples of interactions between atoms. He would prove some Physics concept, such as Newton's conservation of momentum, and he would describe the geometry of the result. For example, that Principle REQUIRES that the cue ball and the object ball ALWAYS travel off at exactly a 90° angle from each other. This bit of news was incredibly useful as I was learning to play pool! Most pool players generally have to "guess" what direction each ball will go, and they become decent pool players only after having watched what happens after thousands of shots! Physics makes it possible to bypass that whole learning curve! As it happened, within just a few weeks of having first picked up a pool cue, I could easily win the vast majority of games! Cool!

Another pool-related subject that Professor described was regarding a characteristic called "spin" in atoms. Again, he used billiard balls as examples. In this case, in addition to the conservation of (linear) momentum mentioned above, there is also a Principle that requires conservation of angular momentum. In simpler terms, however much spinning energy existed in the approaching cue ball (and some direction stuff, too), the combination of the spin in the balls when they leave must still be the same. So, when a player puts "draw" (backspin) or sidespin on the cue ball, the exiting balls are affected, by each having some amount (and direction) of spin. So it is actually possible to PLAN that either the object ball or the cue ball will have a desired type of spin after the collision! Few pool players are even aware of this, except for the professionals. There are situations where it is very handy to know how to do that!

Yet another pool-related subject is that such collisions must always Conserve Energy (The first Law of Thermodynamics) By looking at the geometry of the balls involved, and what you desire to happen, it is generally pretty easy to figure out how much power (linear momentum and energy) and what kind of English (angular momentum and energy) that you need to give the cue ball! With these simple Physics insights, the game becomes MUCH easier! By applying spin (of almost any kind) to the cue ball, it is even possible to slightly alter that 90° angle rule mentioned above, in order to still comply with these various Principles of Physics.

And if you put draw (backspin) on the cue ball and hit an object ball straight on, that ball will then have "follow" (topspin) and also a slightly greater speed! In exploring these things, I had discovered that if THAT ball hits another straight on, it then has some backspin, and if THAT ball hits a fourth ball, a noticeable amount of follow (topspin) is present. Beyond that, I could never see any noticeable transfer of spin, mostly because the balls slip a little in their contact with each other.

In any case, within a month of first picking up a pool cue, three EXTREMELY talented pool shooters, and ESPECIALLY one of them, chose to "take me under their wings" because they said they saw potential in me. They taught me some truly amazing things. By then, I had convinced my parents to buy an old used pool table (for $75), so I had a place to practice. I vividly remember one "lesson" one of them gave me! I was to stand at the head of the table, with no balls on the table except the cue ball. I was to stroke it hard toward the cushion at the foot of the table, and then immediately place my cupped left hand just above my left shoulder. He insisted that I make the ball loft from the table (due to very strong topspin) and land in my hand, without my having to move my hand more than a couple inches in any direction. I stared at him as though he was crazy! Then he demonstrated it to me. Before the cue ball even hit the cushion at the foot of the table, he had already placed his hand up over his shoulder. Moments later, the flying cue ball plopped into his hand! I WAS impressed!

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I spent many hours practicing doing that, thousands of attempts. Eventually, I came to understand what he wanted me to learn, the specific details necessary, and the extreme care needed to accomplish it. Two weeks later, I told him I was ready to try to do it for him. This was a different pool table than I had been practicing on, and the first time I tried it I had to reach to catch the ball. But the second time went perfectly!

That lesson, and others, caused me to have unlimited respect for his knowledge and experience, and for the Principles of Physics.

One of the most important and valuable lessons he taught me was where he handed me a small scrap of paper just before we played a scrimmage game. He wanted to get me to realize how important it is to KNOW where the cue ball would end up AFTER each shot, and so he insisted that I put the small scrap of paper on the table and that the cue ball was to stop, within three inches of it, after EVERY shot. Forever after that, people were always mystified as I stood there staring at the table for several seconds before every shot. They usually thought I was trying to figure out how to MAKE (simple) shots, but I always used those few seconds to DECIDE where I WANTED the cue ball to end up.

During my playing life, most of the people I played against spent every day, all day, shooting pool, so they were all impressive shot-makers. When I realized that my opponent had such skills, I knew that I did NOT want him to have any easy shot! So, if I did not think I was going to make the current shot, I would concentrate on making the cue ball end up in the worst possible place! I rarely ever lost any game, and many of the victims could not understand how or why I would win every game from them! Many simply said that I was the LUCKIEST pool player ever! I would smile at that! It was FINE that such opponents thought I was lucky rather than skilled! And they would often get VERY frustrated at ALWAYS having the cue ball against a rail and behind some obstacle, shot after shot after shot. It was ALL due to that little scrap of paper that I was required to use early on!

(As a side note, those three individuals each paid for their entire College education by gambling on pool. Actually, for them it wasn't really gambling at all, and they always managed to win all games where significant money was involved. After I saw one of them make a blunder and actually lose a game (on which there were just a few dollars riding), in private he explained that it was sometimes "necessary" to lose in order to keep opponents interested and optimistic! I always wondered if that would have been considered a SCAM since it was always totally based on their amazing skill levels! Of course, at that time, all gambling was illegal, anyway!)

If you happen to be familiar with 9-ball, a favorite game for gamblers, you might enjoy the following anecdote. One day, one of the three who was practicing with me (teaching, actually) mentioned that he wanted to go over to the Student Union, because a student from Georgetown University was flying in to play 9-ball with our friend. I thought that somewhat peculiar, for a student during a school day, to fly halfway across the country just to entertain himself playing pool. Shows how naive I am!

If most people gamble on 9-ball, it is for either 25 cents or a dollar, when the nine ball is sunk and the game ends. They used a variation, where a value was placed on when the 1-ball was sunk ($100), when the 5-ball was sunk ($200) and when the 9-ball was sunk ($300). Both of these guys were so good that if some ball was pocketed on the break, they would invariably run the table. That's $600 in what I determined to regularly be around 45 seconds! If NO ball was sunk on the break, the OTHER guy then ran the table. We were standing 20 feet away, to not interfere or distract either of them, but MY knees were shaking! For a while, I tried to keep track of a running total, and I was pretty convinced that my friend was up at least $6,000 within half an hour! (Where do college kids get that kind of money???) The other guy started to do better, and eventually, I had the impression that my friend had around $3,000 extra after a couple hours of playing pool!

I never gambled, before or after or ever, but my friends often told me that if I wanted, I could also pay for my College tuition and expenses by gambling on pool. It was nice for my ego, but I would never have done that!

Getting back to the point at hand:
Since I understand the Physics behind all the things that happen on a pool table, my level of being able to win has always been pretty consistent. Once, after not picked up a cue for around five years, a recent friend was bragging about never losing! He spent at least six hours every single day shooting pool, and he had become very familiar with the game. But I was pretty sure that he did not understand the Physics involved. So I asked if he would play me a game some time. His response was sort of a joke, as he thought that NO ONE could beat him, but he humored me and we met to play.

I wasn't sure what to expect, since I hadn't even been near a pool table for five years, and this was a guy who probably slept on one! But he agreed. When we began, he was mystified why I would often spend 30 seconds studying the table before each shot. But, being uncertain of whether I could make many shots, I was trying to use Physics to know where the cue ball would go! If I had some really easy shot, I took it, but generally, instead of trying a more difficult shot, I would instead make sure to leave the cue ball in some horrendous location! Half a dozen of his friends were around, in that bar, expecting to see their hero squish another victim. By halfway through the game, I could hear them whispering about how incredibly unlucky their friend was, at never having a clear shot at anything! I happened to win that game, apparently the first game he had lost in months! But, since he and his friends were absolutely sure that it had been a fluke, that I only won because he had had such terrible luck, a rematch was immediately requested!

Over the next couple hours, we played at least 10 more games, and I happened to win all but one of them. Even after all that, his friends saw no credit for me, but were sure they had just seen the worst run of luck of anyone who has ever lived! My friend sort of realized that I had something to do with it, and later I described to him what my strategy was. His friends were probably right in a way, because they never saw me make a single difficult shot, and rarely many that were anything other than ducks! It's easy to see how they would have thought I was not a very good pool player, because I really wasn't, due to those years of not being around a table. But I was able to apply Physics until the cows came home! My point: Even in that situation of clearly being outmatched on a skill level and a practice level, I wound up winning nearly all the games. By knowing that he could probably run the table if ever given the chance, I knew that my highest priority was to never allow that possibility to happen.

At this moment, after again not touching a pool cue in several years, I am reasonably that Physics would still allow me to be tough to beat for any but professional pool players. In my opinion, Physics therefore ranks above even practice and skill in that game!

Oh, AFTER that run of lucky games, when we were done playing and the table was clear, I decided to shoot the cue ball into a common billiards shot, which is called a five-cushion-natural shot. On a pool table, with pockets, the idea is to cause the cue ball to hit five rails and then sink in a pocket. I suppose I did that mostly because his friends were hooting at him for having such a bad day, and I thought I would let them see that I actually DID have some skills. Of course, the five-rail-natural sank, and they all got deadly quiet! One finally said, NO ONE could do that! So I did it again, and it again sank. I didn't want my friend to be made fun of by his friends, and I thought that when they saw what looks like a very hard shot, they might have realized that I had been around a pool table before! They WERE convinced. But then, NONE of them understood WHY I would never bet on the games, as they realized that I WOULD win. Oh, well, you can't please everyone!

Going back to MY beginnings at (trying) to shoot pool, I sometimes would practice on a very good table in the basement of one of the school dorms. THAT was when the guy who taught me most of pool happened by, and he just sat and watched. About the third day when I was pushing balls around, he still had never said a word. I had started to get cocky, as I was starting to be able to reliably make shots, so I asked if he wanted to play. At that moment, I ONLY knew about 8-ball, but he suggested that we play 14-1 Continuous. He needed to explain to me the rules of that game! AND that we needed to lag for the break. I had already gotten pretty good at lagging, but he left the cue ball within about one-fourth inch of the head rail, so he WON the lag. It mystified me as to why he decided to let me shoot first! I THOUGHT it was because he realized I was a rookie and he was being nice. So I splattered the rack. Then I stood and watched as he sank around 85 balls during his turn (in a game to 150). I think I sank one or two during my turn and then in his SECOND TURN he sank 65 more to win the game. I had only approached the table TWICE, once with the wild break and the other time in my one turn. AFTER the game, he taught me how to "lag well" and also how to call a Safety and make a break shot which actually puts the opponent in an even worse situation. (ALL standard Physics!!) He demonstrated, of course. He placed the cue ball near the side rail, and just clipped the rear corner ball in the rack, with exact precision. That ball rolled to the foot rail and bounced EXACTLY back into its original location, while the other back corner ball rolled to the side rail and also rolled exactly back to where it started. So the rack was essentially perfect again, but he also had the cue ball bounce off two rails and end up RIGHT on the head rail. The opponent then had to try to do a Safety from a VERY difficult position. The result, if this is all done well, is that the opponent unintentionally causes at least one or two balls to come out of the rack, which then results in a really good shooter to sink at least 30 or 50 balls on that turn.

I was NEVER of the skill level of those friends, who each had occasionally sunk the 150 balls or 300 balls of an entire game on one turn. The most I ever sunk in one turn was 56 balls. But since few pool players ever have any idea of where the cue ball will be after their shot, they tend to accidentally snooker themselves where they rarely can even sink five balls in a turn. So, I could never actually compete against my friend's circle of friends (who would never play unless a lot of money was on the game anyway) but I certainly always had at least 99% success against the people who are generally in pool halls and bars!

Pool is SUCH an excellent game for demonstrating Physics and geometry! I HIGHLY recommend it!





This presentation was first placed on the Internet in November 2002.

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C Johnson, Theoretical Physicist, Physics Degree from Univ of Chicago