Why Some Pool Shots are More Difficult Than Others

The physics behind the game of billiards is rather well understood as is our grasp of classical mechanics. We present here a mathematical explanation of why slice shots are more difficult than direct shots. Despite a large number of treatises dedicated to the study of physics of billiards, it appears that the simple explanation has escaped our attention until now. We show that high impact-parameter shots impart a larger angular spread to the object ball, compared to head-on shots. The effect can be understood in terms of a non-linear relationship between the impact parameter and the scattering angle, and the fact that a real-world pool player does not have a perfect cue ball control; in other words, the impact parameter distribution is not a delta function, but has a finite spread. To keep the mathematics simple and not to obscure the underlying physical principles our treatment ignores the ball's spin, friction, and other well-known effects in the game of pool.