Application of Monte Carlo simulations to improve basketball shooting strategy

摘要

The underlying physics of basketball shooting seems to be a straightforward example of Newtonian mechanics that can easily be traced by using numerical methods. However, a human basketball player does not make use of all the possible basketball trajectories. Instead, a basketball player will build up a database of successful shots and select the trajectory that has the greatest tolerance to the small variations of the real world. We simulate the basketball player's shooting training as a Monte Carlo sequence to build optimal shooting strategies, such as the launch speed and angle of the basketball, and whether to take a direct shot or a bank shot, as a function of the player's court position and height. The phase-space volume Omega that belongs to the successful launch velocities generated by Monte Carlo simulations is then used as the criterion to optimize a shooting strategy that incorporates not only mechanical, but also human, factors.