This article introduces an event–driven approach for high performance computing of the nonlinear trajectory of a basketball. The high-performance approach differs from the analytical approach of finding exact solutions to the basketball shot, which only applies to special cases, and it differs from the time-stepping approach, which only approximates the solutions to the basketball shot. This paper shows that the event-driven approach is computationally faster than the time-stepping approach while being exact—overcoming the disadvantages of the traditional approaches. Furthermore, the event-driven approach's faster computational speed and robust generality is necessary when running millions of simulations, and it is therefore necessary, too, for the analysis of the performance of a player or a shot. Indeed, the event-driven approach will be able to provide a deeper understanding of player and shot performance in the game of basketball. In the event-driven approach, a basketball undergoes a trajectory segment, which ends in a collision with one of a number of possible bodies. The simulation determines automatically the otherwise unknown sequence of collisions. The simulation advances from one trajectory segment to the next, each separated by a collision, until the ball finally falls to the ground. The article contains illustrative examples and provides an easy-to-use MATLAB code.