Optimal Targets for the Bank Shot in Men's Basketball

The purpose of this study was to gain an understanding of the bank shot and ultimately determine the optimal target points on the backboard for the bank shot in men's basketball. The study used over one million three-dimensional simulations of basketball trajectories. Four launch variables were studied: launch height, launch speed, launch angle, and aim angle. The shooter's statistical characteristics were prescribed to yield a 70 percent free throw when launching the ball seven feet above the ground with 3 Hz of back spin. We found that the shooter can select a bank shot over a direct shot with as much as a 20 percent advantage. The distribution over the court of preferences of the bank shot over the direct shot was determined. It was also shown that there is an aim line on the backboard independent of the shooter's location on the court. We also found that at 3.326 inches behind the backboard, there exists a vertical axis that aids in finding the optimal target point on the backboard. The optimal target point is the crossing of the vertical axis and the aim line that is in the shooter's line of sight.