Gender comparison in consistency in the basketball free throw by an event-driven approach

Abstract

This paper compares the free-throw performance of men and women in the National Collegiate Athletic Association (NCAA), taking into account differences in ball size, ball stiffness, and release height. Although some claim that men are more athletic, based on the assumption that athleticism correlates with physical traits, the average free-throw percentages in NCAA Division 1 basketball have been close for decades and across gender. The larger men’s basketball could create a disadvantage for men. On the other hand, the stiffer women’s basketball could create a disadvantage for women. In addition, women typically launch the ball from a lower height above the floor than men do. Therefore, the question of which gender is more consistent was unanswered. To answer this question, we turned to simulations of basketball trajectories. We patched together closed-form trajectory events that terminate at the front rim, back rim, backboard, and a fictitious plane below the ring. This produced what we call speed lines. Using the speed lines and NCAA average free-throw percentages, the consistencies of men- and women-free throws were determined. Examination of the speed lines reveals that they exhibit fractal-like behavior. We analyzed sensitivities with respect to ball size, ball bounce, and release height. We found that the most influential factor in determining free-throw success is the average release height of a gender. Under the stipulated assumptions, this paper found that women are about 3% more consistent than men are.