Ball path curvature and in-game free throw shooting proficiency in the National Basketball Association

TL;DR

This study analyzes how the curvature of the ball's path during free throws relates to shooting success in the NBA, finding that less curvature at the end of the shot correlates with better performance.

Contribution

It introduces a quantitative method to measure ball path smoothness using Bezier curves and identifies the importance of terminal curvature in shooting proficiency.

Findings

Lower terminal curvature is associated with higher free throw accuracy.

Terminal curvature explains more variance in performance than maximum curvature.

Focusing on end-of-shot smoothness may improve coaching strategies.

Abstract

Basketball shooting coaches agree that smoother shooting motions are better, but there is less agreement about what "smooth" means quantitatively or what part of the shooting motion needs to be smooth. Using ball tracking data from the 2023-2024 National Basketball Association regular season, we explore the relationship between ball path curvature and free throw shooting performance. We fit B\'ezier curves to the ball tracking data in the sagittal plane and test different methods of calculating path curvature. We find that both max curvature and terminal curvature are negatively associated with shooting performance, but terminal curvature explains much more of the between-player variance in free throw shooting performance. This suggests that shooting coaches would be better off focusing on the smoothness at the end of the shot rather than at the beginning of the forward motion of the ball.