Title: Spatial Analysis of Basketball Shot Charts: an Application to Michael Jordan's 2001-2002

Report No. 03-05

Date: April 2003

Title: Spatial Analysis of Basketball Shot Charts: An Application to Michael Jordan's 2001-2002 NBA Season

Author(s): DeMarc A. Hickson and Lance A. Waller

Abstract

Michael Jordan, one of the greatest sports celebrities of modern times, returned to the game of professional basketball during the 2001-2002 season. Sports commentators suggest that Jordan settles for jump shots instead of penetrating the defense for a lay-up. We utilize spatial point process methods to determine patterns in his shot selection, i.e., where he is most likely to shoot the basketball and/or make a shot given that he takes a shot. Data were obtained from "shot charts" or maps of the location of each shot taken. Non-parametric kernel smoothing methods allow us to estimate the spatial intensity function of made and missed shots and we compare these intensity functions for each game Jordan played. Straightforward adjustments to the cross validation bandwidth selection allow its use with sparse data for games with few shots. Michael Jordan's shooting patterns suggest fairly consistent results throughout the season with areas of better performance (probability of making a shot given one is taken) on the left side of the court (from the baseline to the free throw line) and around the right portion of the free throw line. Areas of poor performance appear in the lane (between the goal and foul line), on the right side of the court (from the baseline to the free throw line) and around the three point arc. Furthermore, he is more likely to make lay-ups/slam dunks and shots taken 14-18 feet from the goal and miss shots taken within 1-9 and beyond 20 feet from the goal (including three point shots). This statistical analysis provides insight into Jordan's shooting patterns, the variation in such patterns across games, and illustrates a tool for the analysis of "shot chart" data in general.

Keywords: cross validation, independent bivariate density, Michael Jordan, non-parametric kernel smoothing, relative risk, spatial point patterns.