A Spatial Analysis of Basketball Shot Chart Data

• Activity Number: 456
• Type: Contributed
• Date/Time: Wednesday, August 10, 2005 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics in Sports
• Author(s): Brian Reich*+ and Bradley P. Carlin and James Hodges and Adam Reich
• Companies: University of Minnesota and University of Minnesota and University of Minnesota and University of Minnesota
• Keywords: Spatial ; Basketball ; Conditionally ; Autoregressive ; Bayesian

Abstract

In basketball, a common and time-honored statistical summary is the shot chart. This is a spatial representation of every shot attempted by a particular player. While the richness and availability of shot chart data are increasing rapidly, most coaches' sophistication in using such data is not. That is, the charts are used purely as descriptive summaries that show from which parts of the floor various players prefer to shoot and how many of these shots actually go in the basket. But such data also could be used to make valuable inference about a player's shooting tendencies and abilities, and thus offer the potential to dramatically improve a team's ability to defend this player. However, accurate inferences will require a statistical model that incorporates important covariates (both time-varying and not) and acknowledging the obvious spatial association in the data. Our main purpose in this paper is to use hierarchical spatial modeling implemented via now-familiar Markov chain Monte Carlo (MCMC) methods to obtain such inferences. We also want to reflect on their value in the actual practice of coaching. To illustrate our approach, we use the 2003-2004 shot data from Minnesota.