Analysis of Professional Basketball Field Goal Attempts via a Bayesian Matrix Clustering Approach

Abstract

We propose a Bayesian nonparametric matrix clustering approach to analyze the latent heterogeneity structure in the shot selection data collected from professional basketball players in the National Basketball Association (NBA). The proposed method adopts a mixture of finite mixtures framework and fully uses the spatial information via a mixture of matrix normal distribution representation. We propose an efficient Markov chain Monte Carlo algorithm for posterior sampling that allows simultaneous inference on both the number of clusters and the cluster configurations. We also establish large-sample convergence properties for the posterior distribution. The compelling empirical performance of the proposed method is demonstrated via simulation studies and an application to shot chart data from selected players in the NBAs 2017–2018 regular season. Supplementary materials for this article are available online.

Keywords:

• Basketball shot chart
• Bayesian nonparametrics
• Matrix data
• Mixture of finite mixtures
• Model-based clustering

Supplementary Materials

Technical details about the posterior derivation, proof of theorems, additional numerical results are provided in the Online Supplementary Materials. R code and the data for the computations of this work are available at https://github.com/fyin-stats/MFM-MxN.

Acknowledgments

The authors thank Dr. Yishu Xue and Dr. Hou-Cheng Yang for providing the organized data which include the raw shot charts and estimated intensity maps via INLA and R code for data visualization. The authors also thank the reviewers for their helpful comments.

Notes

1 Similar to that of MFM-MxN, we use Dahl’s method for identifying a representative draw for estimating the number of clusters.

Additional information

Funding

Shen’s research is partially supported by Simons Foundation Award 512620.