A Multiresolution Stochastic Process Model for Predicting Basketball Possession Outcomes

ABSTRACT

Basketball games evolve continuously in space and time as players constantly interact with their teammates, the opposing team, and the ball. However, current analyses of basketball outcomes rely on discretized summaries of the game that reduce such interactions to tallies of points, assists, and similar events. In this article, we propose a framework for using optical player tracking data to estimate, in real time, the expected number of points obtained by the end of a possession. This quantity, called expected possession value (EPV), derives from a stochastic process model for the evolution of a basketball possession. We model this process at multiple levels of resolution, differentiating between continuous, infinitesimal movements of players, and discrete events such as shot attempts and turnovers. Transition kernels are estimated using hierarchical spatiotemporal models that share information across players while remaining computationally tractable on very large data sets. In addition to estimating EPV, these models reveal novel insights on players’ decision-making tendencies as a function of their spatial strategy. In the supplementary material, we provide a data sample and R code for further exploration of our model and its results.

Keywords:

• Competing risks
• Gaussian process
• Optical tracking data
• Spatiotemporal model

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Supplementary materials

• EPVDemo.zip: Directory containing a one game sample of optical tracking data (csv), along with R code for visualizing model results and reproducing EPV calculations. Precomputed results of computationally intensive steps are also included as Rdata files, and can be loaded to save time and resources. A reproducible knitr tutorial, EPV_demo.Rnw, introduces the data and demonstrates core code functionality. (ZIP archive)

  This directory is a copy of the EPVDemo GitHub repository, maintained at the first author’s GitHub page.

Acknowledgement

The authors would like to thank Alex Franks, Andrew Miller, Carl Morris, Natesh Pillai, and Edoardo Airoldi for helpful comments, as well as STATS LLC in partnership with the NBA for providing the optical tracking data. The computations in this article were run on the Odyssey cluster supported by the FAS Division of Science, Research Computing Group at Harvard University.

Notes

1 Our data include foul events, but do not specify the type or circumstances of the foul. There are several types of fouls and game situations for which fouls lead to free throws—for instance, shooting fouls, technical/flagrant fouls, clear path fouls, and fouls during the fouling team’s “bonus” period; thus, modeling fouls presents additional complications relative to the other events we model in our EPV model. While drawing fouls can be a valuable and important part of team strategy, we omit modeling such behavior in this article.

2 The time of a possession is bounded, even for pathological examples, by the 12-min length of a quarter; yet we do not leverage this fact and simply assume that possession lengths are almost surely finite.

3 The reason we index transition states by the origin of the pass/shot attempt (and destination of the pass) is to preserve this information under a Markov assumption, where generic “pass” or “shot” states would inappropriately allow future states to be independent of the players involved in the shot or pass.

4 Full details on all covariates used for all macrotransition types are included in the online Appendix A.1.

5 Our rebounding model could be improved by using full-resolution spatiotemporal information, as players’ reactions to the missed shot event are informative of who obtains the rebound.