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A Bayesian marked spatial point processes model for basketball shot chart

Author

Listed:
  • Jiao Jieying
  • Hu Guanyu
  • Yan Jun

    (Department of Statistics, University of Connecticut, Storrs, CT, 06269, USA)

Abstract

The success rate of a basketball shot may be higher at locations where a player makes more shots. For a marked spatial point process, this means that the mark and the intensity are associated. We propose a Bayesian joint model for the mark and the intensity of marked point processes, where the intensity is incorporated in the mark model as a covariate. Inferences are done with a Markov chain Monte Carlo algorithm. Two Bayesian model comparison criteria, the Deviance Information Criterion and the Logarithm of the Pseudo-Marginal Likelihood, were used to assess the model. The performances of the proposed methods were examined in extensive simulation studies. The proposed methods were applied to the shot charts of four players (Curry, Harden, Durant, and James) in the 2017–2018 regular season of the National Basketball Association to analyze their shot intensity in the field and the field goal percentage in detail. Application to the top 50 most frequent shooters in the season suggests that the field goal percentage and the shot intensity are positively associated for a majority of the players. The fitted parameters were used as inputs in a secondary analysis to cluster the players into different groups.

Suggested Citation

  • Jiao Jieying & Hu Guanyu & Yan Jun, 2021. "A Bayesian marked spatial point processes model for basketball shot chart," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 17(2), pages 77-90, June.
    • Handle: RePEc:bpj:jqsprt:v:17:y:2021:i:2:p:77-90:n:2
    DOI: 10.1515/jqas-2019-0106
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    References listed on IDEAS

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    1. Brian Skinner, 2012. "The Problem of Shot Selection in Basketball," PLOS ONE, Public Library of Science, vol. 7(1), pages 1-8, January.
    2. Jeffrey W. Miller & Matthew T. Harrison, 2018. "Mixture Models With a Prior on the Number of Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(521), pages 340-356, January.
    3. Baddeley, Adrian & Turner, Rolf, 2005. "spatstat: An R Package for Analyzing Spatial Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i06).
    4. Ho, Lai Ping & Stoyan, D., 2008. "Modelling marked point patterns by intensity-marked Cox processes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1194-1199, August.
    5. Fionn Murtagh & Pierre Legendre, 2014. "Ward’s Hierarchical Agglomerative Clustering Method: Which Algorithms Implement Ward’s Criterion?," Journal of Classification, Springer;The Classification Society, vol. 31(3), pages 274-295, October.
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