A Bayesian Negative Binomial-Bernoulli Model with Tensor Decomposition: Application to Jointly Analyzing Shot Attempts and Shot Successes in Basketball Games
Pub. online: 9 July 2025
Type: Data Science In Action
Open Access
Open Access
Received
17 September 2024
17 September 2024
Accepted
30 June 2025
30 June 2025
Published
9 July 2025
9 July 2025
Abstract
We propose a Bayesian Negative Binomial-Bernoulli model to jointly analyze the patterns behind field goal attempts and the factors influencing shot success. We apply nonnegative CANDECOMP/PARAFAC tensor decomposition to study shot patterns and use logistic regression to predict successful shots. To maintain the conditional conjugacy of the model, we employ a double Pólya-Gamma data augmentation scheme and devise an efficient variational inference algorithm for estimation. The model is applied to shot chart data from the National Basketball Association, focusing on the regular seasons from 2015–16 to 2022–23. We consistently identify three latent features in shot patterns across all seasons and verify a popular claim from recent years about the increasing importance of three-point shots. Additionally, we find that the home court advantage in field goal accuracy disappears in the 2020–21 regular season, which was the only full season under strict COVID-19 crowd control, aside from the short bubble period in 2019–20. This finding contributes to the literature on the influence of crowd effects on home advantage in basketball games.
Supplementary material
Supplementary MaterialWe have included a supplementary section about the details of the Pólya-Gamma augmentation, the variational EM algorithm outlined in Section 3, and more graphs for the empirical analysis. The codes for downloading the shot chart data and for generating the major results are included in https://github.com/kwho1/NBA_JDS.
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