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STAMP: A shot-type-aware areal multilevel Poisson model for league-wide comparison of basketball shot charts

Kazuhiro Yamada, Keisuke Fujii

Abstract

Shooting location is a core indicator of offensive style in invasion sports. Existing basketball shot-chart analyses often use spatial information for descriptive visualization, location-based efficiency modeling, or clustering players into shooting archetypes, yet few studies provide a unified framework for fair comparison of shot-type-specific tendencies. We propose the shot-type-aware areal multilevel Poisson (STAMP) model, which jointly models team-level field-goal attempts across predefined court regions, seasons, and shot types using a Poisson likelihood with a possession-based exposure offset. The hierarchical random-effects structure combines team, area, team-area, and team-side random effects with shot-type-specific random slopes for key shot categories. We fit the model using approximate Bayesian inference via the Integrated Nested Laplace Approximation (INLA), enabling efficient analysis of more than $3\times 10^{5}$ shots from two seasons of B.LEAGUE (the men's professional basketball league in Japan). The STAMP model achieves better out-of-sample predictive performance than simpler baselines, yielding interpretable relative-rate maps and left-right bias summaries. Case studies illustrate how the model reveals team-specific spatial tendencies for comparative analysis, and we discuss its limitations and potential extensions.

STAMP: A shot-type-aware areal multilevel Poisson model for league-wide comparison of basketball shot charts

Abstract

Shooting location is a core indicator of offensive style in invasion sports. Existing basketball shot-chart analyses often use spatial information for descriptive visualization, location-based efficiency modeling, or clustering players into shooting archetypes, yet few studies provide a unified framework for fair comparison of shot-type-specific tendencies. We propose the shot-type-aware areal multilevel Poisson (STAMP) model, which jointly models team-level field-goal attempts across predefined court regions, seasons, and shot types using a Poisson likelihood with a possession-based exposure offset. The hierarchical random-effects structure combines team, area, team-area, and team-side random effects with shot-type-specific random slopes for key shot categories. We fit the model using approximate Bayesian inference via the Integrated Nested Laplace Approximation (INLA), enabling efficient analysis of more than shots from two seasons of B.LEAGUE (the men's professional basketball league in Japan). The STAMP model achieves better out-of-sample predictive performance than simpler baselines, yielding interpretable relative-rate maps and left-right bias summaries. Case studies illustrate how the model reveals team-specific spatial tendencies for comparative analysis, and we discuss its limitations and potential extensions.
Paper Structure (22 sections, 16 equations, 4 figures, 2 tables)

This paper contains 22 sections, 16 equations, 4 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Results
  3. Dataset
  4. Predictive performance of STAMP model
  5. Spatial patterns and interpretation
  6. Extended team-level slopes
  7. Discussion
  8. Summary and practical implications
  9. Methodological implications and robustness
  10. Limitations and future directions
  11. Methods
  12. Proposed model: shot-type-aware areal multilevel Poisson (STAMP) model
  13. Likelihood and linear predictor
  14. Priors for random effects and hyperparameters
  15. Prior specification and prior predictive checks
  16. ...and 7 more sections

Figures (4)

  • Figure 1: Half-court area divisions; 1: under basket, 2: in the paint, 3: inside right wing, 4: inside right, 5: inside center, 6: inside left, 7: inside left wing, 8: outside right wing, 9: outside right, 10: outside center, 11: outside left, 12: out side leftwing, 13: backcourt.
  • Figure 2: Left-right asymmetry caterpillar plot. The horizontal axis shows the logarithm of the ratio of relative occurrence rates between right and left (aggregated for each team using the geometric mean over the season; values closer to the left indicate a bias toward the left side). The dashed line indicates no left-right bias, the points represent the estimated values, and the horizontal bars represent the approximate 95% confidence interval.
  • Figure 3: Area-specific relative appearance trends for the Utsunomiya Brex in the 2024-25 season (Left: jump_shot, Right: step_pull); side scaling applied. Colors and labels represent team-level percentiles (pXX), with larger values and brighter colors indicating relatively more frequent occurrences.
  • Figure 4: Area-specific relative appearance trends for the Nagoya Diamond Dolphins in the two seasons (left: 2023--24 season, right: 2024--25 season); side scaling applied. Colors and labels represent team-level percentiles (pXX), with larger values and brighter colors indicating relatively more frequent occurrences.