Markov decision processes with dynamic transition probabilities: An analysis of shooting strategies in basketball
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Bibliographic record
Abstract
In this paper we model basketball plays as episodes from team-specific nonstationary Markov decision processes (MDPs) with shot clock dependent transition probabilities. Bayesian hierarchical models are employed in the modeling and parametrization of the transition probabilities to borrow strength across players and through time. To enable computational feasibility, we combine lineup-specific MDPs into team-average MDPs using a novel transition weighting scheme. Specifically, we derive the dynamics of the team-average process such that the expected transition count for an arbitrary state-pair is equal to the weighted sum of the expected counts of the separate lineup-specific MDPs. We then utilize these nonstationary MDPs in the creation of a basketball play simulator with uncertainty propagated via posterior samples of the model components. After calibration, we simulate seasons both on-policy and under altered policies and explore the net changes in efficiency and production under the alternate policies. Additionally, we discuss the game-theoretic ramifications of testing alternative decision policies.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it