Estimating winning percentage of the fourth quarter in close NBA games using Bayesian logistic modeling
Bibliographic record
Abstract
This study examined the fourth quarters in the close games in the regular NBA games in the last decade, ranging from the 2013-14 season to the 2022-2023 season. A close game is categorically defined by a scenario where the point differential is confined within a 10-point margin at the onset of the fourth quarter and narrows further to a 5-point disparity by the end of the game. In total, 2,295 close games were identified in this study. Advanced game statistics, including offensive rate, defensive rate, assistance ratio, pace of game, and true shooting percentage, etc., are obtained from the NBA box scores using a python script. Understanding key factors that determine the outcome of the basketball games is critical, as such can be used to develop predictive models for coaches to design game strategies. This study developed a Bayesian Logistic Modeling approach to estimate the winning probability of a basketball team in the fourth quarter, using the pace of the last quarter and a team's shooting percentage. The accuracy of the model is used to evaluate if the model can correctly classify game outcome based on the identified game statistics in the fourth quarter of a game. The binary outcome of the close game is modeled as a Bernoulli distribution. Results reveal that the True Positive Rate and False Positive Rate is 0.93 and 0.07, respectively. Insights from this study can be used to help design coaching strategies in basketball games, illuminating potential tactical pivots that could tilt the game in their favor.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".