Can the hot hand phenomenon be modelled? A Bayesian hidden Markov approach
Bibliographic record
Abstract
Abstract Sports data analytics has been gaining importance over recent years as an essential topic in applied statistics. Specifically, basketball has emerged as one of the iconic sports where the use and immediate collection of data have become widespread. Within this domain, the hot hand phenomenon has sparked a significant scientific controversy, with sceptics claiming its non-existence while other authors provide evidence for it. We propose a Bayesian longitudinal hidden Markov model that examines the hot hand phenomenon in consecutive shots of a basketball team, each of which can be either missed or made. We assume two states (cold or hot) in the hidden Markov chains associated with each math and model the probability of success for each shot with regard the hidden state, the random effects related the match, and the covariates. This model is applied to real data sets of three teams from the USA National Basketball Association: the Miami Heat team and the Toronto Raptors team in the 2005–2006 season, and the Chicago Bulls in the 2022–2023 season. We show that this model is a powerful tool for assessing the overall performance of a team during a game and, in particular, for quantifying the magnitude of team streaks in probabilistic terms.
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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 | 0.006 | 0.021 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.005 | 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".