A Markov Game model for valuing player actions in ice hockey
Bibliographic record
Abstract
Evaluating player actions is very important for general managers and coaches in the National Hockey League.Researchers have developed a variety of advanced statistics to assist general managers and coaches in evaluating player actions.These advanced statistics fail to account for the context in which an action occurs or to look ahead to the long-term effects of an action.I apply the Markov Game formalism to play-by-play events recorded in the National Hockey League to develop a novel approach to valuing player actions.The Markov Game formalism incorporates context and lookahead across play-byplay sequences.A dynamic programming algorithm for value iteration learns the values of Q-functions in different states of the Markov Game model.These Q-values quantify the impact of actions on goal scoring, receiving penalties, and winning games.Learning is based on a massive dataset that contains over 2.8 million events in the National Hockey League.The impact of player actions varies widely depending on the context, with possible positive and negative effects for the same action.My results show using context features and lookahead makes a substantial difference to the action impact scores.Accounting for context and lookahead also increases the information in the model.Players are ranked according to the aggregate impact of their actions, and compared with previous player metrics, such as plus-minus, total points, and salary, as well as recent advanced statistics metrics.
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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 | 0.003 | 0.012 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.007 | 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".