On the existence of momentum in professional football
Bibliographic record
Abstract
Using United States National Football League play-by-play data for the 2002-2012 seasons, we train a neural network to predict win probability, based on measures of the game state. This predictor's performance is comparable to the point spread at the start of the game and improves thereafter with little bias. We define a measure of success as the change in a team's win probability over the course of a possession, and show that streaks in this measure are highly unlikely to be random. Further, this finding holds when controlling for the effects of clock management in the fourth quarter of football games, when win probability can increase incrementally for the leading team as the game continues. By defining momentum as an increase in win probability over the course of at least three successive changes in possession, we show some ability to anticipate its emergence, based on game state, using a second neural network. The possibility of using this knowledge for strategic advantage is discussed. We consider these results in the context of examples from National Football League games, including that from Super Bowl LI (Atlanta Falcons versus the New England Patriots), and end with some discussion of future extensions to this work.
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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 | 0.018 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".