Meta-analytics: tools for understanding the statistical properties of sports metrics
Bibliographic record
Abstract
Abstract In sports, there is a constant effort to improve metrics that assess player ability, but there has been almost no effort to quantify and compare existing metrics. Any individual making a management, coaching, or gambling decision is quickly overwhelmed with hundreds of statistics. We address this problem by proposing a set of “meta-metrics”, which can be used to identify the metrics that provide the most unique and reliable information for decision-makers. Specifically, we develop methods to evaluate metrics based on three criteria: (1) stability: does the metric measure the same thing over time (2) discrimination: does the metric differentiate between players and (3) independence: does the metric provide new information? Our methods are easy to implement and widely applicable so they should be of interest to the broader sports community. We demonstrate our methods in analyses of both NBA and NHL metrics. Our results indicate the most reliable metrics and highlight how they should be used by sports analysts. The meta-metrics also provide useful insights about how to best construct new metrics that provide independent and reliable information about athletes.
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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 | 0.028 | 0.172 |
| Meta-epidemiology (narrow) | 0.003 | 0.002 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.021 | 0.012 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.008 | 0.013 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| 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".