A Bayesian regression approach to handicapping tennis players based on a rating system
Bibliographic record
Abstract
Abstract This paper builds on a recently developed Markov Decision Process-based (MDP) handicap system for tennis, which aims to make amateur matches more competitive. The system gives points to the weaker player based on skill difference, which is measured by the point-win probability. However, estimating point-win probabilities at the amateur level is challenging since point-level data is generally only available at the professional level. On the other hand, tennis rating systems are widely used and provide an estimate of the difference in ability between players, but a rigorous determination of handicap using rating systems is lacking. Therefore, our goal is to develop a mapping between the Universal Tennis Rating (UTR) system and the MDP-based handicaps, so that two amateur players can determine an appropriate handicap for their match based only on their UTRs. We first develop and validate an approach to extract server-independent point-win probabilities from match scores. Then, we show how to map server-independent point-win probabilities to server-specific point-win probabilities. Finally, we use the estimated probabilities to produce handicaps via the MDP model, which are regressed against UTR differences between pairs of players. We conclude with thoughts on how a handicap system could be implemented in practice.
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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 | 0.005 | 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 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.008 | 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".