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.
Appendix
A Additional figures
Posterior distributions of the Bayesian parameters α, β, and σ corresponding to the Bayesian model (Equation (2)). Red area denotes the 80% posterior interval and black curve denotes the 95% posterior interval. The distributions are unimodal and symmetric with low standard deviations.
Posterior distributions of the Bayesian parameters γ and τ corresponding to the Bayesian linear regression model (Equation (3)) when fitted to the combined data (3686 matches). Red area denotes the 80% posterior interval and black curve denotes the 95% posterior interval. The distributions are unimodal and symmetric with low standard deviations.
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