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A Bayesian regression approach to handicapping tennis players based on a rating system

Author

Listed:
  • Chan Timothy C.Y.

    (Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada)

  • Singal Raghav

    (Department of Industrial Engineering and Operations Research, Columbia University, NYC, NY, USA)

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.

Suggested Citation

  • Chan Timothy C.Y. & Singal Raghav, 2018. "A Bayesian regression approach to handicapping tennis players based on a rating system," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 14(3), pages 131-141, September.
    • Handle: RePEc:bpj:jqsprt:v:14:y:2018:i:3:p:131-141:n:4
    DOI: 10.1515/jqas-2017-0103
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    References listed on IDEAS

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    1. Newton Paul K & Aslam Kamran, 2009. "Monte Carlo Tennis: A Stochastic Markov Chain Model," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 5(3), pages 1-44, July.
    2. Chan Timothy C. Y. & Singal Raghav, 2016. "A Markov Decision Process-based handicap system for tennis," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 12(4), pages 179-188, December.
    3. O'Malley A. James, 2008. "Probability Formulas and Statistical Analysis in Tennis," Journal of Quantitative Analysis in Sports, De Gruyter, vol. 4(2), pages 1-23, April.
    4. Klaassen, Franc J. G. M. & Magnus, Jan R., 2003. "Forecasting the winner of a tennis match," European Journal of Operational Research, Elsevier, vol. 148(2), pages 257-267, July.
    5. Klaassen F. J G M & Magnus J. R., 2001. "Are Points in Tennis Independent and Identically Distributed? Evidence From a Dynamic Binary Panel Data Model," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 500-509, June.
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