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Journal of Quantitative Analysis in Sports

An official journal of the American Statistical Association

Editor-in-Chief: Steve Rigdon, PhD

CiteScore 2017: 0.67

SCImago Journal Rank (SJR) 2017: 0.290
Source Normalized Impact per Paper (SNIP) 2017: 0.853

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Volume 14, Issue 3


Volume 1 (2005)

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

Timothy C.Y. Chan / Raghav Singal
  • Corresponding author
  • Department of Industrial Engineering and Operations Research, Columbia University, NYC, NY, USA
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Published Online: 2018-08-21 | DOI: https://doi.org/10.1515/jqas-2017-0103


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.

Keywords: Bayesian models; handicap; Markov chain; rating systems; tennis


  • Bertsekas, D. P. and J. N. Tsitsiklis. 2002. Introduction to Probability (Vol. 1). Belmont, MA: Athena Scientific.Google Scholar

  • Carpenter, B., A. Gelman, M. Hoffman, D. Lee, B. Goodrich, M. Betancourt, M. A. Brubaker, J. Guo, P. Li, and A. Riddell. 2016. “Stan: A Probabilistic Programming Language.” Journal of Statistical Software 20:1–37.Web of ScienceGoogle Scholar

  • Carter, Jr., W. H. and S. L. Crews. 1974. “An Analysis of the Game of Tennis.” The American Statistician 28:130–134.Google Scholar

  • Chan, T. C. and R. Singal. 2016. “A Markov Decision Process-Based Handicap System for Tennis.” Journal of Quantitative Analysis in Sports 12:179–188.Google Scholar

  • Eisenhauer, J. G. 2003. “Regression Through the Origin.” Teaching Statistics 25:76–80.CrossrefGoogle Scholar

  • Fischer, G. 1980. “Exercise in Probability and Statistics, or the Probability of Winning at Tennis.” American Journal of Physics 48:14–19.CrossrefGoogle Scholar

  • Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2014. Bayesian Data Analysis, volume 2. Boca Raton, FL: CRC Press.Google Scholar

  • Kemeny, J. G. and J. L. Snell. 1960. Finite Markov Chains, volume 356. Princeton, NJ: van Nostrand.Google Scholar

  • Klaassen, F. J. and J. R. Magnus. 2001. “Are Points in Tennis Independent and Identically Distributed? Evidence from a Dynamic Binary Panel Data Model.” Journal of the American Statistical Association 96:500–509.CrossrefGoogle Scholar

  • Klaassen, F. J. and J. R. Magnus. 2003. “Forecasting the Winner of a Tennis Match.” European Journal of Operational Research 148: 257–267.CrossrefGoogle Scholar

  • Liu, Y. 2001. “Random Walks in Tennis.” Missouri Journal of Mathematical Sciences 13(3):1–9.Google Scholar

  • Newton, P. K. and K. Aslam. 2009. “Monte Carlo Tennis: A Stochastic Markov Chain Model.” Journal of Quantitative Analysis in Sports 5(3): Article 7.Google Scholar

  • O’Malley, A. J. 2008. “Probability Formulas and Statistical Analysis in Tennis.” Journal of Quantitative Analysis in Sports 4(2): Article 15.Google Scholar

  • UTR. 2015. “Universal Tennis, Universal Tennis Rating System.” http://universaltennis.com. Accessed: 23-November-2015.

About the article

Published Online: 2018-08-21

Published in Print: 2018-09-25

Citation Information: Journal of Quantitative Analysis in Sports, Volume 14, Issue 3, Pages 131–141, ISSN (Online) 1559-0410, ISSN (Print) 2194-6388, DOI: https://doi.org/10.1515/jqas-2017-0103.

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