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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 12, Issue 4


Volume 1 (2005)

A Markov Decision Process-based handicap system for tennis

Timothy C. Y. Chan / Raghav Singal
  • Corresponding author
  • Columbia University, Department of Industrial Engineering and Operations Research, New York City, NY, USA
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Published Online: 2017-02-10 | DOI: https://doi.org/10.1515/jqas-2016-0057


Handicap systems are used in many sports to improve competitive balance and equalize the match-win probability between opponents of differing ability. Recognizing the absence of such a system in tennis, we develop a novel optimization-based handicap system for tennis using a Markov Decision Process (MDP) model. In our handicap system, the weaker player is given β “free points” or “credits” at the start of the match, which he can use before the start of any point during the match to win the point outright. The MDP model determines two key features of the handicap system: (1) Fairness: the minimum value of β required to equalize the match-win probability, and (2) Achievability: the optimal policy governing usage of the β credits to achieve the desired match-win probability. We test the sensitivity of the handicap values to the model’s input parameters. Finally, we apply the model to real match data to estimate professional handicaps.

Keywords: Markov decision process; optimization; fairness; dynamic handicap; tennis; hierarchical sports


About the article

Received: 2016-11-21

Accepted: 2016-12-26

Published Online: 2017-02-10

Published in Print: 2016-12-01

Citation Information: Journal of Quantitative Analysis in Sports, Volume 12, Issue 4, Pages 179–188, ISSN (Online) 1559-0410, ISSN (Print) 2194-6388, DOI: https://doi.org/10.1515/jqas-2016-0057.

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