A Markov Decision Process-based handicap system for tennis

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 beta "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 beta required to equalize the match-win probability, and (2) Achievability: the optimal policy governing usage of the beta 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.