Abstract
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.
References
Barnett, T., A. Brown and S. R. Clarke. 2004. “Optimal Use of Tennis Resources.” Pp. 57–65 in Seventh Australasian Conference on Mathematics and Computers in Sport. Palmerston North, New Zealand: Massey University.Search in Google Scholar
Bertsekas, D. and J. Tsitsiklis. 2008. Introduction to Probability. Nashua, NH: Athena Scientific.Search in Google Scholar
BGA. 2015. “British Go Association, How to Play.” http://www.britgo.org/intro/intro2.html [Accessed: November 22, 2015].Search in Google Scholar
BHA. 2015. “British Horseracing Authority, Handicapping.” http://www.britishhorseracing.com/bha/what-we-do/handicapping/ [Accessed: November 22, 2015].Search in Google Scholar
Branson, R. 2015. “Shake up Tennis with ‘Richard’s Rules’.” http://www.virgin.com/richard-branson/shake-up-tennis-with-richards-rules [Accessed: November 22, 2015].Search in Google Scholar
Fischer, G. 1980. “Exercise in Probability and Statistics, or the Probability of Winning at Tennis.” American Journal of Physics 48:14–19.Search in Google Scholar
Hooper, D. and K. Whyld. 1992. The Oxford Companion to Chess. Oxford University Press, USA.Search in Google Scholar
ITF. 2015. “International Tennis Federation, Rules of Tennis.” http://www.itftennis.com/officiating/rulebooks/rules-of-tennis.aspx [Accessed: November 22, 2015].Search in Google Scholar
Kemeny, J. G. and J. L. Snell. 1960. Finite Markov Chains, volume 356. Princeton, NJ: van Nostrand.Search in 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.Search in Google Scholar
Morris, C. 1977. “The Most Important Points in Tennis.” Optimal Strategies in Sports 5:131–140.Search in Google Scholar
O’Donoghue, P. G. 2001. “The Most Important Points in Grand Slam Singles Tennis.” Research Quarterly for Exercise and Sport 72:125–131.Search in Google Scholar
Puterman, M. L. 1994. Markov Decision Processes: Discrete Stochastic Dynamic Programming. New York, NY: John Wiley & Sons.Search in Google Scholar
Tencap. 2015. “Tencap Sports, Tencap’s Rating System.” http://www.tencapsports.com/rating.aspx [Accessed: November 22, 2015].Search in Google Scholar
USGA. 2015. “United States Golf Association, Handicap System Manual.” http://ctan.tug.org/tex-archive/info/lshort/english/lshort.pdf [Accessed: November 22, 2015].Search in Google Scholar
©2017 Walter de Gruyter GmbH, Berlin/Boston
