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A stochastic analysis of some two-person sports

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  • Davy Paindaveine
  • Yvik Swan

Abstract

We consider two-person sports where each rally is initiated by a server, the other player (the receiver) becoming the server when he/she wins a rally. Historically, these sports used a scoring based on the side-out scoring system, in which points are only scored by the server. Recently, however, some federations have switched to the rally-point scoring system in which a point is scored on every rally. As various authors before us, we study how much this change affects the game. Our approach is based on a rally-level analysis of the process through which, besides the well-known probability distribution of the scores,we also obtain the distribution of the number of rallies. This yields a comprehensive knowledge of the process at hand, and allows for an in-depth comparison of both scoring systems. In particular, our results help to explain why the transition from one scoring system to the other has more important implications than those predicted from game-winning probabilities alone. Some of our findings are quite surprising, and unattainable through Monte Carlo experiments. Our results are of high practical relevance to international federations and local tournament organizers alike, and also open the way to fficient estimation of the rally-winning probabilities, which should have a significant impact on the quality of ranking procedures.

Suggested Citation

  • Davy Paindaveine & Yvik Swan, 2009. "A stochastic analysis of some two-person sports," Working Papers ECARES 2009_025, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2009_025
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    References listed on IDEAS

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    1. David Strauss & Barry C. Arnold, 1987. "The Rating of Players in Racquetball Tournaments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(2), pages 163-173, June.
    2. D F Percy, 2009. "A mathematical analysis of badminton scoring systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 63-71, January.
    3. John Simmons, 1989. "A Probabilistic Model of Squash: Strategies and Applications," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(1), pages 95-110, March.
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    Cited by:

    1. Christophe Ley & Yves Dominicy, 2017. "Mutual Point-winning Probabilities (MPW): a New Performance Measure for Table Tennis," Working Papers ECARES ECARES 2017-23, ULB -- Universite Libre de Bruxelles.

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