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A mathematical analysis of badminton scoring systems

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  • D F Percy

    (University of Salford)

Abstract

The International Badminton Federation recently introduced rule changes to make the game faster and more entertaining, by influencing how players score points and win games. We assess the fairness of both systems by applying combinatorics, probability theory and simulation to extrapolate known probabilities of winning individual rallies into probabilities of winning games and matches. We also measure how effective the rule changes are by comparing the numbers of rallies per game and the scoring patterns within each game, using data from the 2006 Commonwealth Games to demonstrate our results. We then develop subjective Bayesian methods for specifying the probabilities of winning. Finally, we describe how to propagate this information with observed data to determine posterior predictive distributions that enable us to predict match outcomes before and during play.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:jorsoc:v:60:y:2009:i:1:d:10.1057_palgrave.jors.2602528
    DOI: 10.1057/palgrave.jors.2602528
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    References listed on IDEAS

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    1. Lawrence H. Riddle, 1988. "Probability Models for Tennis Scoring Systems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(3), pages 490-490, November.
    2. Lawrence H. Riddle, 1988. "Probability Models for Tennis Scoring Systems," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 37(1), pages 63-75, 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.
    2. Davy Paindaveine & Yvik Swan, 2009. "A stochastic analysis of some two-person sports," Working Papers ECARES 2009_025, ULB -- Universite Libre de Bruxelles.
    3. S Lessmann & M-C Sung & J E V Johnson, 2011. "Towards a methodology for measuring the true degree of efficiency in a speculative market," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(12), pages 2120-2132, December.
    4. Wright, Mike, 2014. "OR analysis of sporting rules – A survey," European Journal of Operational Research, Elsevier, vol. 232(1), pages 1-8.

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