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.
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Acknowledgements
The author is grateful to Ms Rebecca S Dolman for assisting with the algebraic calculations, computer graphics and data collection for this research.
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Percy, D. A mathematical analysis of badminton scoring systems. J Oper Res Soc 60, 63–71 (2009). https://doi.org/10.1057/palgrave.jors.2602528
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DOI: https://doi.org/10.1057/palgrave.jors.2602528