Making the rules of sports fairer

Steven J. Brams, Mehmet S. Ismail

    Research output: Contribution to journalArticlepeer-review


    The rules of many sports are not fair-they do not ensure that equally skilled competitors have the same probability of winning. As an example, the penalty shootout in soccer, wherein a coin toss determines which team kicks first on all five penalty kicks, gives a substantial advantage to the first-kicking team, both in theory and in practice. We show that a so-called Catch-Up Rule for determining the order of kicking would not only make the shootout fairer but is also essentially strategyproof. By contrast, the so-called Standard Rule now used for the tiebreaker in tennis is fair. We briefly consider several other sports, all of which involve scoring a sufficient number of points to win, and show how they could benefit from certain rule changes which would be straightforward to implement.

    Original languageEnglish (US)
    Pages (from-to)181-202
    Number of pages22
    JournalSIAM Review
    Issue number1
    StatePublished - 2018


    • Fairness
    • Markov process
    • Soccer
    • Sports rules
    • Strategyproofness
    • Tennis

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Computational Mathematics
    • Applied Mathematics


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