Catch-Up: A Rule That Makes Service Sports More Competitive

Steven J. Brams, Mehmet S. Ismail, D. Marc Kilgour, Walter Stromquist

    Research output: Contribution to journalArticle

    Abstract

    Service sports include two-player contests such as volleyball, badminton, and squash. We analyze four rules, including the Standard Rule (SR), in which a player continues to serve until he or she loses. The Catch-Up Rule (CR) gives the serve to the player who has lost the previous point—as opposed to the player who won the previous point, as under SR. We also consider two Trailing Rules that make the server the player who trails in total score. Surprisingly, compared with SR, only CR gives the players the same probability of winning a game while increasing its expected length, thereby making it more competitive and exciting to watch. Unlike one of the Trailing Rules, CR is strategy-proof. By contrast, the rules of tennis fix who serves and when; its tiebreaker, however, keeps play competitive by being fair—not favoring either the player who serves first or who serves second.

    Original languageEnglish (US)
    Pages (from-to)771-796
    Number of pages26
    JournalAmerican Mathematical Monthly
    Volume125
    Issue number9
    DOIs
    StatePublished - Oct 21 2018

    Keywords

    • 91A20
    • MSC: Primary 60J20
    • Secondary 91A80

    ASJC Scopus subject areas

    • Mathematics(all)

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  • Cite this

    Brams, S. J., Ismail, M. S., Kilgour, D. M., & Stromquist, W. (2018). Catch-Up: A Rule That Makes Service Sports More Competitive. American Mathematical Monthly, 125(9), 771-796. https://doi.org/10.1080/00029890.2018.1502544