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

Autor:	Brams, Steven J., Ismail, Mehmet S., Kilgour, D. Marc, Stromquist, Walter
Rok vydání:	2018
Předmět:	Mathematics - History and Overview Economics - Theoretical Economics 60J20 91A80 91A20
Druh dokumentu:	Working Paper
Popis:	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. Comment: 31 pages. Forthcoming in The American Mathematical Monthly, 2018
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1808.06922 Zobrazit plný text záznamu View this record from Arxiv