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

The American Mathematical Monthly, Forthcoming

30 Pages Posted: 19 Dec 2016 Last revised: 20 Feb 2018

Steven J. Brams

New York University (NYU) - Wilf Family Department of Politics

Mehmet Ismail

King's College London, Department of Political Economy

D. Marc Kilgour

Wilfrid Laurier University

Walter Stromquist

Bryn Mawr College

Date Written: February 2018

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.

Keywords: sports rules, service sports, Markov processes, competitiveness, fairness, strategy-proofness

JEL Classification: C72, D63, Z20, L83

Suggested Citation

Brams, Steven J. and Ismail, Mehmet and Kilgour, D. Marc and Stromquist, Walter, Catch-Up: A Rule that Makes Service Sports More Competitive (February 2018). The American Mathematical Monthly, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2887175 or http://dx.doi.org/10.2139/ssrn.2887175

Steven Brams

New York University (NYU) - Wilf Family Department of Politics ( email )

Dept. of Politics
19 West 4th St., 2nd Fl.
New York, NY 10012
United States
212-998-8510 (Phone)
212-995-4184 (Fax)

HOME PAGE: http://politics.as.nyu.edu/object/stevenbrams.html

Mehmet Ismail (Contact Author)

King's College London, Department of Political Economy ( email )

Strand
London, WC2R 2LS
United Kingdom

HOME PAGE: http://sites.google.com/site/mehmetsismail/

D. Marc Kilgour

Wilfrid Laurier University ( email )

75 University Ave W
Waterloo, Ontario N2L 3C5
Canada
519-884-0710 Ext.4208 (Phone)
519-884-5057 (Fax)

Walter Rees Stromquist

Bryn Mawr College ( email )

Bryn Mawr, PA
United States

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