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

TL;DR

This paper compares different serving rules in service sports, finding that the Catch-Up Rule enhances competitiveness and excitement by balancing win probabilities and game length, unlike traditional rules.

Contribution

It introduces and analyzes the Catch-Up Rule, demonstrating its advantages in fairness, competitiveness, and strategy-proofness over existing serving rules.

Findings

CR increases game length and competitiveness.

CR maintains equal winning probabilities for players.

CR is strategy-proof, unlike some trailing rules.

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.