Making the rules of sports fairer

Abstract

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.