Making the Rules of Sports Fairer

Abstract

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.

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

“…Thus, both TRs have a greater expected length than CR, and the length of CR in turn exceeds the length of SR. 5 Theorem 2. In a Best-of-(2k + 1) game for any k ≥ 1 and 0 < p < 1, 0 < q < 1, the expected length of a game is greater under CR than under SR if and only if p + q > 1.…”

“…, are two of many alternating sequences that create adjacent AB or BA blocks. 13 All are 11 Part of this section is adapted from [5]. 12 Arguably, the tiebreaker creates a balance of forces: A is advantaged by serving at the outset, but B is then given a chance to catch up, and even move ahead, by next having two serves in a row.…”

“…It follows that the subset of service schedules under which A wins under SR must be identical to the subset of service schedules under which A wins under CR. Moreover, regardless of the serving rule, any serving schedule that contains n wins for A as server and m wins for B as server must [5].…”

A comparison of penalty shootout designs in soccer

“…FIDE, the governing body of international chess competition, has also recognized the existence of asymmetric psychological pressure, and the colors are reversed halfway through in matches containing twelve scheduled games since at least the World Chess Championship 2006, thus one player plays with the white pieces in the 1st, 3rd, 5th, 8th, 10th, 12th games according to the | sequence. Our point of departure is a central result of Brams and Ismail (2018) that the so-called Catch-Up Rule makes penalty shootouts substantially fairer. A modified version of this mechanism -called the Adjusted Catch-Up Rule -is introduced here, which prohibits the team kicking the first penalty to be the first-mover in the sudden death stage.…”

“…Thus it can be no surprise that there exists a growing literature on penalty shootouts (McGarry and Franks, 2000;Palacios-Huerta, 2003;Jordet et al, 2007;Sainz De Baranda et al, 2008;Bar-Eli and Azar, 2009;Wilson et al, 2009;Memmert et al, 2013;Hubbard and Britto, 2014;Dohmen and Sonnabend, 2018;Vandebroek et al, 2018), and, especially, on their optimal design (Anbarcı et al, 2015(Anbarcı et al, , 2018Brams and Ismail, 2018;Echenique, 2017;Palacios-Huerta, 2012). The latter topic has received some media coverage during the recent FIFA World Cup, for instance, on the pan-European news media service Euronews (Euronews, 2018).…”