Tie-breaking in round-robin soccer tournaments and its influence on the autonomy of relative rankings: UEFA vs. FIFA regulations

Abstract

Research questionMany sports tournaments, or tournament stages, are held in round-robin format. In establishing standings, tie-breaker criteria are often required to assign unique ranks to competitors that are equal on points. During the 2012 Union of European Football Associations (UEFA) European Football Championship, the relative ranking of two teams could possibly be influenced by a match in which neither team was involved, which we refer to as heteronomous relative ranking (HRR). We seek to shed light on the origin and the practical relevance of HRR in soccer competitions.Research methodsWe trace the appearance of HRR back to particularities in the UEFA EURO 2012 tie-breaker criteria, which favor head-to-head records over goal difference, and relate the concept of autonomous relative ranking to Arrow's Independence of Irrelevant Alternatives. Using historical and Monte–Carlo simulated data, we compare HRR occurrence rates under EURO 2012 regulations to those under Fédération Internationale de Football Association (FIFA) 2010 regulations, the latter of which give less importance to head-to-head records.Results and findingsHRR is well explained by tie-breaker criteria, namely the priorities of head-to-head records and goal difference. HRR occurs in more than 10% of four-team soccer groups under EURO 2012 regulations; this rate is further increased in round-robin groups of six teams. FIFA 2010 regulations lead to less than 0.1% HRR.ImplicationsHead-to-head records may result in counterintuitive side effects that should be avoided when designing ranking systems.