On the consequences of draw restrictions in knockout tournaments

The paper analyses how draw constraints influence the outcome of a knockout tournament. The research question is inspired by the rules of European club football competitions: in order to maintain their international character, the organiser usually imposes an association constraint both in the group stage and the first round of the subsequent knockout phase, that is, teams from the same country cannot be drawn against each other. The effects of similar restrictions are explored in both theoretical and simulation models. Using an association constraint in the first round(s) is verified to increase the likelihood of a same nation matchup to approximately the same extent in each subsequent round. Furthermore, if the favourite teams are concentrated in some associations, they have a higher probability to win the tournament in the presence of association constraints. Our results essentially justify a recent decision of the Union of European Football Associations (UEFA).