  The paper analyses how draw constraints influence the outcome of a knockout
tournament. The research question is inspired by European club football
competitions, where the organiser generally imposes an association constraint
in the first round of the knockout phase: teams from the same country cannot be
drawn against each other. Its effects are explored in both theoretical and
simulation models. An association constraint in the first round(s) is found to
increase the likelihood of same nation matchups to approximately the same
extent in each subsequent round. If the favourite teams are concentrated in
some associations, they will have a higher probability to win the tournament
under this policy but the increase is less than linear if it is used in more
rounds. Our results might explain the recent introduction of the association
constraint for both the knockout round play-offs with 16 teams and the Round of
16 in the UEFA Europa League and UEFA Europa Conference League.
