In 2016, for the first time, the UEFA European Championship gathered 24 men`s national teams. It consisted of a group stage made of 6 groups of 4, followed by a knockout stage starting with the round of 16. We critically examine a number of flaws in the design of the knockout bracket that was used by UEFA: group advantage, lack of win incentive, and arbitrary choices. We suggest two fairer procedures that satisfy the balance and group diversity constraints but eliminate group advantage and significantly increase win incentive, hence interest, in the group stage. The suggested procedures use a global ranking of the 16 teams qualified to the knockout stage based on their performance during the group stage. They apply to any tournament consisting of a round robin stage made of 6 groups of 4, followed by a knockout stage. UEFA has decided to keep the 2016 format for Euro 2020, but has used our work to modify the knockout bracket so as to minimize group advantage.
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