  The integrity of a sport can be seriously undermined if its rules punish
winning as this creates incentives for strategic manipulation. Therefore, a
sports tournament can be called unfair if the overall win probabilities are not
ordered according to the teams' ranking based on their past performances. We
present how statistical methods can contribute to choosing a tournament format
that is in line with the above axiom. In particular, the qualification for the
2020 UEFA European Championship is shown to violate this requirement: being a
top team in the lowest-ranked League D of the 2018/19 UEFA Nations League
substantially increases the probability of qualifying compared to being a
bottom team in the higher-ranked League C. The unfairness can be remarkably
reduced or even eliminated with slightly changing the path formation policy of
the UEFA Euro 2020 qualifying play-offs. The misaligned design has severely
punished a team for winning a match years before. Since the deficiency is an
inherent feature of the qualifying process, the Union of European Football
Associations (UEFA) should reconsider the format of future tournaments to
eliminate the unfair advantage enjoyed by certain teams.
