相关论文: UEFA Champions League entry has not satisfied stra…
Fairness has several interpretations in sports, one of them being that the rules should guarantee incentive compatibility, namely, a team cannot be worse off due to better results in any feasible scenario. The current seeding regime of the…
The UEFA Champions League is the major European club football competition, however, most national champions have to play qualification matches to receive a slot in the group stage of the tournament. The paper evaluates the impact of the…
One of the most popular club football tournaments, the UEFA Champions League, will see a fundamental reform from the 2024/25 season: the traditional group stage will be replaced by one league where each of the 36 teams plays eight matches.…
UEFA declares that it is committed to respecting the fundamental values of sports. However, the qualification rules of the post-2024 UEFA Champions League are shown to be unfair: a game with misaligned incentives was narrowly avoided in the…
UEFA European Championship 1996 qualification is known to violate strategy-proofness. It has been proved recently that a team could be better off by exerting a lower effort: it might be optimal to concede some goals in order to achieve a…
Recently, UEFA changed the group stage of its international soccer competitions to an incomplete round robin tournament. Previously, teams were divided into groups, each playing a double round robin tournament with a resulting ranking…
We analyse a mathematical model of seeding for sports contests with round-robin qualifying tournaments. The standard seeding system based on coefficients measuring the historical performance of the teams is shown to be unfair as it might…
Tournament organisers supposedly design rules such that a team cannot be strictly better off by exerting a lower effort. However, the European qualification tournaments for recent FIFA soccer World Cups are known to violate this…
The Union of European Football Associations (UEFA) distributes commercial revenue from its club competitions according to a complex mechanism. Coefficient-based amounts are paid such that the participating teams are ranked on the basis of…
One of the most serious violations of fairness in sports is when a team has clear incentives to lose a match, which hurt a third, innocent team. This is shown to be not only a theoretical possibility as the recently identified incentive…
According to recent empirical studies, the group draw of major sports tournaments can imply a high level of uncertainty, and some lucky teams enjoy an unfair advantage over the other teams. We propose a novel technique to quantify this draw…
Starting in the 2024/25 season, the Union of European Football Associations (UEFA) has fundamentally changed the format of its club competitions: the group stage has been replaced by a league phase played by 36 teams in an incomplete round…
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…
Tanking, the act of deliberately dropping points or losing a game in order to gain some other advantage, is usually seen as being against the spirit of sports. It can be even more serious if playing a draw is a (weakly) dominant strategy…
The outcome of some football matches has benefited both teams at the expense of a third team because head-to-head results were used for breaking ties. Inspired by these examples, our mathematical analysis identifies all possible collusion…
For the 2024/25 season, the Union of European Football Associations (UEFA) introduced an incomplete round-robin format in the Champions League and Europa League, replacing the traditional group stage with a single league table of all 36…
In a round-robin tournament, a team may lack the incentive to win if its final rank does not depend on the outcome of the matches still to be played. This paper introduces a classification scheme to determine these weakly (where one team is…
Competitive balance, which refers to the level of control teams have over a sports competition, is a crucial indicator for tournament organisers. According to previous studies, competitive balance has significantly declined in the UEFA…
If the final position of a team is already secured independently of the outcomes of the remaining games in a round-robin tournament, it might play with little enthusiasm. This is detrimental to attendance and can inspire collusion and…
Existing match classification models in the tournament design literature have two major limitations: a contestant is considered indifferent only if uncertain future results do never affect its prize, and competitive matches are not…