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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 paper investigates the qualification for the UEFA Champions League, the most prestigious club competition in European football with respect to the theoretical property of strategy-proofness. We find that in three seasons (2015-16,…
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…
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 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…
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…
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…
In the last round of the FIFA World Cup group stage, games for which the outcome does not affect the selection of the qualified teams are played with little enthusiasm. Furthermore, a team that has already qualified may take into account…
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…
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…
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…
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…
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…
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…
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…
Multi-stage tournaments consisting of a round-robin group stage followed by a knockout phase are ubiquitous in sports. However, this format is incentive incompatible if at least two teams from a group advance to the knockout stage where the…
In international football (soccer), two-legged knockout ties, with each team playing at home in one leg and the final outcome decided on aggregate, are common. Many players, managers and followers seem to believe in the `second-leg home…
Ranking of agents competing with each other in complex systems may lead to paradoxes according to the pre-chosen different measures. A discussion is presented on such rank-rank, similar or not, correlations based on the case of European…
A paper published in a leading journal of management science has recently analysed the mechanism used for the UEFA Champions League Round of 16 draw. Since the authors have not been familiar with the related sports analytics literature,…
Penalty shootouts play a crucial role in the knockout stage of major football tournaments. Their importance has substantially increased from the 2021/22 season, when the Union of European Football Associations (UEFA) scrapped the away goals…