Related papers: A note on the UEFA Champions League Round of 16 dr…
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 draw of some knockout tournaments requires finding a perfect matching in a balanced bipartite graph. The problem becomes challenging with draw constraints: the two draw procedures used in sports are known to be non-uniformly distributed…
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…
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.…
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…
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Football Associations (UEFA) has fundamentally changed the format of its club competitions: the group stage has been replaced by a league phase played by 36 teams in an incomplete round…
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…
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…
This paper considers the challenge of designing football group draw mechanisms which have the uniform distribution over all valid draw assignments, but are also entertaining, practical, and transparent. We explain how to simulate the FIFA…
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…
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…
Sports data has become widely available in the recent past. With the improvement of machine learning techniques, there have been attempts to use sports data to analyze not only the outcome of individual games but also to improve insights…
Classification of matches played in the last rounds of sports competitions is a well-established tool for evaluating tournament designs. Both deterministic and probabilistic approaches are available for this purpose. Our paper offers the…
Many sports tournaments are organised in a hybrid design consisting of a round-robin group stage followed by a knock-out phase. The traditional seeding regime aims to create balanced groups roughly at the same competition level but may…
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,…
This article presents a Bayesian implementation of a cumulative probit model to forecast the outcomes of the UEFA Champions League matches. The argument of the normal CDF involves a cut-off point, a home vs away playing effect and 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…
Soccer attracts the attention of many researchers and professionals in the sports industry. Therefore, the incorporation of science into the sport is constantly growing, with increasing investments in performance analysis and sports…
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…