Related papers: A new competition format to avoid collusion in thr…
FIFA World Cup is one of the most watched sporting event in the world and its popularity continue to increase. While currently 32 teams participate in this event, starting with 2026 the number of participants will increase to 48. As a…
I present a double-elimination format for the 48-team FIFA World Cup that solves many of the concerns raised about the considered formats with mixed round-robin with groups of 3 or 4 teams and single-elimination strategies. Using a…
A match played in a sports tournament can be called stakeless if at least one team is indifferent to its outcome because it already has qualified or has been eliminated. Such a game threatens fairness since teams may not exert full effort…
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…
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…
Qualifications for several world championships in sports are organised such that distinct sets of teams play in their own tournament for a predetermined number of slots. Inspired by a recent work studying the problem with the tools from the…
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…
The group stage of a sports tournament is often made more appealing by introducing additional constraints in the group draw that promote an attractive and balanced group composition. For example, the number of intra-regional group matches…
Several sports tournaments contain a round-robin group stage where the teams are assigned to groups subject to some constraints. Hence, the organisers usually use a computer-assisted random draw to avoid any dead end, a situation when the…
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…
This paper investigates the fairness of the 2018 FIFA World Cup qualifying competition via Monte Carlo simulations. The qualifying probabilities are calculated for 102 nations, all teams except for African and European countries. A method…
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…
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…
The draw for the 2022 FIFA World Cup has been organised before the identity of three winners of the play-offs is revealed. Seeding has been based on the FIFA World Ranking released on 31 March 2022 but these three teams have been drawn from…
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…
The organisers of major sports competitions use different policies with respect to constraints in the group draw. Our paper aims to rationalise these choices by analysing the trade-off between attractiveness (the number of games played by…
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 study aims to compare different designs for the World Men's Handball Championships. This event, organised in every two years, has adopted four hybrid formats consisting of knockout and round-robin stages in recent decades, including a…
The Traveling Tournament Problem(TTP) is a combinatorial optimization problem where we have to give a scheduling algorithm which minimizes the total distance traveled by all the participating teams of a double round-robin tournament…
Playing in the FIFA World Cup finals is an ambition shared by several nations. Since, besides luck and skill, the probability of qualification depends on the design of the qualifiers, the study of these competitions forms an integral part…