Related papers: Group draw with unknown qualified teams: A lesson …
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
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…
The usual FIFA World Cup-TM group stage format is eight groups of four teams for a total of 32 teams. The top two teams from each group advance to the next round, resulting in a 16-team knockout stage. The next edition of the World Cup will…
In this work, we compare three different modeling approaches for the scores of soccer matches with regard to their predictive performances based on all matches from the four previous FIFA World Cups 2002 - 2014: Poisson regression models,…
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…
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…
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 play-offs of the UEFA Euro 2020 qualifying tournament determine the last four participants in the UEFA European Championship 2020. 16 teams, which have failed to obtain a slot in the qualifying group stage, will be selected and divided…
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…
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…