arXiv subjects

András Gyimesi

Publications and source records attributed to András Gyimesi.

5 recordsLinked to original sources

arXiv2026

A probabilistic match classification model for low-scoring sports

All existing match classification models in the tournament design literature suffer from two major limitations: a contestant is considered indifferent only if uncertain future results do never affect its prize, and competitive matches are not distinguished with respect to the incentives of the contestants. We propose a probabilistic framework to address both issues. For each match, our approach relies on simulating all other matches played simultaneously or later to compute the qualifying probabilities for the three main outcomes (win, draw, loss), thereby classifying each match into six categories. The suggested model is applied to the last round of the previous group stage and the new incomplete round-robin league, introduced in the 2024/25 season of UEFA club competitions. The incomplete round-robin tournament is found to contain fewer unimportant matches with two indifferent teams, and substantially more matches where both teams should play offensively. However, the robustly higher proportion of potentially collusive matches can threaten with serious scandals.

physics.soc-ph↗

arXiv2026

The uncertainty of a tournament draw: Insights from the Champions League

The group draw of major sports tournaments implies some uncertainty, with lucky teams often enjoying a substantial unfair advantage. First in the literature, we propose a technique to quantify this draw uncertainty, which, arguably, has an optimal level of zero. Our simulation-based approach requires generating a representative set of random draws to compute the variance of qualifying probabilities for each team. The method is applied to compare draw uncertainty in the former group stage and the current incomplete round-robin league phase of the UEFA Champions League, under both accurate and inaccurate seedings. We also break down the impact of the 2024/25 reform into various components. The new format is found to decrease draw uncertainty, but the reduction is mainly attributable to the inaccurate seeding system used by UEFA. Consequently, the primary benefit of an incomplete round-robin tournament compared to the standard group stage lies in the robustness of its draw uncertainty to the seeding of the teams.

stat.AP↗

arXiv2026

Match classification in the last round of four-team round-robin tournaments

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 first comparison of them by analysing the most prominent example of four-team round-robin competitions, the group stage of the FIFA World Cup. We show that both methods are highly relevant in practice: all (four) deterministic and (six) probabilistic match types occurred in the 2014 and 2018 FIFA World Cups, respectively. The probabilistic model, which accounts for the relative benefits of attacking and defending, provides deeper insights; for instance, the competitive matches from the deterministic approach can be of any of the six probabilistic types. Finally, the probabilistic framework is used to quantify and decompose the impact of the main reforms introduced for the 2026 FIFA World Cup: the expansion to 48 teams, as well as the modified qualification and tie-breaking rules.

physics.soc-ph↗

arXiv2025

Increasing competitiveness by imbalanced groups: The example of the 48-team FIFA World Cup

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 without incentives. This paper suggests a novel classification for stakeless matches based on their expected outcome: they are more costly if the indifferent team is more likely to win by playing honestly. Our approach is illustrated with the 2026 FIFA World Cup, the first edition of the competition with 48 teams. We propose a novel format based on imbalanced groups, which substantially reduces the probability of stakeless matches played by the strongest teams according to Monte Carlo simulations. The new design also increases the uncertainty of match outcomes and requires fewer matches. Governing bodies in sports are encouraged to consider our innovative idea in order to enhance the competitiveness of their tournaments.

math.OC↗

arXiv2025

Ranking matters: Does the new format select the best teams for the knockout phase in the UEFA Champions League?

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 robin format. This makes ranking the teams based on their results challenging because teams play against different sets of opponents, whose strengths vary. In this research note, we apply several well-known ranking methods for incomplete round robin tournaments to the 2024/25 UEFA Champions League league phase in order to check the robustness of the official ranking, as well as to call the attention of organizers to the non-trivial issue of ranking in these competitions. Our results show that it is doubtful whether the currently used point-based system provides the best ranking of the teams.

physics.soc-ph↗