Selected work

Representative Papers

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

Feb 12, 2025

To address the fairness and spectacle degradation caused by “meaningless matches”—games where teams have already qualified or been eliminated—in large-scale sporting tournaments, this paper proposes an asymmetric group-stage format based on team strength stratification, using the 48-team 2026 FIFA World Cup as a case study. The design strategically concentrates stronger teams into high-competition-intensity groups and weaker teams into lower-pressure groups. Through formal rule modeling and Monte Carlo simulation, we rigorously evaluate its efficacy. Compared to conventional 32-team formats or balanced 48-team designs, our approach reduces the probability of meaningless matches involving top-tier teams by over 60%. It also decreases total match count while significantly increasing the density of high-stakes matchups and outcome uncertainty. This work provides a scalable theoretical framework and empirical validation for optimizing tournament structures in major international championships.

1 citationsRead paper

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

May 25, 2026

This study addresses the evaluation of competitiveness and fairness in the final round of a four-team round-robin tournament format by proposing and systematically comparing a deterministic classification framework with a probabilistic model based on offensive–defensive payoff trade-offs. Leveraging empirical data from the 2014 and 2018 FIFA World Cup group stages, the research validates the practical efficacy and complementarity of both approaches. Furthermore, it quantifies the impact of the expanded 48-team format and revised scheduling rules slated for the 2026 FIFA World Cup on match competitiveness. The analysis reveals, for the first time, the dynamic effects of tournament design in real-world settings, thereby offering both theoretical grounding and empirical support for optimizing competition formats in major sporting events.

0 citationsRead paper

A probabilistic match classification model for sports tournaments

Jan 14, 2026

This study addresses the limitations of existing match classification methods, which fail to accurately capture variations in team incentives across different match outcomes and rely on overly rigid definitions of “meaningless” matches. The authors propose a novel classification framework based on changes in qualification probabilities: by integrating tournament rules with Monte Carlo simulations and probabilistic modeling, they enumerate all possible match outcomes and quantify how each of the three results (win, draw, loss) affects each team’s advancement prospects. This approach enables a fine-grained categorization of matches into six distinct types, offering the first systematic characterization of incentive intensity. Applied to UEFA’s new 2024/25 competition format, the analysis reveals that while the incomplete round-robin structure reduces the number of mutually meaningless matches, it substantially increases the frequency of matches requiring aggressive play and elevates the risk of potential collusion.

0 citationsRead paper

Recent publications

Latest Papers

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

May 25, 2026

This study addresses the evaluation of competitiveness and fairness in the final round of a four-team round-robin tournament format by proposing and systematically comparing a deterministic classification framework with a probabilistic model based on offensive–defensive payoff trade-offs. Leveraging empirical data from the 2014 and 2018 FIFA World Cup group stages, the research validates the practical efficacy and complementarity of both approaches. Furthermore, it quantifies the impact of the expanded 48-team format and revised scheduling rules slated for the 2026 FIFA World Cup on match competitiveness. The analysis reveals, for the first time, the dynamic effects of tournament design in real-world settings, thereby offering both theoretical grounding and empirical support for optimizing competition formats in major sporting events.

0 citationsRead paper

A probabilistic match classification model for sports tournaments

Jan 14, 2026

This study addresses the limitations of existing match classification methods, which fail to accurately capture variations in team incentives across different match outcomes and rely on overly rigid definitions of “meaningless” matches. The authors propose a novel classification framework based on changes in qualification probabilities: by integrating tournament rules with Monte Carlo simulations and probabilistic modeling, they enumerate all possible match outcomes and quantify how each of the three results (win, draw, loss) affects each team’s advancement prospects. This approach enables a fine-grained categorization of matches into six distinct types, offering the first systematic characterization of incentive intensity. Applied to UEFA’s new 2024/25 competition format, the analysis reveals that while the incomplete round-robin structure reduces the number of mutually meaningless matches, it substantially increases the frequency of matches requiring aggressive play and elevates the risk of potential collusion.

0 citationsRead paper

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

Feb 12, 2025

To address the fairness and spectacle degradation caused by “meaningless matches”—games where teams have already qualified or been eliminated—in large-scale sporting tournaments, this paper proposes an asymmetric group-stage format based on team strength stratification, using the 48-team 2026 FIFA World Cup as a case study. The design strategically concentrates stronger teams into high-competition-intensity groups and weaker teams into lower-pressure groups. Through formal rule modeling and Monte Carlo simulation, we rigorously evaluate its efficacy. Compared to conventional 32-team formats or balanced 48-team designs, our approach reduces the probability of meaningless matches involving top-tier teams by over 60%. It also decreases total match count while significantly increasing the density of high-stakes matchups and outcome uncertainty. This work provides a scalable theoretical framework and empirical validation for optimizing tournament structures in major international championships.

1 citationsRead paper