Attractiveness and equal treatment in a group draw
László Csató, Dóra Gréta Petróczy
TL;DR
This paper tackles the tension between maximizing intercontinental group-stage matchups (attractiveness) and maintaining equal treatment in group draws, using the 2025 IHF World Men's Handball Championship as a case study. It develops a Monte Carlo framework to compare 32 geographic constraint sets under two draw mechanisms (Uniform and Skip) and introduces a Herfindahl-Hirschman index–based inequality measure, $I$, to quantify fairness distortions. The results reveal a Pareto frontier across 64 scenario-mechanism combinations, with Constraint E being particularly restrictive and certain constraint sets being dominated by others; the Skip mechanism can produce equal-treatment outcomes that differ from Uniform in systematic ways. The framework provides a practical decision-support tool for policymakers to select draw constraints and motivates applying the approach to other sports and tournament formats, including examining pot order effects and broader draw mechanisms.
Abstract
National teams from different continents can play against each other only in afew sports competitions. Therefore, a reasonable aim is maximising the number of intercontinental games in world cups, as done in basketball and football, in contrast to handball and volleyball. However, this objective requires additional draw constraints that imply the violation of equal treatment. In addition, the standard draw mechanism is non-uniformly distributed on the set of valid assignments, which may lead to further distortions. Our paper analyses this novel trade-off between attractiveness and fairness through the example of the 2025 World Men's Handball Championship. We introduce a measure of inequality, which enables considering 32 sets of reasonable geographical restrictions to determine the Pareto frontier. The proposed methodology can be used by policy-makers to select the optimal set of draw constraints.