Attractiveness and equal treatment in a group draw

TL;DR

This paper examines the trade-off between attractiveness and fairness in sports tournament draws, proposing a methodology to optimize geographical restrictions while considering inequality.

Contribution

It introduces a measure of inequality and a Pareto frontier approach to balance attractiveness and fairness in tournament draw constraints.

Findings

Identified 32 sets of geographical restrictions for the handball championship.

Developed a Pareto frontier to analyze trade-offs between fairness and attractiveness.

Provided a decision-making framework for policy-makers.

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.