How to optimise tournament draws: The case of the FIFA World Cup

TL;DR

This paper presents an optimization framework for FIFA World Cup draws, balancing attractiveness and fairness, and identifies flaws in current procedures through simulations of 2018 and 2022 tournaments.

Contribution

It introduces a parametric model to optimize draw constraints, providing a systematic way to justify and improve tournament draw procedures.

Findings

Pre-assigning the host increases draw distortions.

The framework identifies Pareto efficient draw constraints.

Simulations validate the model's applicability to real tournaments.

Abstract

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 teams from the same geographic zone) and fairness (the departure of the draw mechanism from a uniform distribution). A parametric optimisation model is formulated and applied to the 2018 and 2022 FIFA World Cup draws. A flaw of the draw procedure is identified: the pre-assignment of the host to a group unnecessarily increases the distortions. All Pareto efficient sets of draw constraints are determined via simulations. The proposed framework can be used to find the optimal draw rules and justify the non-uniformity of the draw procedure for the stakeholders.