How could the draw of the European Qualifiers to the 2022 FIFA World Cup have been fairer?

Abstract

The paper discusses two reforms for the draw procedure of sports tournaments with various restrictions on the allocation of the teams into groups. Examples include qualifications for the recent UEFA European Championships, the European Qualifiers to the FIFA World Cup, and the UEFA Nations League. We uncover by Monte Carlo simulations that the draw of the European Qualifiers to the 2022 FIFA World Cup could have been closer to uniform distribution with a careful choice of pot labels and additional randomisation on the size of the groups. The Union of European Football Associations (UEFA) is strongly encouraged to consider our proposals in order to build fairer tournaments in the future.

The European section of the 2022 FIFA World Cup qualification starts with the group stage, where the 55 national teams of the UEFA are drawn into five groups of five teams (Groups A--E) and five groups of six teams (Groups F--J) each to play in a home-away round-robin format. The group winners qualify for the 2022 FIFA World Cup and the runners-up progress to the second round of the qualification.