Does the draw matter in an incomplete round-robin tournament? The case of the UEFA Champions League

Abstract: A fundamental reform has been introduced in the 2024/25 season of club competitions organised by the Union of European Football Associations (UEFA): the well-established group stage has been replaced by an incomplete round-robin format. In this format, the 36 teams are ranked in a single league table, but play against only a subset of the competitors. While this innovative change has highlighted that the incomplete round-robin tournament is a reasonable alternative to the standard design of allocating the teams into round-robin groups, the characteristics of the new format remain unexplored. Our paper contributes to this topic by using simulations to compare the uncertainty generated by the draw in the old format with that in the new format of the UEFA Champions League. We develop a method to break down the impact of the 2024/25 reform into various components for each team. The new format is found to decrease the overall effect of the draw. However, this reduction can mainly be attributed to the inaccurate seeding system used by UEFA. When teams are seeded based on their actual strength, the impact of the draw is about the same in a tournament with an incomplete round-robin league or a group stage.