Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Ranking matters: Does the new format select the best teams for the knockout phase in the UEFA Champions League?

László Csató, Karel Devriesere, Dries Goossens, András Gyimesi, Roel Lambers, Frits Spieksma

Abstract

Starting in the 2024/25 season, the Union of European Football Associations (UEFA) has fundamentally changed the format of its club competitions: the group stage has been replaced by a league phase played by 36 teams in an incomplete round robin format. This makes ranking the teams based on their results challenging because teams play against different sets of opponents, whose strengths vary. In this research note, we apply several well-known ranking methods for incomplete round robin tournaments to the 2024/25 UEFA Champions League league phase in order to check the robustness of the official ranking, as well as to call the attention of organizers to the non-trivial issue of ranking in these competitions. Our results show that it is doubtful whether the currently used point-based system provides the best ranking of the teams.

Ranking matters: Does the new format select the best teams for the knockout phase in the UEFA Champions League?

Abstract

Starting in the 2024/25 season, the Union of European Football Associations (UEFA) has fundamentally changed the format of its club competitions: the group stage has been replaced by a league phase played by 36 teams in an incomplete round robin format. This makes ranking the teams based on their results challenging because teams play against different sets of opponents, whose strengths vary. In this research note, we apply several well-known ranking methods for incomplete round robin tournaments to the 2024/25 UEFA Champions League league phase in order to check the robustness of the official ranking, as well as to call the attention of organizers to the non-trivial issue of ranking in these competitions. Our results show that it is doubtful whether the currently used point-based system provides the best ranking of the teams.

Paper Structure

This paper contains 12 sections, 1 theorem, 11 equations, 3 tables.

Table of Contents

  1. Introduction
  2. Alternative ranking methods
  3. The direct ranking method
  4. Colley
  5. Generalized Row Sum
  6. Least squares
  7. Some connections between ranking methods
  8. The Colley and Generalized Row Sum methods
  9. The Generalized Row Sum and least squares methods
  10. Comparison of the ranking methods
  11. Results
  12. Discussion

Key Result

Proposition 1

Under the $\{ 2,1,0 \}$ scoring system, if every team plays the same number of matches $t$, the GRS ranking with $\varepsilon = 1/2$ is identical to the Colley ranking.

Theorems & Definitions (2)

  • Proposition 1
  • proof