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The allocation of FIFA World Cup slots based on the ranking of confederations

László Csató, László Marcell Kiss, Zsombor Szádoczki

TL;DR

This paper tackles the lack of transparency in FIFA World Cup slot allocation by introducing a confederation-level ranking built from historical World Cup results and inter-continental play-offs. It adapts the FIFA World Ranking Elo framework to compare continental strengths and derives an allocation rule using transitive win-ratio properties. Across multiple seeds and update frequencies, the results consistently favor UEFA and CONMEBOL, with CONCACAF typically ahead of AFC, and reveal the sensitivity of allocations to sample length and seeding. The approach offers a transparent, past-informed alternative to current policy and can be extended to other tournaments or seeding problems.

Abstract

Qualifications for several world championships in sports are organised such that distinct sets of teams play in their own tournament for a predetermined number of slots. Inspired by a recent work studying the problem with the tools from the literature on fair allocation, this paper provides an alternative approach based on historical matches between these sets of teams. We focus on the FIFA World Cup due to the existence of an official rating system and its recent expansion to 48 teams, as well as to allow for a comparison with the already suggested allocations. Our proposal extends the methodology of the FIFA World Ranking to compare the strengths of five confederations. Various allocations are presented depending on the length of the sample, the set of teams considered, as well as the frequency of rating updates. The results show that more European and South American teams should play in the FIFA World Cup. The ranking of continents by the number of deserved slots is different from the ranking implied by FIFA policy. We recommend allocating at least some slots transparently, based on historical performances, similar to the access list of the UEFA Champions League.

The allocation of FIFA World Cup slots based on the ranking of confederations

TL;DR

This paper tackles the lack of transparency in FIFA World Cup slot allocation by introducing a confederation-level ranking built from historical World Cup results and inter-continental play-offs. It adapts the FIFA World Ranking Elo framework to compare continental strengths and derives an allocation rule using transitive win-ratio properties. Across multiple seeds and update frequencies, the results consistently favor UEFA and CONMEBOL, with CONCACAF typically ahead of AFC, and reveal the sensitivity of allocations to sample length and seeding. The approach offers a transparent, past-informed alternative to current policy and can be extended to other tournaments or seeding problems.

Abstract

Qualifications for several world championships in sports are organised such that distinct sets of teams play in their own tournament for a predetermined number of slots. Inspired by a recent work studying the problem with the tools from the literature on fair allocation, this paper provides an alternative approach based on historical matches between these sets of teams. We focus on the FIFA World Cup due to the existence of an official rating system and its recent expansion to 48 teams, as well as to allow for a comparison with the already suggested allocations. Our proposal extends the methodology of the FIFA World Ranking to compare the strengths of five confederations. Various allocations are presented depending on the length of the sample, the set of teams considered, as well as the frequency of rating updates. The results show that more European and South American teams should play in the FIFA World Cup. The ranking of continents by the number of deserved slots is different from the ranking implied by FIFA policy. We recommend allocating at least some slots transparently, based on historical performances, similar to the access list of the UEFA Champions League.
Paper Structure (17 sections, 1 theorem, 11 equations, 2 figures, 6 tables)

This paper contains 17 sections, 1 theorem, 11 equations, 2 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related literature
  3. Data
  4. Ignoring the Oceanian (OFC) zone
  5. Consideration of inter-continental play-offs
  6. Disregarding the last round of group matches
  7. Descriptive statistics
  8. Historical slot allocations
  9. Methodology
  10. Preliminaries
  11. The frequency of updating
  12. The role of match schedule
  13. Separating a set of top teams
  14. The allocation rule
  15. The maximal number of slots for a confederation
  16. ...and 2 more sections

Key Result

Proposition 1

Let $a_{ij} = W_{ij}^E / W_{ji}^E$ mean how many times team $i$ is more likely to win against team $j$ than vice versa. These paired comparisons are transitive, tha is, $a_{ik} = a_{ij} a_{jk}$ for any $i,j,k$.

Figures (2)

  • Figure 1: Evolution of confederation slots I.: Seeded sets S0 and S1
  • Figure 2: Evolution of confederation slots II.: Seeded sets S1 and S2

Theorems & Definitions (3)

  • Proposition 1
  • proof
  • Example 1