Increasing competitiveness by imbalanced groups: The example of the 48-team FIFA World Cup

TL;DR

The paper addresses the fairness risk of stakeless matches in large tournaments and assesses how a 48-team FIFA World Cup could be redesigned to mitigate this issue. It develops a Monte Carlo framework based on World Football Elo Ratings, employing a Poisson goal model with rates $\lambda_{ij}^{(f)}$ and win expectancy $W_{ij} = \frac{1}{1 + 10^{-(E_i - E_j)/400}}$ to compare the official 12 groups-of-four format with a novel imbalanced-groups design that creates Tier 1 and Tier 2 groups and an intermediate play-off. A weighted stakeless metric $S_i^W = S_i \cdot W_{ij}$ is introduced to reflect the cost of non-competitive outcomes for stronger teams, and 1,000,000 simulation runs (across 1,000 random draws per design) are used to quantify performance across formats. The results show the imbalanced design substantially reduces stakeless matches for the strongest teams, increases uncertainty in group and knockout outcomes, and reduces total matches, suggesting a practical path to improve competitiveness while managing player workload; the study also highlights monotonicity and incentive-compatibility considerations that warrant further exploration before adoption by governing bodies.

Abstract

A match played in a sports tournament can be called stakeless if at least one team is indifferent to its outcome because it already has qualified or has been eliminated. Such a game threatens fairness since teams may not exert full effort without incentives. This paper suggests a novel classification for stakeless matches based on their expected outcome: they are more costly if the indifferent team is more likely to win by playing honestly. Our approach is illustrated with the 2026 FIFA World Cup, the first edition of the competition with 48 teams. We propose a novel format based on imbalanced groups, which substantially reduces the probability of stakeless matches played by the strongest teams according to Monte Carlo simulations. The new design also increases the uncertainty of match outcomes and requires fewer matches. Governing bodies in sports are encouraged to consider our innovative idea in order to enhance the competitiveness of their tournaments.

Figures (7)

• Figure 1: Teams in the imbalanced format for the 2026 FIFA World Cup Notes: The two winners of the play-offs are represented by their expected Elo ratings. The black nodes show the three hosts if their Elo ratings are increased by 100 due to home advantage.
• Figure 2: The probability of qualification for the Round of 16 in the two formats for the 2026 FIFA World Cup Notes: The two winners of the play-offs are represented by their expected Elo ratings. The black nodes show the three hosts if their Elo ratings are increased by 100 due to home advantage.
• Figure 3: The expected number of matches in the two formats for the 2026 FIFA World Cup Notes: The two winners of the play-offs are represented by their expected Elo ratings. The black nodes show the three hosts if their Elo ratings are increased by 100 due to home advantage.
• Figure 4: The uncertainty of group stage matches in the two formats for the 2026 FIFA World Cup for each national team Notes: The two winners of the play-offs are represented by their expected Elo ratings. The six black nodes show the three hosts if their Elo ratings are increased by 100 due to home advantage.
• Figure 5: The uncertainty of matches in the two formats for the 2026 FIFA World Cup Note: Round of 32 in the imbalanced format refers to the play-offs for the Round of 16.