[Paper Review] Group draw with unknown qualified teams: A lesson from the 2022 FIFA World Cup draw

Łászló Csató|arXiv (Cornell University)|Mar 31, 2022

Sports Analytics and PerformanceEconomics, Econometrics and Finance19 references14 citations

TL;DR

This paper proposes that FIFA should assign placeholders for unknown World Cup play-off winners based on the higher-ranked potential winner, not the weakest pot. Using simulation, it shows this method minimizes group imbalance, with Seeding A (highest-ranked team) producing the fairest group strengths—especially critical when strong teams are uncertain, as in the 2022 World Cup draw.

ABSTRACT

The draw for the 2022 FIFA World Cup has been organised before the identity of three winners of the play-offs is revealed. Seeding has been based on the FIFA World Ranking released on 31 March 2022 but these three teams have been drawn from the weakest Pot 4. We show that the official seeding policy does not balance the difficulty levels of the groups to the extent possible: a better alternative would have been to assign the placeholders according to the highest-ranked potential winner, similar to the rule used in the UEFA Champions League qualification. Our simulations reinforce that this is the best strategy in general to create balanced groups in the FIFA World Cup.

Motivation & Objective

• To analyze the fairness of the 2022 FIFA World Cup draw procedure, which assigned unknown play-off winners to the weakest pot.
• To evaluate whether seeding placeholders based on the highest-ranked potential winner would improve group balance.
• To compare three seeding policies—highest-ranked, lowest-ranked, and weakest pot—under varying assumptions about play-off outcomes.
• To demonstrate that the official seeding policy disadvantages certain teams, including Ukraine, due to arbitrary assignment of strong potential teams to the weakest pot.
• To advocate for adopting a seeding rule already used in UEFA competitions, improving fairness without changing the overall draw mechanism.

Proposed method

• Simulates 1 million draws under three seeding rules: (A) placeholder assigned to highest-ranked potential winner, (B) to lowest-ranked, (C) to weakest pot (as per FIFA).
• Models group strength as the expected sum of team rankings (lower is better), with team strength derived from FIFA World Ranking (33 - rank).
• Uses three distinct settings: (1) all teams eligible for play-offs, (2) only weakest 21 teams eligible, (3) same as (2) but with higher imbalance in win probabilities.
• Applies random assignment from each pot to form eight groups, ensuring no geographic violations via computer-assisted allocation in alphabetical order.
• Measures fairness via expected group strength and variance across groups, comparing outcomes under each seeding policy.
• Employs a stylized theoretical model to isolate the effect of seeding policy from other variables like match outcomes or confederation constraints.

Experimental results

Research questions

• RQ1 Does assigning unknown play-off winners to the weakest pot (Pot 4) result in a more balanced distribution of group strengths than alternative seeding rules?
• RQ2 How does the expected strength of the strongest group (group of death) vary across different seeding policies?
• RQ3 What is the impact of seeding based on the higher-ranked potential winner compared to the lower-ranked or weakest pot?
• RQ4 How do different assumptions about play-off match outcomes (e.g., stronger vs. weaker teams) affect the fairness of the seeding policy?
• RQ5 Can a simple seeding rule—using the higher-ranked team’s ranking for placeholder assignment—improve fairness without altering the draw procedure?

Key findings

• Seeding A—assigning the placeholder based on the highest-ranked potential winner—produces the most balanced group strengths across all simulation settings.
• Under Setting 1 (all teams eligible), Seeding A reduces the expected strength of the strongest group by 1.5–2.0 points compared to Seeding C (weakest pot), indicating a significantly fairer outcome.
• In Setting 2 (only weakest 21 teams in play-offs), Seeding A still minimizes imbalance across the six strongest groups, though Seeding B (lowest-ranked) performs better for the weakest group (B–H), suggesting trade-offs in extreme cases.
• In Setting 3 (higher imbalance in win probabilities), Seeding A remains optimal overall, as the likelihood of a lower-ranked team winning is low, making the higher-ranked seeding more reliable.
• The official FIFA policy (Seeding C) systematically disadvantages strong potential teams like Ukraine, who were assigned to Pot 4 despite being ranked 24th, leading to a higher risk of facing stronger groups.
• The simulation results are robust across different assumptions, indicating that the direction of the effect—Seeding A being superior—holds under a wide range of plausible conditions.