The fairness of the group draw for the FIFA World Cup

TL;DR

This paper analyzes the fairness of the FIFA World Cup group draw, quantifies its bias, and evaluates its impact on teams' qualification probabilities, highlighting the importance of draw order in tournament fairness.

Contribution

It provides a quantitative assessment of the draw's unfairness and demonstrates how draw order influences qualification probabilities, proposing considerations for fairer draw mechanisms.

Findings

Official draw order reduces unfairness compared to other orders.

Non-uniform draw can alter qualification probabilities by over 1%.

Results inform policymakers on fairness improvements.

Abstract

Several sports tournaments contain a round-robin group stage where the teams are assigned to groups subject to some constraints. Hence, the organisers usually use a computer-assisted random draw to avoid any dead end, a situation when the teams still to be drawn cannot be assigned to the remaining empty slots. This procedure is known to be unfair: the feasible allocations are not equally likely, that is, the draw does not have a uniform distribution. We quantify the implied unfairness of the 2018 FIFA World Cup draw and evaluate its effect on the probability of qualification for the knockout stage for each national team. The official draw order of Pot 1, Pot 2, Pot 3, Pot 4 turns out to be a significantly better option than the 23 other draw orders with respect to the unwanted distortions. Nonetheless, the non-uniform draw distorts the probability of qualification by more than one percentage point for two countries. Our results call attention to the non-negligible role of draw order and make it possible for policymakers to decide whether using fairer draw mechanisms is justified.