Fairness of the 2026 FIFA World Cup group-stage draw

Introduction: We evaluate the ex-ante fairness of the 2026 FIFA World Cup group-stage draw under official rules and two counterfactual mechanisms using a reproducible simulation. A 48-team pool consistent with confederation quotas is paired with an ex-ante team-strength index derived solely from past World Cup final-tournament matches using Lidstone shrinkage, with robustness checks employing the FIFA Ranking (SUM) and Elo ratings. Objective: We compare (i) FIFA-2026: pots by ranking with confederation caps and pre-assigned hosts; (ii) Feasible-uniform: a pot-free feasible baseline under the same confederation caps; and (iii) Fair-greedy: a post-draw, within-pot swap heuristic that accepts only coefficient-of-variation (CV)–reducing moves while preserving all constraints. Discussion: Across N = 500 simulated draws per mechanism, the mean CV of group-average strength is 0.0882 (Feasible-uniform), 0.0684 (FIFA-2026), and 0.0634 (Fair-greedy). Thus, relative to FIFA-2026, Feasible-uniform increases inequality by +0.0198 CV (~+28.9%), while Fair-greedy reduces it by −0.0050 (~−7.3%), with lower upper-tail risk under FIFA-2026 and Fair-greedy. Letter-level diagnostics under FIFA-2026 reveal lower difficulty for host-anchored groups and a concentration of “hardest-group” risk in a subset of non-host letters. Against a historical yardstick (1998–2022), FIFA-2026 and Fair-greedy remain within observed bounds, whereas Feasible-uniform can exceed them at the upper extreme. Conclusions: Overall, our results suggest a simple, constraint-preserving post-draw adjustment that can improve competitive balance without changing the live-draw structure.