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How to optimise tournament draws: The case of the FIFA World Cup

László Csató

TL;DR

The paper tackles the trade-off between attractiveness and fairness in constrained group draws for major tournaments, proposing a parametric optimization framework to balance inter-continental matchups against deviation from a uniform draw. It applies the model to the FIFA World Cup draws of 2018 and 2022, comparing the Skip mechanism with a uniform draw via Monte Carlo simulations and quantifying non-uniformity with Delta and Omega alongside intra-confederation match counts. Key findings include the suboptimality of pre-assigning the host to Group A, the sensitivity of fairness to draw constraints (notably Constraint E), and a Pareto frontier that reduces to a small set of efficient constraint combinations, offering practical guidance for policy design. The framework enables stakeholders to justify draw rules and quantify trade-offs, with broad applicability to other tournaments and geographic constraint settings.

Abstract

The organisers of major sports competitions use different policies with respect to constraints in the group draw. Our paper aims to rationalise these choices by analysing the trade-off between attractiveness (the number of games played by teams from the same geographic zone) and fairness (the departure of the draw mechanism from a uniform distribution). A parametric optimisation model is formulated and applied to the 2018 and 2022 FIFA World Cup draws. A flaw of the draw procedure is identified: the pre-assignment of the host to a group unnecessarily increases the distortions. All Pareto efficient sets of draw constraints are determined via simulations. The proposed framework can be used to find the optimal draw rules and justify the non-uniformity of the draw procedure for the stakeholders.

How to optimise tournament draws: The case of the FIFA World Cup

TL;DR

The paper tackles the trade-off between attractiveness and fairness in constrained group draws for major tournaments, proposing a parametric optimization framework to balance inter-continental matchups against deviation from a uniform draw. It applies the model to the FIFA World Cup draws of 2018 and 2022, comparing the Skip mechanism with a uniform draw via Monte Carlo simulations and quantifying non-uniformity with Delta and Omega alongside intra-confederation match counts. Key findings include the suboptimality of pre-assigning the host to Group A, the sensitivity of fairness to draw constraints (notably Constraint E), and a Pareto frontier that reduces to a small set of efficient constraint combinations, offering practical guidance for policy design. The framework enables stakeholders to justify draw rules and quantify trade-offs, with broad applicability to other tournaments and geographic constraint settings.

Abstract

The organisers of major sports competitions use different policies with respect to constraints in the group draw. Our paper aims to rationalise these choices by analysing the trade-off between attractiveness (the number of games played by teams from the same geographic zone) and fairness (the departure of the draw mechanism from a uniform distribution). A parametric optimisation model is formulated and applied to the 2018 and 2022 FIFA World Cup draws. A flaw of the draw procedure is identified: the pre-assignment of the host to a group unnecessarily increases the distortions. All Pareto efficient sets of draw constraints are determined via simulations. The proposed framework can be used to find the optimal draw rules and justify the non-uniformity of the draw procedure for the stakeholders.
Paper Structure (12 sections, 5 equations, 8 figures, 6 tables)

This paper contains 12 sections, 5 equations, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Related literature
  3. Methodology
  4. Draw procedures
  5. The rules of the 2018 and 2022 FIFA World Cup draws
  6. The optimisation model
  7. Details of the computation
  8. Results
  9. The suboptimality of pre-assigning the host
  10. The impact of draw constraints
  11. The Pareto frontier of the draw constraints
  12. Concluding remarks

Figures (8)

  • Figure 1: The average absolute bias of the Skip mechanism for all countries
  • Figure 2: The average number of intra-continental games and the chance of feasibility
  • Figure 3: The aggregated bias of the Skip mechanism for the 32 sets of draw constraints, 2018 FIFA World Cup draw
  • Figure 4: The aggregated bias of the Skip mechanism for the 32 sets of draw constraints, 2022 FIFA World Cup draw
  • Figure 5: The trade-off between intra-continental group matches and non-uniformity, 2018 FIFA World Cup Note: The dotted black line shows the Pareto frontier.
  • ...and 3 more figures

Theorems & Definitions (1)

  • Example 1