A numerical study of tournament structure and seeding policy for the soccer World Cup Finals

Tournament outcome uncertainty depends on: the design of the tournament; and the relative strengths of the competitors – the competitive balance. A tournament design comprises the arrangement of the individual matches, which we call the tournament structure, the seeding policy and the progression rules. In this paper, we investigate the effect of seeding policy for various tournament structures, while taking account of competitive balance. Our methodology uses tournament outcome uncertainty to consider the effect of seeding policy and other design changes. The tournament outcome uncertainty is measured using the tournament outcome characteristic which is the probability Pq,R that a team in the top 100q pre-tournament rank percentile progresses forward from round R, for all q and R.We use Monte Carlo simulation to calculate the values of this metric. We find that, in general, seeding favours stronger competitors, but that the degree of favouritism varies with the type of seeding. Reseeding after each round favours the strong to the greatest extent.The ideas in the paper are illustrated using the soccer World Cup Finals tournament.