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

Abstract

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 P q,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.

OR analysis of sporting rules – A survey

“…Why should the number 2 seed be given this advantage which is denied to other weaker players? The reason is clearly to ensure high CI, especially at the latter stages of a tournament, even though it is at the expense of fairness, as we noted earlier following the analysis of Scarf and Yusof (2011). Baumann et al (2010) examine the issue of seeding in relation to the NCAA Basketball tournament between US Colleges popularly known as "March Madness", and they show that standard systems of seeding do not always maximise CI.…”

“…Scarf and Yusof (2011) used statistical analysis and simulation to gauge the effect of seeding the strongest competitors, using the FIFA World Cup to illustrate the analysis. They concluded that seeding was inherently unfair in that it always favoured the strongest competitors (since they are prevented from meeting other strong opponents early in the tournament), but that there was a compensatory increase in competitive balance (i.e.…”

Impact of Playoffs on Seasonal Uncertainty in Czech Ice Hockey Extraliga

“…First, each pair of teams plays up to seven matches to determine which team moves to the next round; this is much more than one or two matches typically used in soccer. Second, teams are reseeded for each round; this type of seeding was shown to help the strongest teams the most by Scarf and Yusof (2011). Third, higher-seeded teams play any decisive match in the series on their home ice.…”

“…The round-robin design (which would be extremely impractical in reality due to a large number of matches) maximized the probability of the best team winning the tournament, while the unseeded 2 leg design maximized the uncertainty of outcome. A similar approach was used in Scarf and Yusof (2011) to show that seeding favors stronger teams and thus reduces uncertainty of outcome in FIFA World Cup finals. This paper uses an approach similar to Scarf et al (2008) to analyze the tournament design of the top Czech ice-hockey competition "Extraliga".…”

It is Harder, Not Easier, to Predict the Winner of the Champions League

“…Appleton, 1995;McGarry and Schutz, 1997;Scarf et al, 2009;Scarf and Yusof, 2011;Koning and McHale, 2012). For this purpose prediction models are used to simulate the expected outcomes of games between two teams.…”