A quantitative analysis of sports tournament designs

In this study, we develop quantitative methodology to investigate optimal designs and fairness in sports tournaments. We propose a number of tournament metrics that can be used to measure the success of sporting contests or tournaments, and describe how these metrics may be evaluated for a particular tournament design. Our principal metric is based on tournament outcome uncertainty. Tournament outcome uncertainty depends on: the structure of the tournament (such as round-robin, knock-out and hybrids of these); the relative strengths of the competitors (competitive balance); and the assignment of teams to individual matches or groups (seeding). Tournament outcome uncertainty is measured using the tournament outcome characteristic which is the probability that a particular team in the top 100# pre-tournament rank percentile progresses forward from round R, for all q and R. We show how tournament designs (the structure, seeding policy and progression rule) and competitive balance influences uncertainty of outcome. We use Monte Carlo simulation to calculate the values of the tournament metrics. Two match prediction models are employed for the simulation of individual match outcomes: (1) the double Poisson model and (2) the Bradley-Terry model. These individual match outcome models are then used to run a complete simulation of a tournament. The simulation studies show that the tournament design and competitive balance have significant effects on the progression of teams in the tournament. Our methodology is illustrated for various tournaments: the UEFA Champions League, the FIFA soccer World Cup Finals and the ICC cricket World Cup. Seeding policy is found to favour stronger competitors, but the degree of favouritism varies with type of seeding. Reseeding after each round favours the strong to the greatest extent. A new efficiency measure for a tournament is also proposed based on the ability of the tournament to discriminate between competitors' strengths (power) and the size of the tournament. Under these notions the round robin is more powerful but less efficient than the knockout design. Comparative studies on seeding techniques show that random seeding reduces the power and efficiency of the tournament.