A quantitative analysis of sports tournament designs

In this study, we develop quantitative methodology to investigate optimal designs andfairness in sports tournaments. We propose a number of tournament metrics that can beused to measure the success of sporting contests or tournaments, and describe how thesemetrics may be evaluated for a particular tournament design. Our principal metric isbased on tournament outcome uncertainty. Tournament outcome uncertainty dependson: the structure of the tournament (such as round-robin, knock-out and hybrids ofthese); the relative strengths of the competitors (competitive balance); and theassignment of teams to individual matches or groups (seeding). Tournament outcomeuncertainty is measured using the tournament outcome characteristic which is theprobability that a particular team in the top 100# pre-tournament rank percentileprogresses forward from round R, for all q and R. We show how tournament designs(the structure, seeding policy and progression rule) and competitive balance influencesuncertainty of outcome. We use Monte Carlo simulation to calculate the values of thetournament metrics. Two match prediction models are employed for the simulation ofindividual match outcomes: (1) the double Poisson model and (2) the Bradley-Terrymodel. These individual match outcome models are then used to run a completesimulation of a tournament. The simulation studies show that the tournament design andcompetitive balance have significant effects on the progression of teams in thetournament. Our methodology is illustrated for various tournaments: the UEFAChampions 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 favouritismvaries with type of seeding. Reseeding after each round favours the strong to thegreatest extent. A new efficiency measure for a tournament is also proposed based onthe ability of the tournament to discriminate between competitors' strengths (power)and the size of the tournament. Under these notions the round robin is more powerfulbut less efficient than the knockout design. Comparative studies on seeding techniquesshow that random seeding reduces the power and efficiency of the tournament