A quantitative analysis of sports tournament designs

Mat Yusof, M

Abstract

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.

Citation

Mat Yusof, M. A quantitative analysis of sports tournament designs. (Thesis). University of Salford

• Thesis Type: Thesis
• Deposit Date: Aug 4, 2021
• Award Date: Jan 1, 2012