Tournament qualification, seeding and selection efficiency : an analysis of the PGA TOUR's FedExCup

Analytical descriptions of tournament selection efficiency properties are elusive for realistic tournament structures. For example, with more than four competitors, there are very few robust analytical tournament selection efficiency measures. Combining a Monte Carlo simulation with a statistical model of player skill and random variation in scoring, we estimate the seeding and selection efficiency of the PGA TOUR's FedExCup, a very complex multi-stage golf competition, which distributes $35 million in prize money, including $10 million to the winner. Our assessments of efficiency are based on traditional selection efficiency measures along with several new measures which focus on the ability of a given tournament structure to identify properly the relative skills of all tournament participants and to distribute efficiently all of the tournament's prize money. Using these measures, we also estimate the relative efficiency of several alternative formats for the FedExCup Finals. We conclude that despite its lack of transparency compared with alternative Finals formats, the present Finals format appears to be the most efficient using all selection efficiency measures