Fair and Efficient Ranking in Incomplete Tournaments

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Fernando Leiva Bertran


I discuss basic desirable fairness standards for the case of ranking teams in incomplete tournaments. I present a parsimonious family of scoring methods that uniquely satisfies these standards. It includes the win percentage method as a special case. I analyze this family of scoring methods in terms of efficiency, defined as how close a scoring method comes to capturing what the teams’ win percentages would have been, in a complete tournament. I show that efficient scoring methods are typically unfair. Finally, using data on betting odds, I calibrate the family of scoring methods to match, as closely as possible, the actual rankings that were used to determine the teams that would go on to compete for the championship of the NCAA division 1 football tournament between 2011 and 2017. I find that the rankings used by the NCAA were generally efficient and unfair, and I quantify the biases present in each year’s ranking.