Inferring Relative Ability from Winning Probability in Multientrant Contests

Abstract

We provide a fast and scalable numerical algorithm for inferring the distributions of participant scores in a contest under the assumption that each participant's score distribution is a translation of every other's. We term this the horse race problem, as the solution provides one way of assigning a coherent joint probability to all outcomes and pricing arbitrarily complex horse racing wagers. However, the algorithm may also find use anywhere winning probabilities are apparent, such as with e-commerce product placement, in Web search, or, as we show, in addressing a fundamental problem of trade: who to call, based on market share statistics and inquiry cost.