Assigning Probabilities to the Outcomes of Multi-Entry Competitions

Abstract The problem discussed is one of assessing the probabilities of the various possible orders of finish of a horse race or, more generally, of assigning probabilities to the various possible outcomes of any multientry competition. An assumption is introduced that makes it possible to obtain the probability associated with any complete outcome in terms of only the ‘win’ probabilities. The results were applied to data from 335 thoroughbred horse races, where the win probabilities were taken to be those determined by the public through pari-mutuel betting.