An approximation to ordering probabilities of multi-entry competitions

Abstract

To predict the ordering probabilities of multi-entry competitions (e.g. horse-races), Harville (1973) proposed a simple way of computing the ordering probabilities based on the simple, winning probabilities. This simple model essentially assumes the underlying model (e.g. running time in horse-racing) is independent exponential. Henery (1981) and Stern (1990) respectively proposed to use normal and gamma distributions for the running time. However both the Henery and Stern model are too complicated to use in practice. Bacon-Shone, Lo & Busche (1992,b) have shown that the Henery model fits better in horse-racing using particular data sets. In this paper, we propose to use a simple way of computing ordering probabilities which approximate both the Henery and Stern model quite well. Using Hong Kong. U.S. and Japanese data, a large scale empirical investigation is undertaken.