Probability models on horse-race outcomes

SUMMARY A number of models have been examined for modelling probability based on rankings. Most prominent among these are the gamma and normal probability models. The accuracy of these models in predicting the outcomes of horse races is investigated in this paper. The parameters of these models are estimated by the maximum likelihood method, using the information on win pool fractions. These models are used to estimate the probabilities that race entrants ® nish second or third in a race. These probabilities are then compared with the corresponding objective probabilities estimated from actual race outcomes. The data are obtained from over 15 000 races. it is found that all the models tend to overestimate the probability of a horse ® nishing second or third when the horse has a high probability of such a result, but underestimate the probability of a horse ® nishing second or third when this probability is low.