Simulation of a Probabilistic Model for Multi-Contestant Races

Abstract

Predictions of sports games have been recognized as an important area of study for their economic significance. Most models for such games cover two-player games and the resulting championships or study individual players or teams and their resulting comparative position. In this paper, we elaborate on a model for such multi-contestant races based on order statistics of the negative exponential distribution for race times. The games involve only a fixed number of athletes out of a broader pool of several athletes. Several large samples of games of ten athletes that play four at a time are generated, and Maximum Likelihood Estimators are calculated for the relative dominance parameters of the athletes. The estimated parameters are then used to test the predictive validity of the model. The results are discussed. Subsequently the model is modified for Erland-2 distributed race times. New samples are generated and the predictive validity of the new model is discussed. The paper concludes with a discussion of future research directions for improving the predictive validity and establishing confidence levels.