Ordinal versus nominal regression models and the problem of correctly predicting draws in soccer

Abstract

Ordinal regression models are frequently used in academic literature to model outcomes of soccer matches, and seem to be preferred over nominal models. One reason is that, obviously, there is a natural hierarchy of outcomes, with victory being preferred to a draw and a draw being preferred to a loss. However, the often used ordinal models have an assumption of proportional odds: the influence of an independent variable on the log odds is the same for each outcome. This paper illustrates how ordinal regression models therefore fail to fully utilize independent variables that contain information about the likelihood of matches ending in a draw. However, in practice, this flaw does not seem to have a substantial effect on the predictive accuracy of an ordered logit regression model when compared to a multinomial logistic regression model. Keywords: association football, forecasting, ordered regression