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.

Modelling team performance in soccer using tactical features derived from position tracking data

“…As we wanted to compute the win probability for a team to allow giving feedback to decisionmakers, and because they are typically noisy without clear patterns, we first omitted draws (N = 74) from the training and validation process, as we were mainly interested in predicting winners and losers, and draws-which can be regarded a research line of their own-would be a source of added noise (Hvattum, 2017). Furthermore, we needed classifiers that allow interpretation on the level of individual features and perform relatively well on a small dataset.…”

“…Finally, future work could resolve some of the limitations we currently encountered. For example, given their added noise (Hvattum, 2017), we deliberately omitted draws from the current study, but it would definitely be interesting to study what differentiates draws from matches with a clear winner and loser.…”