The binomial-match, outcome uncertainty, and the case of netball

Abstract

We introduce the binomial-match as a model for the bivariate score in a paired-contest. This model is naturally associated with sports in which the restart alternates following a goal. The model is a challenger to the Poisson-match, a pair of independent Poisson random variables whose means are related to the strengths of the competing teams. We use the binomial-match primarily to study the relationship between outcome uncertainty and scoring-rate, particularly for high values of the scoring-rate. Netball has a high scoring-rate and motivates our model development. In the binomial-match framework, we also evaluate rule-variations, and study tactical play in netball. Our analysis suggests that the binomial-match is not a better forecaster than the Poisson-match, but it is better for representing outcome uncertainty and evaluating rule-variations and tactics. In general, we find that the binomial-match implies greater outcome uncertainty than the Poisson match, for a given scoring-rate, and that an alternating-restart is a good rule for reducing the frequency of tied outcomes. For netball in particular, we show that starting the final quarter with possession in a close, balanced match may confer a significant advantage.