In this paper we investigate the relationship between outcome uncertainty and scoring rates in the framework of a "Poisson match". We argue that increasing scoring rates in the hope of increasing entertainment may have a detrimental impact on the popularity of sport. The basis of our argument is that higher scoring-rates decrease outcome uncertainty. We use international rugby to demonstrate our findings and show that scoring rates have indeed increased significantly over the previous half-century in this sport. Therefore, administrators should recognise our general point and we suggest that rugby union administrators in particular ought to consider the introduction of new laws to reduce scoring-rates. Scenarios in which the scoring-rate is radically reduced are illustrated through a simulation of the Rugby World Cup tournament.
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.
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