On outcome uncertainty and scoring rates in sport: The case of international rugby union

Abstract

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.

A Variance Gamma model for Rugby Union matches

“…Alongside the statistical modelling of empirical match data (Boshnakov, Kharrat and McHale 2015) the classical Poisson model also possesses a surprising degree of theoretical elegance. This is discussed in Scarf et al (2019) but arguably goes much deeper.…”

“…The modelling of Rugby Union matches is of independent interest in its own right (Scarf, Parma and McHale 2019). There is a large literature centred around Poisson models for soccer (see e.g.…”

“…Maher 1982). Whilst aspects of the Poisson model remain instructive, Rugby's complex scoring system is a significant complication (Scarf et al 2019). Whilst direct extensions of the classical Poisson model are possible they are highly parameterised (e.g.…”

“…single Poisson models for each mode of scoring) and important aspects of the intuition and analytical tractability may be lost. Alternative parametric models for Rugby Union are discussed in Scarf et al (2019). We add to this discussion by proposing a Variance Gamma model.…”

Predicting the national football league potential of college quarterbacks

“…Kendall and Lenten (2017) examine sports rules from an OR perspective to explain situations where rules led to unforeseen and/or unwanted consequences. Scarf et al (2019) examine the relationship between outcome uncertainty and scoring rates in international rugby union and conclude that increased scoring rates may reduce spectator interest. Arlegi and Dimitrov (2020) analyze the fairness of alternative elimination-type structures for sporting competitions.…”