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.

摘要

我们将二项式匹配作为配对比赛中双变量得分的模型。这种模式自然与重新开始在目标之后交替进行的运动相关联。该模型是泊松匹配的挑战者，泊松匹配是一对独立的泊松随机变量，其均值与竞争球队的实力有关。我们主要使用二项式匹配来研究结果不确定性和评分率之间的关系，特别是对于评分率的高值。无挡板篮球的得分率很高，并推动了我们的模型开发。在二项式匹配框架中，我们还评估规则变化，并研究无挡板篮球的战术打法。我们的分析表明，二项式匹配并不是比泊松匹配更好的预测器，但它更适合表示结果不确定性和评估规则变化和策略。总的来说，我们发现对于给定的得分率，二项式匹配意味着比泊松匹配更大的结果不确定性，并且交替重启是减少并列结果频率的好规则。特别是对于无挡板篮球，我们表明，在最后一节开始时，在一场势均力敌的比赛中控球可能会带来显着的优势。