Abstract

This paper considers sports matches in which two teams compete to score more points within a set amount of time (e.g. football, ice hockey). We focus on the order in which the competing teams score during the match (order of scoring). This type of order of scoring problem has not been addressed previously, and doing so here gives new insights into sports matches. For example, our analysis can deal with a situation that spectators find matches that involve comebacks particularly exciting. To describe such problems mathematically, we formulate the probabilities of (i) the favourite team leading throughout the match and (ii) the favourite team falling behind the opposing team but then making a comeback. These probabilities are derived using an independent Poisson model and lattice path enumeration, the latter of which involves the well-known ballot theorem. The independence assumption allows lattice path enumeration to be applied directly to the Poisson model and various scoring patterns to be addressed. We confirm that the values obtained from the proposed models agree well with actual sports data from football, futsal and ice hockey.

中文翻译：

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建模团队运动中的得分顺序

摘要

本文考虑的是体育比赛，其中两支球队竞争在规定的时间内得分（例如足球，冰球）。我们专注于比赛中各支球队得分的顺序（得分顺序）。以前没有解决过这种类型的得分问题，在这里这样做可以为体育比赛提供新的见解。例如，我们的分析可以应对观众发现与卷土重来有关的比赛特别令人兴奋的情况。为了用数学方法描述此类问题，我们制定了（i）在整个比赛中领先的最爱球队，以及（ii）最喜欢的球队落后于对方球队但又卷土重来的概率。这些概率是使用独立的Poisson模型和晶格路径枚举得出的，后者涉及众所周知的投票定理。独立性假设允许将晶格路径枚举直接应用于Poisson模型，并解决各种计分模式。我们确认从提议的模型中获得的值与来自足球，五人制足球和冰球的实际体育数据非常吻合。