竞技团队运动中的安全领先和领先变化
Safe Leads and Lead Changes in Competitive Team Sports
摘要：
我们调查的时间演变的领先优势的变化在个人比赛的竞争性团队运动。利用随机漫步理论的思想，单个游戏中的领先变化数量遵循高斯分布。我们表明，最后的铅变化和最大的铅大小的时间的概率是由相同的反正弦定律，双峰分布，在游戏的开始和结束时发散。我们还确定了概率，一个给定的铅是"安全的"作为其大小$L$和游戏时间$t$的函数。我们的预测通常与四个专业或半专业团队运动中大约40，000场比赛中超过125万次得分事件的综合数据一致，并且比目前用于体育分析的流行预测学更准确。
英文摘要：
We investigate the time evolution of lead changes within individual games of competitive team sports. Exploiting ideas from the theory of random walks, the number of lead changes within a single game follows a Gaussian distribution. We show that the probability that the last lead change and the time of the largest lead size are governed by the same arcsine law, a bimodal distribution that diverges at the start and at the end of the game. We also determine the probability that a given lead is "safe" as a function of its size $L$ and game time $t$. Our predictions generally agree with comprehensive data on more than 1.25 million scoring events in roughly 40,000 games across four professional or semi-professional team sports, and are more accurate than popular heuristics currently used in sports analytics.
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