失败者的得分策略：确定最佳运动策略的通用定量方法
Scoring Strategies for the Underdog: A general, quantitative method for determining optimal sports strategies
摘要：
当面对一个非常有利的对手时，一个失败者必须愿意承担高于平均水平的风险。用统计学的语言来说，人们会说，处于劣势的一方必须愿意采取一种结果方差大于平均值的策略。困难的问题是一个团队应该愿意接受多大的风险。这相当于询问团队应该愿意从其平均得分中牺牲多少来增加得分的方差。在本文中，一般的，分析方法是定量地解决这个问题。在假设每场比赛在统计上是独立的情况下，球队进攻输出的均值和方差都可以用二项分布来描述。这种描述允许在采用特定策略时直接计算获胜概率，因此允许计算最佳进攻策略。本文发展了这种方法来计算最优策略，然后提出了一个简单的启发式，以确定是否应采用给定的策略。然后探讨了一些有趣和违反直觉的例子，包括拖延时间的优点，美式足球中的跑位/传球/万福玛利亚选择，以及正确使用哈克沙克。
英文摘要：
When facing a heavily-favored opponent, an underdog must be willing to assume greater-than-average risk. In statistical language, one would say that an underdog must be willing to adopt a strategy whose outcome has a larger-than-average variance. The difficult question is how much risk a team should be willing to accept. This is equivalent to asking how much the team should be willing to sacrifice from its mean score in order to increase the score's variance. In this paper a general, analytical method is developed for addressing this question quantitatively. Under the assumption that every play in a game is statistically independent, both the mean and the variance of a team's offensive output can be described using the binomial distribution. This description allows for direct calculations of the winning probability when a particular strategy is employed, and therefore allows one to calculate optimal offensive strategies. This paper develops this method for calculating optimal strategies exactly and then presents a simple heuristic for determining whether a given strategy should be adopted. A number of interesting and counterintuitive examples are then explored, including the merits of stalling for time, the run/pass/Hail Mary choice in American football, and the correct use of Hack-a-Shaq.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
