Abstract We use a Markov decision process to model the value of the sacrifice bunt. Specifically, we consider a nine-inning baseball game with non-identical batters and compute the degree to which sacrificing increases the probability of winning the game. We populate our model using data covering the National League of Major League Baseball, and demonstrate the importance of using the probability of winning the game when analyzing the value of the sacrifice bunt. We show how and why the criterion of maximizing the probability of winning is superior to that of maximizing the expected number of runs scored or the probability of scoring at least one run in the half inning. Our model enables us to investigate situations that are not possible to investigate using earlier models, and find that the sacrifice bunt is more beneficial than previously thought. We also discuss the effect sizes of individual sacrifice bunts, and the effect of model simplifications on runner advancement or ignoring double plays.

中文翻译：

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使用马尔可夫决策过程对牺牲旗布的价值进行建模

摘要我们使用马尔可夫决策过程对牺牲床的价值进行建模。具体来说，我们考虑击球手不一样的九局棒球比赛，并计算牺牲的程度会增加赢得比赛的可能性。我们使用涵盖美国职棒大联盟全国联赛的数据填充模型，并证明了在分析牺牲bun头的价值时使用获胜概率的重要性。我们展示了如何以及为什么最大化获胜概率的标准优于最大化最大化预期得分数或在半局中得分至少一次的概率。我们的模型使我们能够调查使用早期模型无法调查的情况，并发现牺牲bun比以前想像的要有益。我们还讨论了单个牺牲短棍的效应大小，以及简化模型对跑步者前进或忽略双打的效应。