Defensive repositioning strategies (shifts) have become more prevalent in Major League Baseball in recent years. In 2018, batters faced some form of the shift in 34% of their plate appearances (Sawchik, Travis. 2019. “Don’t Worry, MLB–Hitters Are Killing The Shift On Their Own.” FiveThirtyEight , January 17, 2019. Also available at fivethirtyeight.com/features/dont-worry-mlb-hitters-are-killing-the-shift-on-their-own/). Most teams use a shift that overloads one side of the infield and adjusts the positioning of the outfield. In this work we describe a mathematical approach to the positioning of players over the entire field of play without the limitations of traditional positions or current methods of shifting. The model uses historical data for individual batters, and it leaves open the possibility of fewer than four infielders. The model also incorporates risk penalties for positioning players too far from areas of the field in which extra-base hits are more likely. This work is meant to serve as a decision-making tool for coaches and managers to best use their defensive assets. Our simulations show that an optimal positioning with three infielders lowered predicted batting average on balls in play (BABIP) by 5.9% for right-handers and by 10.3% for left-handers on average when compared to a standard four-infielder placement of players.

中文翻译：

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挥杆动作：棒球防守位置的数学方法

近年来，防守调整策略（转变）在美国职棒大联盟中变得越来越普遍。在2018年，击球手的板球出场率发生了某种形式的变化（Sawchik，Travis。2019年。“别担心，美国职业棒球大联盟-击剑者正在自行消除这一变化。” FiveThirtyEight，2019年1月17日。另可在fourthirtyeight.com/features/dont-worry-mlb-hitters-killing-the-shift-on-the-own/上找到）。大多数团队使用的换挡会使内场的一侧过载，并调整外场的位置。在这项工作中，我们描述了一种数学方法来确定球员在整个比赛场上的位置，而不受传统位置或当前换挡方法的限制。该模型使用了单个击球手的历史数据，并且留下了少于四个内野手的可能性。该模型还纳入了风险惩罚措施，以将玩家定位在离基础命中率更高的领域之外的地方。这项工作旨在作为教练和经理人最佳利用其防守资产的决策工具。我们的模拟显示，与标准的四个内场球员位置相比，具有三个内场球员的最佳位置可使右手投手的平均比赛球击球率（BABIP）降低5.9％，向左手球员平均降低10.3％。