对手统计量的普适性及其在MLB中的应用
Universal Behavior of Opponent Statistics and Applications to the MLB
摘要：
在大多数流行的体育联盟中，如MLB，NBA和NFL，没有一个常用的统计数据考虑到球员面对的对手的实力。其中一个主要原因是传统的信念，一个球员的运气往往会在一个赛季的过程中。另一个主要原因是很难找到一个合理的算法来量化对手的实力，并将这种量化纳入球员的统计数据的重新规范化。在本文中，我们首先认为，某些统计数据，如赢得运行平均（ERA）或菲尔丁独立投球（FIP）可以显着扭曲对手的实力在美国职棒大联盟。然后，我们提出了一个算法来重新规范化这样的统计数据，使用FIP作为主要的例子。这是通过观察MLB中所有30支球队的某些对手统计数据（例如，在一个赛季的过程中收集每场比赛的对手FIP值）遵循泛分布来实现的，直到缩放和移位。这使我们能够建立一个假设的平均球队的数据集，并开发一个投手统计的基础上FIP占投手的时间表，通过基于等百分位数等值的方法的强度。它被称为aFIP，它衡量一个投手的FIP会是什么，如果他面对一个联盟平均进攻球队每次他投球。我们发现，在2019赛季和其他赛季，一些投手的aFIP和FIP之间存在显著差异，为球员评估增加了一个新的工具。这可能会在球员合同和球队的利润上产生数百万美元的差异，因为他们提高了球员收购的准确性。我们观察到的泛分布在整个体育界也有许多可能的未来应用。
英文摘要：
In most popular sports leagues, like the MLB, NBA, and NFL, none of the commonly used statistics take into account the strengths of the opponents a player faces. One of the main reasons for this is the conventional belief that a player's luck tends to even out over the course of a season. The other main reason is the difficulties of finding a sensible algorithm to both quantify the strengths of the opponents and incorporate such quantifications into a renormalization of a player's statistics. In this paper, we first argue that certain statistics, such as Earned Run Average (ERA) or Fielding Independent Pitching (FIP) can be significantly skewed by opponents' strengths in the MLB. We then present an algorithm to renormalize such statistics, using FIP as the main example. This is achieved by observing that certain opponent statistics for all 30 teams in the MLB (e.g. the collection of each game's opponent FIP value over the course of a season) follow a universal distribution, up to scaling and shift. This enables us to establish a data set for a hypothetical average team and to develop a pitching statistic based on FIP which accounts for the strength of a pitcher's schedule through methods based on equipercentile equating. It is called aFIP, which measures what a pitcher's FIP would have been if he had faced a league-average offensive team every time he pitched. We find that there is a significant difference between aFIP and FIP for some pitchers during the 2019 season and other seasons as well, adding a new tool for player evaluation. This could make millions of dollars of difference in player contracts and in profits for teams as they enhance the accuracy with which they make player acquisitions. The universal distribution we observed also has many possible future applications throughout the sports world.
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。
