Department of Data Science, Seoul National University of Science and Technology, Seoul, South Korea.
Department of Operation Research, OTIS Elevator Company, Farmington, CT, USA.
J Sports Sci. 2024 Jun;42(11):959-970. doi: 10.1080/02640414.2024.2355423. Epub 2024 Jul 15.
This study constructs a discrete-time Markov Chain (DTMC) model for a baseball plate appearance (PA) employing Major League Baseball's pitch-by-pitch dataset. Based on the DTMC model, we propose a novel measure for a baseball PA, termed the Importance of Moment (IOM). The IOM quantifies the criticality of each ball-strike count situation, by assessing the probabilistic difference between the pitcher's and hitter's favourable outcomes (out vs reaching base). If the favours significantly vary right after a particular ball-strike count, then the count is deemed critical and is assigned a high IOM value. We empirically verify that IOM explains pitchers' behaviour of fastball speed. We then further investigate whether the behaviour of ace pitchers differs significantly from the majority. Several interesting properties are found from the analysis. Firstly, the path independence assumption generally holds, with the exception of the ball-strike count of 2B1S. Second, pitchers tend to throw the faster fastball at counts with higher IOM values. Lastly, ace pitchers are capable of pitching even faster fastball in two-strike situations in which IOM is high. The DTMC effectively models the probabilistic structure of a baseball PA, and the proposed IOM measure serves as a useful tool for explaining player behaviour.
本研究构建了一个用于棒球击球表现（PA）的离散时间马尔可夫链（DTMC）模型，该模型使用了美国职业棒球大联盟的逐拍数据集。基于这个 DTMC 模型，我们提出了一个新的棒球 PA 度量标准，称为重要时刻（IOM）。IOM 通过评估投手和击球手有利结果（出局或上垒）之间的概率差异，来量化每个球-击数情况的关键性。如果在特定的球-击数之后，有利情况有明显变化，那么这个球-击数就是关键的，并且会被赋予一个高的 IOM 值。我们通过实证验证了 IOM 可以解释投手的快球速度行为。然后，我们进一步研究了王牌投手的行为是否与大多数投手有显著差异。从分析中发现了几个有趣的性质。首先，路径独立性假设通常成立，但 2B1S 的球-击数除外。其次，投手往往会在 IOM 值较高的球-击数时投出更快的快球。最后，王牌投手在 IOM 值较高的两击情况下，能够投出更快的快球。DTMC 有效地模拟了棒球 PA 的概率结构，而提出的 IOM 度量标准则是解释球员行为的有用工具。
