During the first ten seasons of integrated Major League Baseball, black batters were hit by pitches about 86% more often per plate-appearance than white batters. However, on average black players during this period were superior players. To investigate to what extent the difference in hit-by-pitch can be explained by performance and characteristics other than race, we use a fractional logit model to estimate hit-by-pitch per plate appearance during a season. Our data are from Baseball-Reference.com . Controlling for differences in performance and other characteristics and including interaction terms with race, the difference falls to about 42%. A little over half the difference is explained by factors beyond race. The remaining difference might reflect different batting styles for early black batters. However, when observations where hit-by-pitch per plate appearance are in the top 2.5% of the sample are removed, black players were about 46% more likely to be hit. Plots of the marginal effects from a model using interactive terms show that the likelihood of a black player being hit rose relative to that of a white player as base-on-balls, singles, doubles, home runs, or stolen bases per plate appearance rose. Some pitchers may have exhibited animosity towards black players either by hitting them or taking less care to avoid hitting them. Our findings support previous research that better batters and batters who play for teams who score more runs are more likely to be hit by pitches. Because empirical evidence suggests pitchers might alter pitches to intimidate, discriminate, or retaliate, changes to existing rules could reduce the frequency of hits-by-pitch .

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恐吓、歧视和报复：美国职业棒球大联盟整合过程中的投球命中率

在美国职业棒球大联盟的前十个赛季中，黑人击球手在每次上场时被球击中的频率比白人击球手高 86%。然而，平均而言，这一时期的黑人球员是优秀的球员。为了研究在多大程度上可以通过比赛以外的表现和特征来解释击球率的差异，我们使用分数 logit 模型来估计一个赛季中每个板块出现的击球率。我们的数据来自 Baseball-Reference.com。控制性能和其他特征的差异，包括与种族的交互项，差异下降到约 42%。超过一半的差异是由种族以外的因素解释的。其余的差异可能反映了早期黑人击球手的不同击球风格。然而，当观察到每块板的击球次数位于样本的前 2.5% 时，黑人球员被击中的可能性增加了约 46%。使用交互式术语的模型的边际效应图显示，相对于白人球员，黑人球员被击中的可能性上升，因为每盘出现的垒球、单打、双打、本垒打或被盗垒上升. 一些投手可能对黑人球员表现出敌意，要么打他们，要么不太小心避免打他们。我们的发现支持之前的研究，即更好的击球手和为得分更多的球队效力的击球手更有可能被投球击中。因为经验证据表明投手可能会改变投球方式来恐吓、歧视或报复，