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Is There Really Racism Among MLB Umpires? Revisiting the Hamermesh Study Phil Birnbaum www.philbirnbaum.com

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The Hamermesh Study "Strike Three: Umpires' Demand for Discrimination" "Strike Three: Umpires' Demand for Discrimination" By Christopher A. Parsons, Johan Sulaeman, Michael C. Yates, and Daniel S. Hamermesh Original August, 2007; update December, 2007

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The Hamermesh Study Discussed in Time, USA Today, Business WeekTimeUSA TodayBusiness Week Claims to have found widespread discrimination – umpires (unconsciously) discriminate in favor of pitches of their own race Call more strikes for pitchers of the same race as them "Basically, it's an expression of deep-down preferences," says Hamermesh. "Am I sure it's there? Oh, yeah." – Business Week

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Situations When looking at all pitches, no discrimination found But lots of apparent racial bias when QuesTec not in use And even more apparent racial bias when attendance is low Study claims: when umpires are not being scrutinized, they discriminate

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Low Attendance I don't have the authors' data; I duplicated as best as I could But my results are similar to the study's Differences won't affect any conclusions here

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Low-Attendance Games White Pitchers Hispanic Pitchers Black Pitchers White Umpires 31.88 (376,954) 31.27 (107,434) 31.27 (10,471) 31.73 Hispanic Umpires 31.41 (10,334) 32.47 (2,864) 28.29 (258) 31.58 Black Umpires 31.22 (23,603) 31.21 (6,585) 32.52 (695) 31.25 31.8331.3131.2831.70

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Is There Racial Bias? Model each cell as: Baseline % strikes Plus effect for the race of the umpire Plus effect for the race of the pitcher Plus effect if the umpire's race matches the pitcher's ("UPM") If the UPM is different from zero, there's racial discrimination

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The Study's Conclusion After adjusting for race of umpire and pitcher, the pitch is 0.76 percentage points more likely to be called a strike if the umpire is the same race as the pitcher. Statistically significant result (Real study: 0.84, even more significant)

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Implications Lots of discrimination apparent 0.76% of same race pitches: 1 in 130! Almost 5,000 pitches affected If only ¼ of pitches are borderline, the 1 in 130 becomes 1 in 30 Wow!!

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The Updated Fit White Pitchers Hispanic Pitchers Black Pitchers White Umpires 31.88 31.1231.27 Hispanic Umpires 31.41 32.47 31.7128.29 Black Umpires 31.2231.21 32.52 31.76

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But Why Those Three Cells? There are lots of other ways to modify the matrix to remove discrimination

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How About This Instead? White Pitchers Hispanic Pitchers Black Pitchers White Umpires 31.8831.27 Hispanic Umpires 31.4132.47 30.80 28.29 30.80 Black Umpires 31.2231.21 30.61 32.52 30.61

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Why Didn't the Study Do That? Because the authors insisted that all races of umpires must discriminate the same Hidden assumption in the regression model But why? Discrimination normally goes one way more than the other Do blacks really discriminate against whites exactly as much as whites discriminate against blacks? Doesn't seem right to me

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Alternative Assumptions There are lots of ways in which to adjust the 3x3 chart to achieve NO discrimination. The way I chose minimizes the number of pitches affected But my choice means there's discrimination among minority umps only

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Number of Pitches Affected White Pitchers Hispanic Pitchers Black Pitchers White Umpires 000 Hispanic Umpires 0 1.67% * 2864 48 -1.49% * 258 4 Black Umpires 0 -0.61% * 6585 40 1.91% * 695 14

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Pitches Affected Total pitches affected: 116 Fewer than 1 in 4,000 Original study had 5,000 pitches affected – 43 times as many! Still statistically significant

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Assumption I think it's necessary to consider all possible alternatives to the study's hidden assumption that all groups discriminate equally If you do, then the only conclusion you can draw is statistical significance SOMETHING is going on, but we don't know what We don't know which races of umpire discriminate which races they discriminate against how much they discriminate

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Another Hidden Assumption A second hidden assumption: all umpires discriminate equally Not just that white umpires overall discriminate the same amount as black, but that every white umpire discriminates the same amount as every black umpire

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Do All Umpires Discriminate Equally? Different humans have different attitudes towards other races There are racists, advocates of race- neutrality, and advocates of affirmative action Why should umpires be any different in how much they discriminate?

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Checking for Individual Variation If there were no bias, apparent umpire bias would occur by chance Just by random luck, some white umpires would see fewer legitimate strikes from black pitchers We can predict exactly what would happen – a bell curve with a certain spread It turns out that real life is almost exactly what would occur by chance In binomial Z-scores, sample variance was 1.04 (expected 1.00). If there were significant differences in how umpires discriminate, the variance would be much higher

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Possibilities The possibilities of umpire bias are: 1. Many or all umps discriminate: (1a) a lot, and equally (1b) a lot, but unequally (1c) very, very little and equally (1d) very, very little but unequally 2. No umps discriminate 3. At most a few umps discriminate I argue that (1a) is implausible. The previous slide eliminated (1b). The statistical significance of the findings contradicts (1c), (1d), and (2). That leaves (3).

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At Most a Few Umpires Discriminate It could be that a small number of umpires are responsible for the entire effect! There were only 2 hispanic umpires and 4 black umpires Look at individual umpires

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Umpires vs. Hispanic Pitchers Individual umpires ranked by how much they appear to favor hispanic pitchers, in descending order of favorable discrimination. (X's are hispanic umps, hyphens are non- hispanic umps) ---X--------X---------------------------------- The two hispanic umps favor hispanic pitchers more than most

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Umpires vs. Black Pitchers Individual umpires ranked by how much they appear to favor black pitchers, in descending order of favorable discrmination. (X's are black umps, hyphens are non-black umps) X--------X---------X-------------------X------- Two of the four black umps favor black pitchers more than most

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Significance If there were no racial bias, the Xs would be balanced around the center If you remove ONE umpire... Either hispanic umpire The most extreme black umpire... then the results are no longer statistically significant! Next step: look closely at those individual umpires (review game tapes, for instance)

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Two Competing Theories Hamermesh et al Assumptions All races of umpires discriminate equally Every umpire discriminates equally Every umpire and race discriminates Conclusions Huge numbers of pitches are affected Because there are so many white umpires, minority pitchers are at a disadvantage

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Two Competing Theories Me Assumptions Discrimination can vary by umpire Conclusions The observed effect is likely caused by a small number of minority umpires, maybe even one Only a small number of pitches is affected Because the umpires involved are minorities, minority pitchers are probably beneficiaries of this discrimination

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Other Explanations From the Hamermesh authors' FAQ:FAQ "Suppose for example, that youth baseball coaching is different in Latin America than elsewhere, and that Hispanic pitchers consequently develop pitching “styles” that differ from those of Black, Asian, or White pitchers. If Hispanic umpires and pitchers both espouse similar styles that differ from other races/ethnicities, then what appears as discrimination may simply reflect these stylistic differences." Statistical significance is not proof There might be something else happening

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