Upload
drake-malden
View
216
Download
0
Embed Size (px)
Citation preview
Is There Really Racism Among MLB Umpires? Revisiting the Hamermesh Study
Phil Birnbaumwww.philbirnbaum.com
The Hamermesh Study "Strike Three: Umpires' Demand fo
r Discrimination" By Christopher A. Parsons, Johan
Sulaeman, Michael C. Yates, and Daniel S. Hamermesh
Original August, 2007; update December, 2007
The Hamermesh Study Discussed in Time, USA Today, Business 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
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
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
Low-Attendance GamesWhite 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
31.83 31.31 31.28 31.70
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
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)
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!!
The Updated FitWhite
PitchersHispanic Pitchers
Black Pitchers
White Umpires
31.8831.12 31.27 31.27
Hispanic Umpires
31.4132.4731.71 28.29
Black Umpires
31.22 31.2132.5231.76
But Why Those Three Cells? There are lots of other ways to
modify the matrix to remove discrimination
How About This Instead?White
PitchersHispanic Pitchers
Black Pitchers
White Umpires
31.88 31.27 31.27
Hispanic Umpires
31.41 32.4730.80
28.2930.80
Black Umpires
31.22 31.2130.61
32.5230.61
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
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
Number of Pitches Affected
White Pitchers
Hispanic Pitchers
Black Pitchers
White Umpires
0 0 0
Hispanic Umpires
0 1.67% * 2864
48-1.49% * 258
4
Black Umpires
0 -0.61% * 6585
40
1.91% * 695
14
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
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
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
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?
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
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).
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
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
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
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)
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
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
Other Explanations From the Hamermesh authors' 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