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