Discussion Papers In Economics
And Business

Pitch Call Discrimination in Major League Baseball:
The Effect on the Observed Performance and the Salaries

Reio Tanji
Discussion Paper 22-02

August 2022

Graduate School of Economics
Osaka University, Toyonaka, Osaka 560-0043, JAPANPitch Call Discrimination in Major League Baseball:
The Eﬀect on the Observed Performance and theSalaries
Reio Tanji†

Abstract
This paper identiﬁes discrimination in the professional baseball league in the
United States. We consider players, umpires, and team managers as employees,
middle managers, and employers in general workplaces. Using huge pitch-bypitch tracking data of the Major League Baseball reveals that umpires from North
America favor players with the same region when a pitcher from North America
and a batter from other regions are facing. The impact of this is dramatic: players
from other regions lose their chances to hit by the unfair pitch call, which values toloss of about $130,000 for in three years.
■JEL Classiﬁcation: D91, J01■keywords: sports, discrimination, in-group bias, baseball† Osaka University, Graduate School of Economics. email:u280537h@ecs.osaka.u-ac.jp

1

1 Introduction
Labor economics studies have long examined discrimination and have classiﬁed the favoritism
exhibited by evaluators toward individuals belonging to the same group as themselves, as ingroup bias. In-group bias has severe implications for the labor market.
This study presents an empirical analysis of in-group bias using a large dataset from Major
League Baseball (MLB). Situations there are common in the US even in the present day, withregular reports of incidents of discrimination. Thus, understanding the extent of discriminationin the MLB is essential for visualizing the existence of discrimination in society as a whole.
Speciﬁcally, we use a radar-based high-precision ballistic measurement device called the
Trackman, which was installed in all franchise ballparks of MLB teams from 2015 to 2019 torecord and disclose detailed information on the pitchers’ thrown ball trajectory and the batters’
batted ball launch angle and launch velocity. This study focuses on the pitch location as it passes
the home plate. When the pitcher throws a pitch and the batter does not hit it (takes), the plateumpire judges whether it is a strike or ball. Although there is a strict regulation where a pitch
should be called a strike, the umpire’s decision is visually validated. Thus, two pitches passing
through an exact location can be given diﬀerent calls, especially near the edge of the strikezone. This study considers this system can identify the objective information of the pitches.
By comparing this to the actual pitch calls, an evaluation by the plate umpire, we can examine
how their demographic characteristics aﬀect the evaluator’s (plate umpire) assessment of theachievement of the workers (players).
Because we can use workers’ (athletes’) performance as an objective measure, and because
it constitutes a large dataset, there has been a large body of literature on discrimination using
sports data. Among these, the most relevant to this paper is Parsons et al. (2011). They use
the MLB tracking data to analyze the impact of racial discrimination by the plate umpire, as inthis paper. The most important advantage of this dataset is the random assignment of umpires
and almost external variation in installations of "QuesTec."1 They found that racial diﬀerencesin pitchers and umpires increased the rate of strike calls. Tainsky et al. (2015) also conducted afollow-up study using the same data.
Compared to the previous studies, we emphasize the following new contributions: First,
we focus on how umpires’ bias distorts the players’ performance statistics; we also quantify
the magnitude of the eﬀect on the salary players receive. Objective information about pitch
locations enables us to see the probability that a speciﬁed pitch should be called strike and to
1 "QuesTec" is a technology installed in some of the franchise stadiums of the MLB teams, to provide feedback toumpires on the accuracy of their decisions.

2compare this result with the actual call. This, in turn, allows us to argue about the size of the
impact umpires have through pitch calls. Notably, this bias may distort the performance data of
discriminated players, making their performance appear worse than it is in reality. This negativeeﬀect is particularly important, because general managers oﬀer contracts based on observed
performance indicators. Hence, players discriminated against by umpires may be forced to sign
contracts on unfavorable terms/contracts of a lower monetary value than those favored.
To explore this problem this study takes advantage of a video-based judgment review systemcalled "Manager Challenge." Using this system, we can capture almost all indirect negative
impacts of umpire bias on player compensation. This study is unique as it deals with two sourcesof discrimination in the same context. One is the discrimination exhibited by umpires(evaluatorsin the workplace), and the other is by managers (principals) who oﬀer contracts to players (player
contracts). In a typical workplace, middle managers evaluate worker performance. Hence,
based on their reports, company heads decide whether to renew the contract with workers. This
environment is similar to the example we address in this study and provides suggestive results for
distinguishing between discrimination by middle managers and discrimination by the president.
From this perspective, this study also has implications for the more general context of labor
economics.
Second, this study provides a more evidence-based discussion of the endogeneity problem
implied by pitch tracking data, which is suggested in the prior literature. For example, pitchers
discriminated against may avoid pitching to the edge of the strike zone. Moreover, batters
may swing more aggressively, and we cannot observe such pitches as ones to be called. If so,biased calls may result in worse performance for batted balls hit by minority players. This study
explores this concern by analyzing the behavioral responses of batters toward pitches.
Our main results are as follows. First, the pitch calls made by umpires from the United States(US) suggest the inﬂuence of a nationality bias, based on batter nationality. Speciﬁcally, insituations where the pitcher is from the same country as the umpire but the batter is not, theumpire calls strikes at a higher rate (i.e., decisions are largely made in favor of the pitcher).
Based on the average probability of a strike call estimated from the information about the twodimensional location of the pitch, the variance of the probability in such a situation is about 0.3
percentage points per taken pitch.
The second result attempts to determine the monetary cost of nationality bias. Based on theﬁrst result, minority batters who consistently have their names in the lineup are called about
38 more strikes per year. This worsens the performance statistics that the managers observe,
resulting in a loss of approximately $40,000 in compensation per year that they could havereceived.
The third result concerns endogeneity in players’ decision-making. Discrimination by plate3

umpires may cause behavioral changes in players who perceive it, but the analysis conducted inthis study did not provide strong evidence to support these behavioral changes.
The remainder of this paper is organized as follows. Section 2 reviews the literature on
discrimination, especially empirical literature in the sports context. Section 3 explains theinstitutional background of baseball or MLB and the decision making of plate umpires in pitch
calls. Section 4 discusses the empirical data. Section 5 presents the empirical model used for
identiﬁcation, and Section 6 provides the results. Section 7 discusses the results, and Section 8
concludes the study.

2 Literature Review
Owing to the availability of rich datasets, many empirical studies use the MLB context for
research on in-group or racial bias. Scully (1974), who conducted one of the oldest and mostwell-known studies on the topic, estimated the proﬁt function of MLB teams and analyzed thecharacteristics of the players and the team’s revenue, proxied by the number of attendees. They
highlighted that an increase in the percentage of African American players in the team’s roster
harms the team’s revenue, and also discussed consumer bias by the audience. A similar study byHill et al. (1982) demonstrated that, if the home team’s starting pitcher announced in advance isa minority pitcher, attendance for that game decreases. Nardinelli and Simon (1990) examined
the MLB player card market and found that non-white pitchers with comparable performance
were valued about 13% lower than white pitchers (10% lower for non-pitchers).
Another target of research on discrimination using data from professional sports is discrimination by teams oﬀering contracts to players. We can observe the quantiﬁed contribution of eachplayer to the team through performance statistics, such as the number of homeruns or strikeouts.
Moreover, we can see the amount of compensation each player receives ( i.e., the evaluationby the general managers). This situation allows us to argue whether the salary for a player isadequate or not. Many studies test the existence of racial discrimination by team managers.
Krautmann et al. (2000) regarded performance statistics as performance indicators and showedthat non-white players are more cost-eﬀective compared to white players. Essentially, teams
can acquire non-white players through cheaper contracts. Non-white players are discriminatedagainst by companies (teams) in the player labor market. Similarly, Holmes (2011) conductedanalyses on discrimination by estimating the relationship between player performance indicatorsand compensation.

4

3 Background
3.1 Pitch Call in the MLB
First, we describe the process of judging balls and strikes. Hereafter, we refer to this process
as "pitch calls."
In MLB, typically, there are four umpires: the plate umpire and the respective base umpires
at the ﬁrst, second, and third bases. The four umpires comprise a unit called a "crew," As a rule,
the league assigns one crew to each game in the regular season. An umpire does not specialize
in any single position but rotates across all four positions sequentially. Hence, an umpire will
be a plate umpire in approximately one out of every four games. Many umpires are graduates oftechnical schools and, as players, work their way up through ranks in lower categories (Minor
League Baseball, or MiLB), to earn MLB contracts. Salaries paid to umpires are comparable tothose paid to highly skilled professionals2 . Because their decisions are televised throughout the
US and worldwide, they have incentives to make accurate and unbiased decisions.
Making pitch calls is one of the plate umpire’s most important tasks. If the batter takes (doesnot swing) the pitch, the plate umpire calls "ball" or "strike" based on the pitch location as it
crosses home plate. The strike zone is deﬁned as follows:
The oﬃcial strike zone is the area over home plate from the midpoint between a batter’sshoulders and the top of the uniform pants – when the batter is in his stance and preparedto swing at a pitched ball – and a point just below the kneecap. In order to get a strike
call, part of the ball must cross over part of home plate while in the aforementioned area.
quoted from MLB.com: Strike Zone
In each plate appearance, if an umpire calls the third strike (caught by the catcher) before thebatter hits the pitch into fair territory, the batter is out (strikeout). However, if four pitches passoutside the strike zone and the batter takes them, he is entitled to move to ﬁrst base. The numberof balls and strikes during the at-bat (pitch count) also signiﬁcantly aﬀects the result of eachplate appearance (see Table 1). Moreover, whether an individual pitch is called a strike or a ballis a pivotal issue in player performance (see Table 1).
Although the strike zone is well-deﬁned, not all decisions follow it. Figure 1 illustrates thephysical pitch location and actual decision. The bold rectangle in the ﬁgure shows the strikezone according to the deﬁnition—any pitch that passes inside this zone should be called a strike.

2 For more detailed information about MLB umpires, see Much required to become MLB umpire

5

Table 1 wOBA by Pitch Counts
Balls \ Strikes

0

1

2

0

.406

.372

.173

1

.413

.390

.186

2

.430

.407

.210

3

.678

.580

.389

wOBA (the abbreviation for Weighted OnBase Average) is one of the most important and popular statistics to evaluate batters. See https://library.fangraphs.com/
offense/woba/ for the details.

However, in practice, a pitch that passes through the strike zone can be called a ball and viceversa. The plate umpire judges each pitch visually; this judgment cannot be overturned once it
has been called. Therefore, if the umpire makes a discriminatory decision (regardless of whether
the tendency occurs subconsciously), the eﬀect will be to the detriment of minorities in the formof a lower performance index because of an unfavorable decision.
Figure 1 Pitch location and Pitch calls

63.2 Pitch Tracking System in the MLB
We will now explain how MLB acquires pitch-tracking data in each game and how these data
are utilized in empirical analyses. Tracking data include physical information on players andballs using cameras and radar technology. This system accumulates pitch-by-pitch data and theresults of each play, with tags for players and games. In MLB, the velocity and rotation of pitches
and the two-dimensional position of the ball as it passes the home plate are recorded for eachpitch (i.e., pitch location), along with other information on the game. In each game, information
on about 300 pitches is accumulated. The MLB regular season consists of approximately 2,400
games 3 , so we obtained data on approximately 720,000 pitches for every season.
In 2004, the ﬁrst MLB team started to install equipment to acquire tracking data. This system,
called Pitch F/X, uses cameras to capture the trajectory of each pitch and movement produced byball rotation. Because this dataset provides objective information on pitch locations, they began
to use it to provide feedback on the pitch calls. In Parsons et al. (2011), the authors exploitedthe exogenous diﬀerences in the presence of this feedback system, called QuesTec.4 . In 2008,
all 30 MLB teams installed the Pitch F/X system in their franchise ballparks. Since then, thedataset has been available in Baseball Savant.
In 2015, another tracking system, TrackMan5 , replaced Pitch F/X. This new instrument uses
Doppler radar to capture balls, instead of using high-speed cameras, making the capture of theexit velocity or exit angle of the batted balls possible, in addition to pitches. This system allows
us to more objectively estimate the quality of batted balls. Based on the physical information
about the ball, we can quantify the probability of whether the ball will be a hit or home run.
Using sabermetrics, we can also calculate the number of runs the batted ball creates. All theMLB ballparks were installed with TrackMan at the beginning of the 2015 season; hence, data
are available for almost all the games played each year6 . Tagged by information of the games andplayers, data tracked by the radar constitute a vast dataset. This dataset includes more detailed
information, such as defensive shifts recorded by high-precision cameras or the eﬃciency of
3 The regular-season game is held to determine the champions of the six divisions (two leagues × three divisions).

Each team plays 162 games and, based on the results, their right to enter postseason games to compete with the
all-league champion, called the World champion, is determined.
4 In ballparks equipped with QuesTec, every pitch call is recorded and evaluated by the League. Conversely, those
without the system do not observe the actual locations of the pitches; hence, umpires may feel less monitored,
which may lead to more biased judgments.
5 The Pitch F/X system continued until the 2020 season; however, the oﬃcial version of the dataset was tracked
via TrackMan.
6 Most of the oﬃcial MLB games are held at MLB franchise ballparks. Only a few games have taken place outside
the US (such as in Japan, Mexico, or China). Portable devices enable the acquisition of data even in stadiums
without TrackMan, as in the United Kingdom in 2019.

7

routes used by ﬁelders to track batted balls7 . This system is called Statcast.

3.3 Video-Based Judge Review System
Another essential institutional background for the analysis in this study is the introduction ofa replay system. At the start of each game in the regular season, the managers of both teams
receive a one-time right to request a replay review of close plays. If they exercise the right inthe short interval before the next play, a video replay of the previous play is reviewed. The
umpires cannot refuse to entertain a review request. If the coach’s request is right, the judge isoverturned. Currently, each team keeps staﬀ outside the dugout to review the video, and they are
responsible for determining whether the play should be challenged and for informing the coach.
Additionally, the umpires may also request a review when they regard it as necessary.
In all cases, it is not the umpires in charge of each game that reviews the judge but umpires
operating in a specialized facility called the "Replay Command Center" in New York. They
scrutinize the replay without initial judgments. Hence, their ﬁnal judgment cannot be inﬂuenced
by anything but the play itself.
Since the 2015 season, coaches can challenge most of the plays (fair or foul, in or out of theballpark, and fan interference), except for pitch calls. This expansion allowed us to quantify
most of the eﬀects of discrimination suﬀered by minority players in discrimination research.
Figure 2 summarizes what types of plays in baseball are reviewable and what are not. The
Manager Challenge system enabled them to overturn the judgments, even if the initial ones werebiased. There are, however, some exceptions: checked swings8 , pitch calls, and some easy
plays9 are not reviewable. Among them, the number of plays of pitch call is far more signiﬁcantthan other unreviewable ones, so we assume that analyzing the bias of this context reveals almost
the full eﬀects of in-group bias in MLB games.

3.4 What is Unique to See This Context?
Figure 3 illustrates the eﬀects of discrimination against minority athletes. Prejudice in pitch
calls leads to disadvantages for minorities through two paths: direct and indirect eﬀects.
The direct impact means that an umpire’s decision conceals a player’s ability to perform betterat-bat or in the game. As previous sections have mentioned, a strike call instead of a ball has

7 Some information on ﬁelders’ defense is unavailable to the public; however, we can observe aggregate data on

television, through Internet coverage or data sites such as Baseball Savant.
8 Checked swings: When the batter stops swinging midway, umpires judge whether he swang or not.
9 When the plays occurred in the inﬁeld (enough close to the umpires to watch the plays), the rights of the managers

to claim reviews are restricted. Section 6 also discusses the magnitude of the impact of these plays.

8Figure 2 Illustration of the umpire review

a signiﬁcantly negative impact on the batter’s performance (if it is the third strike, it ends his
chance with a strikeout.). It makes it impossible for minority players to perform as well as theywould have without such discrimination.
Conversely, the indirect impact corresponds to the arrow extending from "Biased performancestatistics" to "Biased contract" in Figure 3. The indirect eﬀect occurs when the team to which
the players belong oﬀers (or opts out) a contract for the following year based on performancestatistics. Managers evaluate minority players according to their performance statistics; however,these statistics are already compromised as a result of biased umpire calls. Managers are often
unaware of the observed downward bias in performance metrics—even if they are aware of it,they do not need to take it into account—and oﬀer lower-value contracts to players. Therefore,
even if the team’s management does not discriminate against minorities, 10 it indirectly harms
players.
This study aims to distinguish between three types of discrimination (direct/indirect eﬀects
of biased calls and discrimination in player evaluation by team management) in Figure 3 anddiscusses which sources to prioritize to improve the situation.
As mentioned previously, almost all discrimination in the playﬁeld occurs in pitch calls.
Therefore, analyzing such calls allows us to quantify the conclusive impact of discrimination.
We believe this study is the ﬁrst to address this question, which was also mentioned in Parsons
et al. (2011).

10 Whether they are caused by taste-based discrimination or consumer discrimination is not an issue here.

9Figure 3 Path of the Eﬀects of Discrimination against Minority Players

4 DataThis section describes the data used in the analysis. Creating the necessary variables requires
tracking (1) the data on each pitch, including pitch location; (2) data on the country of originof players and umpires; and (3) data on player performance statistics and contracts. We merged
them and built a unique dataset.
The analysis will cover the regular-season games in the 2016-2018 seasons. Note that wetake a one-year lag about the information on the monetary compensation (See Section 4.3)
because general managers design player contracts based on the previous year’s performance.
For example, the annual salary for 2017–2019 is merged with the statistics for 2016–2018,
respectively. 11 .

4.1 Pitch Tracking DataFirst, we start to explain pitch tracking data. Baseball Savant aggregates tracking data acquired
during MLB games and publishes quantitative analysis that predicts players’ performance using
11 In 2020, because of the COVID-19 outbreak, the number of regular-season games changed from 162 to 60.

Moreover, the player’s earnest money was limited to 37 percent of the contract they originally signed (see How
60-game 2020 MLB season impacts salaries of baseball’s highest- and lowest-paid players ). Additionally, gamesof the MiLB, the MLB’s subordinate organization, were canceled. Each player was then given the right todecide on participation in the season owing to health risks; several players withdrew from the games themselves.
Therefore, the study excluded 2019 and 2020 data from the sample.

10

physical information such as batted ball velocity and qualitative characteristics of pitches. Muchof the data used in the study is available to the public, and we can visit the site to get pitch-by-pitch
datasets tied to game and player information.
The total number of games played from 2016 to 2018 was 9,722 and the number of pitches
thrown during the games was 20,189,706. In our main analysis, we will focus on the pitches
that batters forfeited without swinging at (N = 1, 130, 048).
Table 2 # of pitches with potential bias

UmpireNorth America

Other

Umpire, Batter, and Pitcher from the same region538,117

5,266

Only the umpire from other region

80,26044,520

Possible bias to the batter

266,357

11,930

Possible bias to the pitcher

163,313

20,285

Table 2 lists the number of pitches devided by plate umpires, pitchers, and the region thebatter is from. As discussed below, the majority of MLB certiﬁed umpires are from the U.S., so
the ratio is somewhat skewed, but in situations where either the pitcher or the batter is from thesame country with the place umpire, i.e., where plate umpire discrimination is likely to occur,
the number of pitches thrown should be at least 10,000. A sample of about 10,000 pitches canbe obtained.

4.2 Nationalities of the Players and Umpires
Table 3 and 4 display summaries of the birthplaces the players and the umpires are from.
During the sample period, 2475 players and 108 umpires are rostered as the MLB players andumpires, respectively. The vast majority about both the players and the umpires is the UnitedStates, especially for the umpires. Umpires from the United States account for almost 90% of
all the umpires.
Chadwick Baseball Bureau contains almost all the players and oﬃcials involved in modern
American sports. The published dataset includes the year in which a player or an umpire ﬁrst/lastplayed an MLB game, as well as the unique ID of each player on major websites such as Baseball
Savant, Baseball Reference, and Fangraphs. Using the data, the author can merge the tracking
data described above with information on the country of origin of players and umpires scraped
from Baseball Reference, and data from Fangraphs as described below.
One of the most important determinants of the strike zone is the height of the batter. If thebatter’s height varies signiﬁcantly depending on the player’s region of origin, these characteristics
may be the source of diﬀerences based on race. However, we did not identify any statistically11country#player#umpire#pitches as pitcher#pitches as batter#pitches as umpire

1

Aruba

1

0

0

4572

0

Latin

Region Group

2

Australia

6

1

3439

37

0

others3

Brazil

5

0

552

2911

0

Latin

4

Canada

28

1

9400

12006

12591

5

Colombia

16

0

10973

1882

0

6

Cuba

48

1

9117

42625

13868

Latin

7

Curacao

5

0

1673

9567

0

Latin
Latin

North America
Latin

8

Dominican Republic

265

11138311247449371

9

Germany

5

0

2245

6649

0

10

Guam

1

0

350

5

0

others11

Honduras

1

0

0

0

0

Latin

12

Hong Kong

1

0

665

14

0

Asia

13

Jamaica

1

1

0

0

12374

Latin

14

Japan

16

0

16101

4193

0

Asia

15

Lithuania

1

0

502

0

0

Europe16

Mexico

24

1

26121

1753

14177

17

Netherlands

1

0

0

2878

0

Europe18

Nicaragua

5

0

4225

1545

0

Latin

19

Panama

15

0

4078

3843

0

Latin

20

Peru

1

0

0

0

0

Latin

21

Puerto Rico

43

1

9726

33863

4691

Latin

22

Saudi Arabia

1

0

1534

0

0

others23

South Africa

2

0

0

219

0

others24

South Korea

10

0

3696

9222

0

Asia

25

Taiwan

10

0

3165

452

0

Asia

26

U. S. Virgin Islands

3

0

1554

758

0

Latin

27

United Kingdom

2

0

79

5

0

28

United States

1783

97

8782067620251041454

29

Venezuela

175

2

55012

13047628158

EuropeLatin

EuropeNorth America
Latin

Table 3 # players and # pitches by birthplacesigniﬁcant diﬀerences in mean height between regions in our sample. This may be due to asurvival bias, in which a certain level of height is required for a player to be able to compete in
MLB games, but in any case, it explains why there is not a signiﬁcant diﬀerence in the physiqueof the players that the umpires actually face.

4.3 Contracts
The data for player contracts and the performance are obtained from Baseball Reference andFangraphs. These are privately owned and operated sites that calculate and publish objective
player evaluation indicators based on sabermetrics.
Only a few players are able to play under a season-long contract in MLB, and many aretemporarily promoted to MLB and then ﬁred or demoted to MiLB and re-signed. As a result,the number of players for whom we have data on salary during the period in question is small
compared to the number of players who have played at least one game. In this section, we will
discuss the results of our analysis. The sample size was 611.

12

Country/Regions

Region Group#players

Ratio% pitchers

Height (cm)United States

North America

1783

72.04

57.88

187.87s.d.
(5.71)

Weight (cm)94.64

(8.86)

s.d.

Dominican Republic

Latin

265

10.71

58.49

186.31(5.34)

94.60(11.47)

Venezuela

Latin

175

7.07

43.43

184.06(5.46)

94.14(11.81)

Cuba

Latin

48

1.94

35.42

185.69(5.82)

94.15(9.99)

Puerto Rico

Latin

43

1.74

25.58

184.37(5.91)

93.02(11.31)

CanadaNorth America

28

1.13

57.14

190.25(5.67)

99.89(7.89)

Mexico

Latin

24

0.97

83.33

184.46(4.09)

90.62(8.90)

Colombia

Latin

16

0.65

50.00

183.31(6.75)

94.38(4.40)

Japan

Asia

16

0.65

75.00

184.31(5.76)

86.50(6.83)

Panama

Latin

15

0.61

60.00

184.80(4.93)

90.47(12.86)South Korea

Asia

10

0.40

20.00

184.80(4.52)

100.40(9.49)

Taiwan

Asia

10

0.40

80.00

184.20(4.71)

84.90(11.30)Australia

others

6

0.24

83.33

186.50(2.59)

94.50(9.57)

Brazil

Latin

5

0.20

60.00

188.40(0.89)

99.40(12.10)Curacao

Latin

5

0.20

20.00

185.00(8.34)

94.00(17.61)

Germany

Europe

5

0.20

20.00

190.00(4.42)

101.00(6.78)

Nicaragua

Latin

5

0.20

60.00

183.40(7.60)

93.00(14.40)U. S. Virgin Islands

Latin

3

0.12

66.67

187.00(8.19)

96.00(8.72)South Africa

others

2

0.08

50.00

181.50(12.02)86.50(4.95)

United Kingdom

Europe20.08

100.00185.00(7.07)

94.50(10.61)

Aruba

Latin

1

0.04

0.00

185.00

( NA)

95.00

( NA)

Guam

others1

0.04

100.00190.00

( NA)

99.00

( NA)

Honduras

Latin

1

0.04

0.00

183.00

( NA)

72.00

( NA)

Hong Kong

Asia

1

0.04

100.00193.00( NA)

106.00( NA)

Jamaica

Latin

1

0.04

100.00198.00( NA)

117.00( NA)

Lithuania

Europe1

0.04

100.00190.00( NA)

102.00( NA)

Netherlands

Europe

1

0.04

0.00

190.00

( NA)

92.00

( NA)

Peru

Latin

1

0.04

100.00183.00

( NA)

94.00

( NA)

Saudi Arabia

others1

0.04

100.00183.00

( NA)

99.00

( NA)

Table 4 Countries Players from
Table 5 Performance Stats for the Pitchers
All

Asia

EuropeLatin

North America

others# of Pitchers

1166

19

3

262

877

5

Strike%

63.6

65.5

60.9

63.4

63.6

62.9

Games as a Pitcher

53.06

56.58

35.33

51.23

53.22

118.40s.d.

(54.33)(54.34)(28.11)(55.38)(53.83)(73.79)Innings Pitched

111.54146.60104.00102.30113.49123.93s.d.

(60.01)(134.34)(156.93)(130.10)(128.92)(135.76)

Runs Above Replacement

10.5

18.1

-1.4

9.6

10.7

7.3

s.d.

(23.1)(28.4)(5.1)(20.2)(23.9)(12.3)

Wins Above Replacement

1.1

1.9

-0.1

1.0

1.1

0.8

s.d.

(2.4)

(3.0)

(0.6)

(2.1)

(2.5)

(1.3)

5 Identiﬁcation Strategy
This section describes the empirical strategy to identify the existance and the size of the eﬀectof umpires’ discrimination. Using the variables described in Section 4, the estimation equation
using the ordinary least squares method is deﬁned as follows.
13

Table 6 Performance Stats for the Batters
All# Batters

1957

Asia
30

EuropeLatin

North America

others

7

494

1419

7

Games Attended

108.73

95.97

192.86126.58102.4591.86

s.d(119.76)(85.49)(176.30)(131.91)(115.06)(75.92)

Plate Appearances

283.60207.20678.71366.21

255.8315.71

s.d(503.86)(332.83)(759.28)(563.91)(480.14)(30.50)

-1.2

-1.4

-2.1

-1.7

-1.0

-1.3

(15.7)(9.3)(10.2)(16.1)(15.7)(2.2)

Batting Runs Createds.dBaserunning Runs Created

0.0

-0.3

1.2

-0.5

0.2

0.1

s.d.

(3.3)

(1.4)

(5.5)

(3.9)

(3.1)

(0.1)

Fielding Runs Created

0.0

-0.8

2.1

-0.1

0.1

-0.1

s.d.

(5.9)

(3.1)

(7.1)

(7.0)

(5.6)

(0.3)

Runs Above Replacement

8.6

3.4

25.3

10.4

8.0

-0.6

(26.5)(9.6)(43.7)(28.1)(26.1)(1.2)

s.d.
Wins Above Replacement

0.9

0.4

2.5

1.1

0.8

-0.1

s.d

(2.7)

(1.0)

(4.4)

(2.9)

(2.7)

(0.1)

Table 7 Salary and Ages
RegionAsia# players% Players Salary Available

Mean Salarys.d.

Mean Age

s.d

37

56.8

17155880.95(21305447.82)

33.24(5.08)

Europe966.76232000.00(9561010.80)

28.67(3.33)

Latin

608

57.1

9169858.09(14556144.82)

28.92(4.51)

North America

1811

52.8

9080632.93(15573221.13)

29.78(3.80)

10

40.0

2781350.00(2096420.27)

32.75(4.99)

othersFor each individual pitch i thrown by pitcher p, to batter b, and called by plate umpire u,1(Strikei |Calledi ) = β 1 + β 2 Nationalityi + β 3 fˆ(plate_xi , plate_zi )+ β 4 Xi + δb + γ p + λu + ui .

(1)

1(Strikei |Calledi ) is a dummy for that the pitch i is called strike, given that the batter takes thepitch. The parameters of interest are β 2 , which correspond to the average eﬀects of the nationalityof the pitcher, the batter, and the umpire. Xi stands for the pitch-, game-, or situation-speciﬁccharacteristics, and δ, γ, and λ are the pitcher, batter, and umpire’s ﬁxed eﬀects, respectively.
The nationality dummies include roughly 4 statuses in sum:1. All of the related agents (the pitcher, the batter, and the plate umpire) are from the same
country (baseline),
2. Either the pitcher or the batter is from the same country as the plate umpire while theother is from another one,
3. The pitcher and the batter are from the same country, and the plate umpire is not,4. Both the pitcher and the batter are from diﬀerent countries with the plate umpire.
14

Theoretically, as a whole, plate umpires are likely to favor players from the same country.
Therefore, discrimination by the umpire may occur in the situation (2). Each case, furthermore,is classiﬁed according to the nationality of the plate umpires. The vast majority of the oﬃcial
MLB umpires are from the United States, so those from other countries are regarded as aminority. This paper distinguishes discrimination against the minority from one by minority
umpires against the majority (from the United States) players.
The third term of the equation (1) is the predicted value of the average probability that thepitch is called strike, using the 2-dimensional pitch location. This probability is expressedby Pr(StrikeCalled|plate_x, plate_z), where plate_x and plate_z are the horizontal and verticallocations of each pitch. As is described in Section 3.1., It is not unusual for two pitches thatpass through the exact same area to be judged diﬀerently. Thus, to estimate the eﬀect of theumpire discrimination quantitatively, we should control the average probability of the called
strikes given the pitch locations, instead of comparing the ratio of the called strikes among
diﬀerent nationality statuses. To control the information from the pitch location linearly, we use
a generalized additive model (GAM) to estimate the density function of strike-call, conditionalon the location of the pitches12 . The following is the equation to estimate the value of fˆ.
()
1
1{StrikeCalled} ∼ Bin θ =1 + exp(− g(x))
where g(x) = s(plate_x) + s(plate_x, plate_z) + s(plate_z)

(2)
(3)

The function g(.) in equation (3) is a two-dimensional spline regression of the pitch locations.
Taking logit transformation of g(.) (equation (2)), we can obtain the estimated probability ofcalled strikes for each individual pitch with pitch location. Including this term into the OLS
regression in equation (1), we can quantify the impact of nationality on pitch calls. If there isno plate-umpire discrimination against the minority players, no deviation is to be observed fromthe average probability for each location: the rules regarding pitch calls state that plate umpires
are to call pitches according only to the pitch locations.
Almost all of the studies on situational strike zone using tracking data suggest that the size ofthe strike zone varies with pitch count and with the batter’s handedness. The latter variation isdue to the reversal of the batter’s standing position13 . On the other hand, the former diﬀerenceis caused by the psychology of umpires, called omission bias. They tend to avoid judging strikes
12 This methodology is often used to quantify the catchers’ technique to get more called strikes.
13 Figure 4 and 5 suggest that the strike zone is not perfectly symmetrical between right and left handed batters.

This is said to be related to the fact that the catcher’s catching technique (called "framing") is also likely to aﬀect
the pitch call, and that most catchers who play in MLB are right-handed. In any case, this paper assumes thatthey do not make a critical diﬀerence in the same at-bat.

15

when two strikes and balls when three balls, which are decisions that end the at-bat without thebatter hitting the ball into fair territory.
Figure 4 and 5 illustrate the predicted call probability by batter-handedness (The left-hand side
for typical left-handed batters, while the right-hand side is for the typical right-handed batters.).
To show that pitch counts dramatically aﬀect the average probabilities, we show two anecdotal
cases: 0 balls and 2 strikes (0-2 counts) and 3 balls and 0 strikes (3-0). Graphically, you can
see that in 0 - 2 counts, umpires favor batters: less likely to call a strike. Figure 5 suggests
the opposite implication in 3-0 counts. These primitive results are consistent with previous
literature on the umpires in sabermetrics14 .
As will be discussed in Section 6, the estimated probability using GAM has a very large eﬀect
on the actual pitch call. In this paper, the sample is divided into 24 subsamples of 12 (0-2strikes × 0-3 balls) × 2, distinguishing between pitch counts and batter left and right, and theprobability of each is estimated by GAM and included in the regression in equation (1).

6 Results
6.1 Main Result
This section discusses the eﬀect of bias due to plate umpire on pitch calls.
Initially, we present results for the sample where the plate umpire is from the United States.
Table 8 shows the results of the estimated equation 1. The nationalities of the pitcher and batterare listed in rows 3 through 5, with the texts before the underscore (_) indicating the nationality ofthe pitcher, and the nationality of the batter follows after it. For example, "NoUS_US" indicatesthat the batter is from the United States and the pitcher is from elsewhere. The pitcher’s
choice and the manager’s decision on which pitcher to play against which batter are endogenous
variables. Including these variables may be "bad controls," as pointed out by Angrist and Pischke(2008). In the ﬁrst column of Table 8, we show the results with only the estimated strike callprobability fˆ and nationality information as explanatory variables.
The estimation results were consistent with the hypothesis. When the pitcher is from the U.S.
and the batter is from elsewhere, the plate umpire from the United States tends to decide infavor of the pitcher. Speciﬁcally, an average deviation of 0.3-0.4 percentage points from theprobability of a strike call estimated solely by the location of the pitch’s passage occurs, i.e.,the batter is more likely to have a strike called. The estimates were statistically signiﬁcant (at14 The term "sabermetrics" refers to an attempt to analyze baseball from an objective standpoint using scientiﬁcmethods and to gain new insights that could not be obtained with the old methodology of analysis based solely
on experience and feeling.

16

Figure 4 Predicted Strike-Call Probability: 0 Balls and 2 Strikes

Figure 5 Predicted Strike-Call Probability: 3 Balls and 0 Strikes

the 0.1% level). On the other hand, if the pitcher is from a non-U.S. country and the batter isfrom the United States, the pitch call will favor the batter. However, the point estimates wererelatively small for batters, and the estimation results in column 4, which contained the mostexplanatory variables, were no longer statistically signiﬁcant.
The result where both the pitcher and the batter are not from the United States does not support
17

Table 8 Discrimination by the American Umpires(Intercept)
prob
NoUS_NoUS
US_NoUSNoUS_US(1)(2)

0.002 ***

0.002 ***

(3)

(4)

(0.000)(0.000)0.992 ***

0.992 ***

0.992 ***

0.991 ***

0.991 ***

(0.001)(0.001)(0.001)(0.001)(0.001)0.003 **

0.001

0.001

0.002 *

0.002 *

(0.001)(0.001)(0.001)(0.001)(0.001)0.003 ***

0.003 ***

0.004 ***

0.004 ***

0.004 ***

(0.001)(0.001)(0.001)(0.001)(0.001)-0.002 *-0.002 *-0.002 *-0.001 *-0.001(0.001)(0.001)(0.001)(0.001)(0.001)

0.021 ***

0.022 ***

0.022 ***

(0.002)(0.002)(0.002)0.004 ***

0.004 ***

pitcher_hitting
away_batting(0.000)
Fixed Eﬀects#observations(5)1048047(0.000)catchercatchercatcher, pitch_type

1048047

1048047

1043840

1043840

0.752

0.752

R squared

0.751

0.751

F statistic

1021865.000

1021865.000

P value

0.000

0.000

0.752

*** p < 0.001; ** p < 0.01; * p < 0.05.

the hypothesis. In this matchup with no intuitive conﬂict with the umpire the theory predicts
to show similar results to the baseline case where both pitcher and batter were from the UnitedStates. However, some of the results suggested that the plate umpire would call in favor of thepitcher.
In addition, the results pointed to count-dependent changes in the strike zone and the existenceof a hometown bias. These are consistent with the previous results. For example, the percentage
of strike calls increases by 0.4 percentage points in the innings table, where most games hit
the visiting team. Although these are not the main focus of this study, the fact that they are
consistent with previous studies implies the validity of the analysis in this study. In particular,
the eﬀect of pitch count is much larger than the ones of player nationality and other factors, withapproximately tenfold variation occurring.
As shown in Figures 4 and 5, the probability of an average strike call changes rapidly at theedge of the strike zone. The plate umpire is also less sensitive to nationality since a pitch thatpasses through a position with an extremely high or low average probability is a strike ball forall. Table 9 shows the estimation results when the sample is restricted to pitches with average
strike call probabilities fˆ between 30% and 70%. This region is called the "shadow zone" and isempirically considered to be the pitches for which the strike zone is likely to change dependingon the context.

18

Table 9 Edge of the Strike Zone
(1)
(Intercept)
prob
NoUS_NoUS
US_NoUSNoUS_US

(2)

(3)

(4)

0.011

0.011

(0.007)(0.007)0.919 ***

0.919 ***

0.918 ***

0.919 ***

0.919 ***

(0.013)(0.013)(0.013)(0.013)(0.013)

0.007

0.007

0.010

0.009

0.012 *

(0.006)(0.006)(0.006)(0.006)(0.006)0.008 *

0.008 *

0.011 **

0.011 **

0.012 **

(0.004)(0.004)(0.004)(0.004)(0.004)-0.005-0.005-0.004-0.005-0.002(0.004)(0.004)(0.004)(0.004)(0.005)0.069 ***

0.074 ***

0.067 ***

(0.009)(0.010)(0.010)0.014 ***

0.014 ***

pitcher_hitting
away_batting(0.003)Fixed Eﬀects#observations(5)100359(0.003)catchercatchercatcher, pitch_type

100359100359

99994

99994

0.064

0.065

R squared

0.054

0.054

F statistic

1218.814

1218.814

P value

0.000

0.000

0.070

*** p < 0.001; ** p < 0.01; * p < 0.05.

The results are consistent with our prediction, especially in situations where batters are
discriminated against, and the point estimates show 0.8 percentage points to 1.2 percentage
points. In other words, the estimates in the full sample are relatively large due to this part of theeﬀect. However, the eﬀect of discrimination was also present for obvious strikes and obvious
balls are thrown with an average strike call probability of less than 10 % or more than 90 %.
The last result of the main estimation is about the judgement of the non-American plate umpire.
Table 10 shows the OLS results with the sample restricted to umpires from countries other thanthe US. Statistically, the results do not provide strong support for reverse discrimination byminorities. None of the dummy variables for nationality were dominant at the 10% level.
However, the signs of the point estimates are all consistent with the hypotheses, especiallywhen the pitcher is non-American and the batter is American, and the coeﬃcient estimates are
relatively large, ranging from 0.3 percentage points to 0.6 percentage points.
These results indicate that plate umpires from the U.S. make pitch calls that are inﬂuenced
by nationalistic bias based on the country of origin of the pitcher and batter. The eﬀect isparticularly large in situations where batters are discriminated against, and they are more likely
to underperform themselves by being called more strikes.

19

Table 10 Reverse Discrimination(Intercept)
prob
NoUS_NoUS
US_NoUSNoUS_US(1)(2)-0.002-0.002

(3)

(4)

(5)

(0.003)(0.003)0.984 ***

0.984 ***

0.984 ***

0.983 ***

0.984 ***

(0.002)(0.002)(0.002)(0.002)(0.002)

0.003

0.003

0.001

0.001

-0.001(0.003)(0.003)(0.003)(0.003)(0.003)-0.000-0.000-0.001-0.001-0.001(0.004)(0.004)(0.004)(0.004)(0.004)

0.006

0.006

0.005

0.005

0.003

(0.004)(0.004)(0.004)(0.004)(0.004)0.025 ***

0.027 ***

0.025 ***

(0.006)(0.006)(0.006)

pitcher_hitting
away_batting
Fixed Eﬀects

0.004 *

0.003 *

(0.002)(0.002)

catchercatchercatcher, pitch_type
81796#observations

82001

82001

82001

81796

R squared

0.743

0.743

0.745

0.745

F statistic72288.430

72288.430

P value

0.000

0.000

0.745

*** p < 0.001; ** p < 0.01; * p < 0.05.

6.2 Size of Eﬀect: Indirect Eﬀects on Players’ Salary
Next, we discuss the average impact of discrimination in size: from Section 6.1. when theplate umpire and pitcher are from the U.S. and the batter is from the rest of the world, theprobability of a strike call increases by .4 percentage points per pitch. In this paper, we quantify
how much of a ﬁnancial loss this causes to minority players.
Table 11 quantiﬁes the impact of improvements in player performance metrics on subsequentseasons using data on hitter performance from 2016 to 2018 and annual salary the following
year. Speciﬁcally, we regress the following equation.

Wi = α + βNationalityi + γPerfObsi + bXi(4)

To account for issues such as multi-year contracts and applications for annual salary arbitration,
we sum up performance measures and the annual salary data over the three years. Wi in equation(4) represents the annual salary over the three years, and PerfObsi is a proxy variable for the
performance measure used by team managers to consider the annual salary for their players. In
20

Table 11 The Return to Performance on 3-year Conpensation
salarylog-salarysalarylog-salary

5207970.404 **0.621 ***

6876505.684 ***0.813 ***

(1827345.814)(0.154)(1616971.340)(0.151)

Age_squared-58552.821-0.007 **-88374.735 **-0.011 ***(32027.095)(0.003)(27932.541)(0.003)

Asia-953576.469

0.264-3956462.722

0.012(6824475.892)(0.345)(6526262.934)(0.345)2162256.495

0.342 ***

3186830.082 **0.442 ***

(1157596.818)(0.095)(1181647.678)(0.117)-1614844.584

0.226

2479869.411

0.613(1222698.060)(0.513)(4167365.210)(0.747)224003.728 ***0.024 ***

(18381.413)(0.001)276739.262 ***0.023 ***

(35286.391)(0.002)-71511.698

0.009(129943.009)(0.010)Fld264458.450 ***0.026 ***

(66378.611)(0.005)

Pos-137458.304-0.002(80851.681)(0.006)

611

611

Age

Latin
EuropeRAR
Bat
BsR#observations

611

611

R squared

0.437

0.570

0.398

0.378

F statistic

63.089183.13731.02757.595

P value

0.000

0.000

0.000

0.000

*** p < 0.001; ** p < 0.01; * p < 0.05.

other words, this value is subject to umpire bias.
PerfObsi can be further decomposed into the following deﬁnition.
PerfObsi = PerfPoti + ϕ × Attendancei(5)

PerfPoti represents the potential, i.e., the true ability of the batter, that would be observed if
there were no discrimination by the umpire. Attendancei represents the number of opportunities
distributed to the player. It can be interpreted, in other words, as the frequency with which
players who would be subject to discrimination appear on the ﬁeld. The value of Φ represents
the impact of discrimination as estimated in the main results section and indicates that the moreminority batters are plate-appearances, the greater the downward bias on the measure of runcreation for that player.
The two performance indicators used in this paper are "Runs Above Replacement (RAR)"
21

and "Bat (Batting)." RAR is a measure of "how many more points a player contributes thana replacement-level15 player", and the number can be converted to points per score (runs) inbaseball. Therefore, the coeﬃcient value of RAR in equation (4) represents the rate of increasein annual salary when the player’s contribution to the team’s runs increases by one point (overthree years). In short, it stands for the return on contribution. "Bat" is a similar measure of aplayer’s hitting-related ability on a scale of scoring contributions created.
As shown in Equation (4), this regression also includes a proxy variable for the player’s homeregion. This corresponds to the eﬀect of the player’s region of origin on the annual salaryamount, which remains even after accounting for diﬀerences in the player’s track record. The
estimated coeﬃcients of these dummy variables are statistically signiﬁcant if there is an eﬀect
of discrimination against minority players by team management or consumers (see Figure 3).
Consider the results in Table 11. First, there was no strong support for the possibility of
discrimination by team or fan, at least when controlling for factors such as player performanceand age. None of the estimates for the regional dummies were statistically signiﬁcant, or
represented treatment that favored minority players. The remainder of the discussion will focus
on the eﬀects of discrimination by ballplayers. Rows 5 and 6 of Table 11 show the return of runs
scored by players relative to their annual salary. It shows that the return on an increase of one
point in runs scored by a player over three years is estimated to be about $224,000, or 2.4%. The
coeﬃcient values are statistically signiﬁcant (at the 0.1% level) when using either RAR or Bat,
and the point estimates show similar impact size. As mentioned earlier, since these indicators
implies a player’s ability in the form of runs, quantifying the negative runs creations producedby pitch-calling bias would allow us to measure the impact of the decision in monetary value.
The impact of pitch calls on the creation of runs is done using the concept of Runs Expectancy16
used in MLB. We can regard baseball as a dynamic game of discrete time in which a pitcher anda batter play against each other with intervals in between. For example, a double by the batterat the beginning of an inning changes the situation from no outs and no runners on base to noouts and no runners on second base. For each state17 , if we average the runs scored going into
the rest of the inning, we get the Runs Expectancy table as shown in Table 12. For example,
with bases loaded, if there are no outs, we can expect to score 2.23 more runs on average inthat inning. However, if there is one out, that number decreases to 1.55 runs.In other words,
striking out with the bases loaded and no outs create a negative score of 0.68 (1.55 - 2.23). By

15 The replacement level indicates the level of competence of the players in the MLB player market who are beingsought, i.e., those whom teams can be immediately acquire by paying minimum guaranteed salary.It will not be
explained in detail here. It is suﬃcient to understand that a player’s value can be evaluated in terms of points.
16 For more information on the concept of expected runs scored, please refer to the Sabermetrics website.
17 Out count: 0, 1, or 2 × 3 with or without runners on base, 8 ways = 24 diﬀerent states deﬁned.

22averaging this change in expected score for example, strikeouts, we can estimate the average(state-independent) run creation value of a strikeout. Similarly, we can calculate how many
points the expected score would be reduced (A strike is a decision that disadvantages the batter.)on average if the umpire calls a strike instead of a ball when the batter takes the ball. According
to this, the average scoring creation for being taken one strike is about -1.4 points.
Table 12 Runs Expectancy by 24 States

Outs/Runners_on

0

1

2

___

0.50

0.27

0.10

__3

1.39

0.97

0.37

_2_

1.14

0.69

0.32

_23

1.98

1.40

0.56

1__

0.88

0.52

0.22

1_3

1.78

1.21

0.49

12_

1.46

0.93

0.43

123

2.23

1.55

0.76

Minority batters are on average 0.4 percentage points more likely to have a strike called per
pitch, so for example, 100 pitches against an American-born player with an American-born
umpire would score -1.4 points × 0.004 percent per pitch × 100 pitches = 0.56 points. It will
harm the observed ability to runs creation. Figure 6 quantiﬁes the sum of the runs created lost
over three years by minority players for whom Salary data are available. Since players withfewer opportunities to bat are also less likely to be discriminated against, many players appear
to have little impact on the total over the three years. On the other hand, hitters who are the core
players of their teams and bat all year long have more opportunities to bat in situations where
they are discriminated against, which means that they lose nearly two runs in three years due
to discriminatory pitch calls. In particular, the best players in the top 25 percentile among theminorities lost an average of 0.58 points worth of runs. As shown in Table 11, the return per runs
created is $224,000, so the estimated salary they lose over three years is about $130,000. Someof the players signed before free agency sign the contract with about the minimum compensation
set at about $570,000. This is a loss that we should not ignore.

6.3 Endogeneity: Bahavioral Response of the Batters
The impact size discussed in the two sections is a lower bound. This is because, in the context
of the strike zone, signiﬁcant endogeneity is noted.

23

Figure 6 Distribution of the Negative Contribution by the Biased Calls

If minority hitters are empirically (or quantitatively) aware of the existence of discriminationby plate umpires, they will decide whether or not to swing at a pitch given a wider strike zone.

Us = E[Runsvalue|Contact] × Pr (Contact) + E[Runsvalue|Missed] × (1 − Pr (Contact))(6)
Ut = E[Runsvalue|Called Strike] × Pr (Called Strike)+ E[Runsvalue|Called Ball] × (1 − Pr (Called Strike))(7)

The batter’s decision to swing or take can be described by the following utility function The
expressions (6) and (7) represent the incremental scoring contribution created when the batterswings at the pitch, respectively. When a swing is made, if the batter contacts the ball, theexpected value of the contribution created by the generated pitch is generated, while a loss of
one strike always occurs if the batter swings and misses. On the other hand, if the pitch is taken,
it is determined whether the pitch is a ball or a strike based on the average strike call probabilityfˆ estimated by 2. Taking convex combination of the value of one strike and one ball by theaverage probability of a strike for the pitch location of that pitch, we can calculate the expectedvalue of taking a pitch as measured by scoring creation.
Therefore, the above two equations can be rewritten as a function of pitch location(plate_x, plate_z) as follows.

24

Us =S(plate_x, plate_z)(8)

Ut = E[Runsvalue|Called Strike] × fˆ(plate_x, plate_z)+ E[Runsvalue|Called Ball] × (1 − fˆ(plate_x, plate_z))(9)Table 13 shows the variant of the average expected score when a pitch was a strike, a ball, ora foul in each pitch count. Substituting these values into the equation (9) calculates the averagevalue when a pitch is taken.
For example, consider the case of taking a pitch from 0 balls and 2 strikes (e.g. "3-2" represents
3 balls and 2 strikes) such that fˆ = 50%. If the pitch is ruled a strike, the value is -0.164; if it isa ball, it is 0.043. Thus, the value of taking this pitch is−0.164 × 0.5 + 0.043 × (1 − 0.5) = −0.0605.
Table 13 ∆ Run Expectation at Each Pitch CountCount

if strikeif ball

if foul

0-0-0.0420.037-0.0421-0-0.0550.060-0.0552-0-0.0790.097-0.0793-0-0.0830.116-0.0830-1-0.0590.024-0.0591-1-0.0400.036-0.0402-1-0.0420.093-0.0423-1-0.0030.200-0.0030-2-0.164

0.043

0

1-2

-0.207

0.034

0

2-2

-0.241

0.132

0

3-2

-0.3730.203

0In a similar way to ﬁnding fˆ, we use the expected value of run creation when a batter swings
at a pitch that has passed a speciﬁc pitch location, the function S(., .) can be calculated.

S(plate_x, plate_z) = r (plate_x) + r (plate_x, plate_z) + r (plate_z)r (., .) is the spline regression.

25

(10)

Table 14 Run Values of Each PlayEventsRun Value

Homerun1.38

Triple1.06

Dounle

0.76

Error

0.49

Single0.45

Catcher Interference

0.34

Hit By Pitch

0.33

Bases-on-Balls

0.31

Intentional Walk

0.17

Fielders Choice-0.23

Strikeout-0.27

Batted-Ball Outs

-0.27

If the batter strikes out on a pitch, the value of "if strike" in the Table 13 is used as the
explained variable according to the pitch count. On the other hand, if the batter hits a double,
for example, the average scoring value of a double, 0.76, is the value of the swing. Table 14
shows the average value that each play has.
Using these values, we can quantify the extent to which incentives exist to swing at a ballpitched at a particular pitch location. For a pitch i,
Incentivei =S(plate_x, plate_z) − fˆ(plate_x, plate_z) × Value when Strikei− (1 − fˆ(plate_x, plate_z)) × Value when Balli(11)

This corresponds to the diﬀerence between the equations (8) and (9), where the larger thenumber, the larger the expected value of runs created by swinging at a pitch rather than taking it.
Figure 7 illustrates these values given pitch locations, seperating the handedness of the pitchers
and the batters. There are diﬀerences depending on the pitcher’s or batter’s handedness, but ingeneral, you will ﬁnd that the expected value is higher when you swing around the heart of thestrike zone.
Using this, we estimate the following regression.

1(Swung)i = β 1 + ψNationalityi + β 2 Incentivei + β 4 X(12)Nationalityi corresponds to the nationality of the player and plate umpire, as in equation (1).
26

Figure 7 Expected Run Values when Swinging

The dependent variable is the dummy that indicates if the batter swings or not. If minority
players are aware of the existence of discrimination and expect their probability of calling astrike to increase when facing an American pitcher, they will swing more even in situations
where the incentive to swing is relatively small.
Table 15 shows the estimation results for OLS, where columns 1 and 2 include all pitches inthe sample, and columns 3 and 4 restrict the sample to the "shadow zone" where the percentage
of strike calls predicted by the location of the pitch’s path is between 30% and 70%. Since thesample is limited to cases where a minority batter is at bat, there are three nationality states:
the pitcher is from the US, the plate umpire is from the US, and both of them are from the US.
The estimation results did not support the existence of a change in batter behavior according
to nationality. The value of the point estimate varied above and below zero depending on thesample selected, and when all pitches were included in the sample, it even resulted in a rather
low percentage of swings in situations where he himself was discriminated against.

7 Discussion
The probability variation of strike calls by nationality bias was generally as predicted by thetheory. Many studies dealing with the strike zone context, including Parsons et al. (2011),
27

Table 15 Behavioral Responses of the Minority Batters

US Umpire

US Pitcher

US Umpire & US Pitcher

(1)

(2)

-0.003-0.003

0.017

0.022

(0.004)(0.004)(0.012)(0.012)-0.007-0.0040.022

0.034 **

(0.004)(0.004)(0.013)(0.013)-0.009 **-0.006

0.007

0.020

(0.004)(0.004)(0.012)(0.012)

Fixed Eﬀects#observations

Edge

pitch_type
739969737581

pitch_type
80508

R squared

0.247

F statistic

63467.440

2702.338

0.000

0.000

P value

0.256

Edge

0.130

79946
0.149

*** p < 0.001; ** p < 0.01; * p < 0.05.

have used the race of the player as a proxy variable instead of nationality. On the other hand,for example, Sandberg (2017) pointed out the existence of in-group bias by the nationalityof the umpire using a dressage dataset. Since some studies in the context of the strike zone
use country-of-origin-dependent Latino/Asian identiﬁcation and lists of black athletes in major
media articles as a way to identify their race, whether the bias is due to nationality or race Thereis room for debate as to whether the bias is due to nationality or race. On the other hand, in
MLB games, the names of the players at bat and the pitchers on the mound are called out by
speakers in the stadium, and their names are written on the scoreboard attached to the batter’seye. In this situation, the umpire can know their names at any time. Using data from theirexperiments, Bertrand and Mullainathan (2004) and Edelman et al. (2017) have pointed out thatpeople’s names may be used as cues to determine their race. In addition, the plate umpire, inparticular, is located at a very close distance to the player and can easily know the skin color of
the player. Monk (2015)and others have argued that people’s skin color predicts the degree of
discrimination they are subjected to, and intuitively, these eﬀects are likely to occur in baseball.
Since the faces of athletes are available to the public, further research in this area using such data
may provide insights into discriminating between nationality bias and racial discrimination.

28

8 Conclusion
This paper has used the context of strike calls in the MLB to show evidence for minority
discrimination by evaluators (umpires). The in-group bias that occurs when evaluating theachievements of workers (players) also causes workers to suﬀer economic losses through subjective evaluations by employers (team managers) who enter into contracts with workers basedon the bias. This paper suggests that even though umpires are highly skilled professionals, they
are aﬀected by their in-group bias. Such a problem can occur even in a more general work
environment that lacks objective measures of worker performance and so we can consider our
results as a contribution to the labor economics literature using empirical data.
Another advantage of research using MLB data is that it allows us to track the behaviorof workers discriminated against, as discussed in Section 6.3. According to the results, battersdiscriminated against would recognize it and make behavioral changes, while the ﬁnancial losses
caused by discrimination were very severe. The fact that the eﬀects of such bias exist in the
MLB labor market, which attracts players from all over the world, may shed some light on thedebate over the introduction of non-human entities such as robot umpires.

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