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Sports Economics
Does the Baseball Labor Market Properly Value Pitchers?
John Charles Bradbury
Journal of Sports Economics 2007 8: 616 originally published online 3 April 2007
DOI: 10.1177/1527002506296366
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Does the Baseball Labor Market
Properly Value Pitchers?
JOHN CHARLES BRADBURY
Kennesaw State University
Defense in baseball is a product of team production in which pitchers and fielders
jointly prevent runs. This means that raw run-prevention statistics that economists often
use to gauge the value of pitchers, such as earned run average, may not properly
assign credit for their performances. Therefore, marginal revenue product derivations
based on such statistics contain some erroneous information that may bias the estimates.
In this article, the author examines a method for isolating pitcher contributions to the
team production of defense. Evidence from the labor market suggests that pitchers are
paid according to their individual contributions, consistent with the areas in which pitchers possess skill.
Keywords: baseball; joint production; marginal revenue product; pitchers; salary
E
stimating the marginal revenue products (MRPs) of individual athletes engaged
in professional team sports is not a simple task. With many players independently
acting to achieve the goals of the team, it is not obvious how much each individual
contributes to the final output. However, estimating MRPs is a practical problem
that general managers, agents, and arbitrators must solve. In baseball, the calculation of MRPs is simpler than in most team sports because it consists of many individual batter pitcher contests.1 However, on defense, distinguishing between the
separate contributions of fielders and pitchers is much more complicated because
preventing runs is a joint product of multiple inputs. When a pitcher allows a ball
to be hit into play, it must be handled by fielders; therefore, the outcome of the
play is jointly determined. This may be one explanation why some recent estimates
of baseball player MRPs have excluded pitchers from the analysis (Blass, 1992;
Krautmann, 1999).
The problem with this is that the main metric analysts typically use to evaluate
pitchers’ skills in preventing runs, the earned run average (ERA), is a joint output
metric. The ERA is the number of earned runs allowed by a pitcher per nine innings pitched. Although the ‘‘earned’’ component, which extracts runs produced by
JOURNAL OF SPORTS ECONOMICS, Vol. 8 No. 6, December 2007
DOI: 10.1177/1527002506296366
Ó 2007 Sage Publications
616–632
616
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Bradbury / PITCHERS IN THE BASEBALL LABOR MARKET
617
official scorer-determined fielding errors, controls for some of the impact of particularly bad fielding, it does not entirely separate the contribution of fielders and
pitchers. For balls that fielders turn into outs, it is difficult to isolate the contributions of pitchers or fielders in producing the outcome. Does the pitcher throw the
ball in a way that leads to outs, or do fielders turn some typical hits into outs
because of spectacular plays?
In his original (1974) and updated (1989) estimates of Major League Baseball
(MLB) pitcher MRPs, Gerald Scully does not use ERA to proxy pitching skill;
instead, he employs the strikeout-to-walk ratio. However, Zimbalist (1992)
modifies Scully’s technique by replacing the strikeout-to-walk ratio with ERA
and suggests this metric is superior because it better predicts team winning
percentage. Kahn (1993) and Krautmann, Gustafson, and Hadley (2003) also
use ERA, along with several other metrics, to estimate pitcher contributions
toward winning. Although there is no doubt that allowing fewer runs produces
more wins, it is not necessarily the case that the ERA is the best measure for
estimating the MRPs of pitchers. If factors outside a pitcher’s control pollute
ERA, then it will capture something more than the pitcher’s contribution to run
prevention. This is something Scully may have been aware of when he chose
the strikeout-to-walk ratio as his proxy for pitcher quality—fielders do not participate in walks and strikeouts—though he does not explicitly state this. Even
without explicitly considering estimated MRPs, there is little debate that most
analysts consider ERA to be the main statistic for judging pitchers; therefore,
the topic is worthy of further investigation.
ERA may be the best method for imputing pitcher marginal products, but the
case has not yet been made. Further study is necessary, especially in light of some
evidence that pitchers seem to have very little control over outcomes on balls
in play (McCracken, 2001). However, this finding, though widely accepted, has
not been tested with sufficient statistical rigor, nor has it undergone formal peer
review. In this article, I investigate the determinants of pitcher quality by looking
at individual retention of pitcher skills in preventing runs. I find that factors outside of a pitcher’s control influence ERA and that superior estimators of pitcher
performance exist. In addition, the labor market values pitchers in the areas that
they possess skills in preventing runs. The second section examines the correlation of player skills over time and uses multiple regression analysis to estimate
the determinants of pitcher run prevention from year to year. The third section
explores the extent to which pitchers affect defense in the area of joint production.
The fourth section compares how the baseball labor market values pitchers to the
results in the preceding sections. The fifth section concludes the article.
WHAT SKILLS DO PITCHERS POSSESS?
If a pitcher is entirely responsible for his ERA, one has to assume that pitchers control all aspects of defense or that official scoring rules perfectly separate
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618
JOURNAL OF SPORTS ECONOMICS / December 2007
fielder and pitcher contributions. Certainly, neither is the case; thus, it would be
helpful to know how much control pitchers have over batting outcomes. When a
batter steps to the plate, there exist two different classes of outcomes: those that
the pitcher produces without help from fielders and those on which he must rely
on his fielders. The first group of outcomes includes strikeouts, walks, hit batters, and home runs. These outcomes are produced without the help or hindrance
of fielders, which is why McCracken (2001) refers to these statistics as defenseindependent pitching statistics (DIPS).
DIPS provide a unique opportunity to examine pitcher performances absent
fielder spillovers. McCracken (2001) finds that knowing how a pitcher performed without the help of fielders yields nearly all of the information necessary
to evaluate pitchers and thereby reaches the conclusion that pitchers have little
control over outcomes on balls in play. Although the strong relationship
between DIPS and pitcher performance is well known in the analytical baseball
community, the concept has undergone very little formal scrutiny and is not a
part of the economics literature. However, it is clear that if McCracken’s findings are correct, they have relevant implications for economic studies that
require the evaluation of pitching talent. Therefore, it is important to verify if
these findings are correct using the proper econometric techniques.
To identify in what areas pitchers possess skills, I look at the consistency
of performance for pitchers over time. Outcomes are a product of skill and
random chance. Skill should persist over time, whereas random chance should
not. To begin, I examine the areas of defense that pitchers can possibly control: strikeouts, walks, hit batters, home runs, and hits on balls in play. All
but the last of these statistics are defense independent.2 I normalize the DIPS
metrics as a rate per nine innings pitched—the way in which earned runs are
normalized for ERA—and hits allowed as a percentage of balls placed into
the field of play, which is a batting average allowed on balls in play (BABIP).
To obtain an adequate sample, I include all pitchers who pitched more than
100 innings for consecutive seasons from 1980 to 2004.3 Table 1 lists the
season-to-season correlations for several pitching skills in descending order
of association. A strong correlation is an indicator that pitchers possess skill in
the area, and a weak correlation is an indicator that pitchers lack skill in the
area.
The fielder-independent metrics are much more strongly correlated than are
BABIP and ERA. This is an interesting finding considering that pitchers are
more commonly judged by ERA than any of the more strongly correlated
metrics. Because ERA is a function of hits allowed on balls in play and DIPS,
then BABIP, over which it seems pitchers have little control, may be heavily
polluting ERA.
To quantify how much BABIP affects pitchers’ ERAs, I use multiple regression analysis to estimate the impact of the contributions of several factors in
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Bradbury / PITCHERS IN THE BASEBALL LABOR MARKET
619
TABLE 1: Season-to-Season Correlation of Pitching Statistics (1980-2004)
Statistic
Correlation
Strikeouts
Walks
Hit batters
Home runs
Earned run average
BABIP
.78
.64
.51
.47
.35
.25
Note: BABIP = batting average allowed on balls in play.
determining ERA in this same sample. Equation 1 lists the econometric
specification.
aERAit or aRAit = lPit + bBABIPit + gXit + tt + To control for the different run environments of home parks, I adjust ERA and
the runs allowed average (RA) using the ‘‘pitcher park factor’’ run deflator
available in the Lahman Baseball Database (The Baseball Archive, 2005) to
create the dependent variables aERA and aRA.4 Though ERA is the traditional
statistic for judging pitchers, RA captures the sum of pitcher and fielder contributions to run prevention. It is useful for comparison to ERA and for determining how much pitchers and fielders contribute to defense. Vector P includes
strikeouts, walks, home runs, and hit batters—normalized per nine innings
pitched—which are all defense independent.5 I also include BABIP, for which
pitchers and fielders are jointly responsible.
Vector X includes other relevant factors. To control for the quality of fielders,
which ought to affect a pitcher’s individual BABIP, I include the pitcher’s team’s
BABIP, which is the BABIP allowed by the other pitchers on the pitcher’s team.
Although this proxy is not perfect, the same defenders who cover the field behind
the pitcher ought to similarly limit hits on balls in play to all pitchers. Knowledge
and intuition that come with experience may also influence ERA by outthinking
batters in crucial situations; thus, I include pitcher age to proxy this potential
effect. I include a dummy for the National League, which produces fewer runs
because of its lack of the designated hitter. t is a vector of year dummies to control for the changing run production of the league over time. I estimate the model
using the Baltagi-Wu random-effects method to correct for detected first-order
serial correlation. Table 2 lists the summary statistics for the variables.
Table 3 lists the results, and it is clear that BABIP has a large impact on
ERA. A one standard deviation change in BABIP (0.024) is associated with a
one-half standard deviation change in ERA (0.44). This effect is much larger
than the impact of any of the other metrics included in the model. Because
BABIP wildly fluctuates from year to year and because BABIP is a large
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620
JOURNAL OF SPORTS ECONOMICS / December 2007
TABLE 2: Summary Statistics
Variable
Earned run average
Strikeouts
Walks
Home runs
BABIP
Team BABIP
Age
Age2
National League
ln(salary)
Service
Service2
Arbitration eligible
Nonarbitration
M
SD
Min
Max
4.04
5.76
3.08
0.92
0.284
0.287
29.37
882.99
0.48
13.87
6.93
68.31
0.026
0.17
0.909
1.625
0.914
0.337
0.024
0.013
4.491
279.538
0.500
1.314
4.50
84.50
0.44
0.37
1.47
2.27
0.66
0.09
0.196
0.243
20
400
0
11.00
0
0
0
0
7.63
13.41
8.81
2.66
0.381
0.327
48
2304
1
16.68
26
676
0
1
Note: BABIP = batting average allowed on balls in play.
determinant of ERA, it seems that ERA may be capturing outside factors that
pitchers cannot control. Therefore, this lends support to the conjecture that for
estimating pitcher MRPs, ERA may be a suboptimal metric. The model similarly predicts for RA.
These models are also important because they set a baseline for the analysis.
The estimates of the impact of the metrics on run prevention are consistent with
those generated by Thorn and Palmer (1984) from play-by-play data. With R2
values of .77 and .76, the full models (Models 1 and 3) predict earned and
unearned runs well.6 As to the power of the DIPS-only models, Models 2 and 4
include only year effects and a league dummy. The R2 values of .58 and .56
show that the categories in which the pitchers do not rely on defense explain
quite a bit of the variance in runs allowed. Pitching explains approximately 73%
of runs allowed, and fielding explains 27% (:56 :76 ¼ 73%).7
The next step is to estimate the marginal impact of individual performance
measures of the preceding seasons on ERA in the following season. Using lagged
metrics to proxy skill is a method employed by statisticians. Skills should persist
through time, whereas random outcomes should not; therefore, we expect strong
correlations in areas where ability exists.8 Equation 2 is similar to Equation 1,
except some of the variables are lagged.
aERAit or aRAit = lPit1 + yFit1 + gX it + tt + The variables in vectors P and F are pitchers’ previous season performances
in fielder-independent and fielder-dependent areas. Again, vector P includes
strikeouts, walks, home runs, and hit batters. Vector F includes BABIP and
ERA. I include lagged ERA in some specifications to estimate its effect with
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Bradbury / PITCHERS IN THE BASEBALL LABOR MARKET
621
TABLE 3: Determinants of Pitcher Run Prevention in the Current Season (1980-2004)
Variable
Strikeoutst
Walkst
Home runst
Hit batterst
BABIPt
Team BABIPt
Aget
Age2t
National Leaguet
Year effects
Observations
Number of players
R2
Estimate Type
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
1
2
3
4
aERA
aERA
aRA
aRA
−0.171
−0.244
24.77∗∗
0.299
0.228
26.93∗∗
1.419
0.322
45.22∗∗
0.338
0.020
5.69∗∗
18.160
1.278
46.02∗∗
−2.753
−0.195
3.29∗∗
−0.050
−0.366
2.22∗
8.25E-04
1.80E-01
2.26∗
−0.052
−0.006
2.49∗
Yes
2,565
671
.77
−0.173
−0.247
19.09∗∗
0.323
0.246
22.19∗∗
1.406
0.319
34.34∗∗
0.356
0.021
4.46∗∗
−0.197
−0.254
26.41∗∗
0.334
0.230
27.73∗∗
1.410
0.290
41.30∗∗
0.422
0.023
6.53∗∗
19.950
1.272
46.44∗∗
−2.545
−0.164
2.78∗∗
−0.045
−0.294
1.80
0.001
0.145
1.83y
−0.027
−0.003
1.21
Yes
2,565
671
.76
−0.201
−0.200
20.39∗∗
0.360
0.360
22.68∗∗
1.392
1.392
30.21∗∗
0.441
0.441
5.07∗∗
−0.096
−0.011
3.53∗∗
Yes
2,565
671
.60
−0.078
−0.078
2.63∗∗
Yes
2,565
671
.56
Note: BABIP = batting average allowed on balls in play; aERA = adjusted earned run average;
aRA = adjusted runs allowed average. z statistics are absolute value.
y
Significant at 10%. ∗ Significant at 5%. ∗∗ Significant at 1%.
and without the other metrics. I estimate the former to generate a comparison
between the DIPS-only model because knowing a pitcher’s DIPS is only useful
if it correlates better with future earned run prevention than does ERA on its
own. There is also a possibility that, even after controlling for all of the factors
that influence ERA, a pitcher’s ERA in the previous season may reflect an ability to pitch well or poorly when the stakes are the highest. Pitchers with better
ERAs, all else being equal, may possibly have a skill to pitch out of tight
situations.
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622
JOURNAL OF SPORTS ECONOMICS / December 2007
Vector X includes variables that control for other factors of ERA in the current year. These factors include defense, age, and league. Aging plays a larger
role in this model than in Equation 1 because improvement and decline with age
ought to influence the impact of change in performance from year to year.
Table 4 presents the results of several models. Model 1 estimates aERA as a
function of all of the DIPS variables, BABIP, and the control variables. Model 2
reports the estimates on aRA, which are not much different from aERA. Model
3 excludes hit batters because the estimate is not statistically significant, which
is not surprising given the rarity with which hit batters occur. Strikeouts, walks,
and home runs are all statistically significant and affect ERA as predicted. Interestingly, the impact on strikeouts from the previous year is nearly the same as
strikeouts in the current year, listed in Table 3. Every strikeout per nine innings
lowers a pitcher’s ERA by about 0.18 in the following year. Every walk and
home run per nine innings raises a pitcher’s ERA by about 0.15 and 0.25,
respectively, in the following year.
BABIP is statistically significant but negative. This counterintuitive result is
most likely the result of outliers regressing to the mean. To be sure, I re-estimate
the model using least absolute deviation (LAD), which minimizes the impact of
extreme values. Model 6 lists the results, and BABIP is no longer statistically
significant.
Model 4 includes only ERA from the preceding year with the control variables. ERA is not statistically significant, and the fit of the model, as measured
by the R2 , is much worse than the individual component models. Model 5
includes the other variables with ERA to see if ERA captures some ‘‘clutch’’
skill of pitchers. The lag of ERA is negatively associated with ERA; however,
like the counterintuitive result for BABIP, this result is probably the result of
outliers. The LAD estimate (Model 6) of the lag of ERA is insignificant.
The results reveal something important: Knowing how a pitcher performs in
areas that do not require inputs from fielders—mainly strikeouts, walks, and
home runs—provides better information about the ability of pitchers to prevent
runs than do metrics that include fielder participation. In fact, because pitchers
do not appear to have identifiable control in preventing hits on balls in play,
ERA provides misleading information about a pitcher’s marginal product. As
Model 7 indicates, eliminating the performance on balls in play, where defense
is a joint product, does not remove meaningful information to the prediction of
ERA, and the R2 is nearly double the ERA-only model (Model 4).
DO PITCHERS HAVE ANY CONTROL OVER
JOINTLY PRODUCED OUTCOMES?
The results from the previous section might indicate that pitchers have no
identifiable control to affect their ERAs through outcomes on balls in play.
From season to season, the marginal impact of BABIP on ERA is nonexistent;
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623
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
Strikeoutst-1
Age2t-1
Aget-1
Team BABIPt-1
Earned run averaget-1
BABIPt-1
Hit batterst-1
Home runst-1
Walkst-1
Estimate Type
Variable
−0.197
−0.258
13.94∗∗
0.148
0.100
6.29∗∗
0.149
0.029
2.16∗
−0.038
−0.002
0.29
−1.923
−0.121
2.37∗
−0.176
−0.255
13.42∗∗
0.136
0.101
6.20∗∗
0.202
0.044
3.14∗∗
−0.082
−0.005
0.68
−1.630
−0.113
2.16∗
4.726
0.302
2.66∗∗
−0.014
−0.092
0.27
3.03E −04
0.062
aRA
aERA
3.840
0.270
2.33∗
−0.019
−0.142
0.41
3.96E −04
8.86E −02
2
1
3.786
0.267
2.30∗
−0.019
−0.136
0.39
3.81E −04
8.53E −02
−1.632
−0.113
2.16∗
−0.176
−0.255
13.43∗∗
0.133
0.099
6.20∗∗
0.204
0.044
3.17∗∗
aERA
3
TABLE 4: Determinants of Pitcher Run Prevention in the Following Season (1980-2004)
0.011
0.010
0.47
3.229
0.225
1.89y
−0.008
−0.059
0.15
2.69E −04
5.96E −02
aERA
4
−0.256
−0.018
0.25
−0.125
−0.119
3.10∗∗
3.499
0.246
2.12∗
−0.023
−0.167
0.46
4.49E −04
1.00E −01
−0.190
−0.274
12.64∗∗
0.155
0.116
6.16∗∗
0.305
0.066
3.56∗∗
aERA
5
1.195
0.084
0.91
0.012
0.012
0.24
2.849
0.203
1.38
−0.027
−0.204
0.53
4.79E −04
1.09E −01
−0.191
−0.279
11.30∗∗
0.175
0.133
6.05∗∗
0.450
0.098
4.24∗∗
aERA
6
(Continued)
3.637
0.256
2.23∗
−0.021
−0.156
0.47
4.29E −04
9.61E −02
−0.180
−0.260
14.02∗∗
0.142
0.106
6.73∗∗
0.254
0.055
3.99∗∗
aERA
7
624
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551
z statistic
Marginal effect
Elasticity
z statistic
Estimate Type
0.38
−0.264
−0.028
6.24∗∗
Yes
2,174
551
.27
aRA
aERA
0.53
−0.274
−0.032
6.97∗∗
Yes
2,174
551
.28
2
1
0.51
−0.273
−0.032
6.95∗∗
Yes
2,174
551
.28
aERA
3
0.32
−0.378
−0.044
8.60∗∗
Yes
2,174
551
.16
aERA
4
0.57
−0.295
−0.035
7.23∗∗
Yes
2,174
551
.26
aERA
5
0.59
−0.193
−0.023
4.34∗∗
Yes
2,174
551
.16a
aERA
6
.29
0.60
−0.260
−0.031
6.80∗∗
Yes
2,174
aERA
7
Note: BABIP = batting average allowed on balls in play; aERA = adjusted earned run average; aRA = adjusted runs allowed average. z statistics are absolute
value.
a. Pseudo R2.
y
Significant at 10%. ∗ Significant at 5%. ∗∗ Significant at 1%.
Year effects
Observations
Number of players
R2
National Leaguet-1
Variable
TABLE 4: (Continued)
Bradbury / PITCHERS IN THE BASEBALL LABOR MARKET
625
therefore, outcomes when pitchers put the ball in play appear to be a function of
defense and random chance. However, this does not necessarily mean that pitchers do not have any skill at preventing hits on balls in play. The multiple regression estimate reveals that when holding other factors constant, pitchers’ BABIP
does not predictably affect ERA from season to season. Though the DIPS do
directly lower and raise pitcher ERAs, it is possible that pitcher ability in strikeouts, walks, and home runs correlates with ability to affect BABIP. For example,
pitchers who strike out many batters may cause hitters to make poor contact on
batted balls, which causes them to be turned into outs.
To see if this is the case, I estimate the impact of pitcher performance on
BABIP using current and lagged independent variables. Table 5 lists the results.
Model 1 reports the impact of the variables on the current season’s BABIP.
Model 2 includes only the DIPS components, league, and year effects. Walks
are statistically significant, but the impact is tiny. Every batter a pitcher walks
per nine innings pitched raises his BABIP by approximately 0.001, which is too
small to be practically relevant given the rate at which pitchers walk batters.
Models 3 and 4 report estimates of the preceding season’s variables on
BABIP, with and without the preceding season’s BABIP included. The lag of
BABIP is statistically significant, but of the wrong sign, just as it is for ERA.
This is more evidence that measures that include BABIP outcomes contain
erroneous information. Strikeouts are statistically significant, though they are
not in the current season models, which is curious. The fact that strikeouts are
negatively correlated with BABIP in the following season is not surprising
because strikeout pitchers keep hitters off balance, even when they do not ultimately strikeout the batter. This effect is meaningful, but still small. A pitcher
with the maximum strikeout rate in the sample—13.41 (Randy Johnson’s 2001
season with Arizona), which is just less than 5 standard deviations above the
average—will have a BABIP that is 0.025 below the average. Using the estimate
of the impact of BABIP on ERA in Table 3, this lowers the predicted ERA
in the following season by 0.45 (18.16 × 0.025 = 0.45). The impact on
earned-run prevention is equivalent to averaging 2.6 additional strikeouts per
nine innings (0:45 0:171 ¼ 2:6).
In summary, it appears that pitchers do have some minor control over hits on
balls in play, but this influence is small. From a practical standpoint, this finding
is irrelevant because the DIPS variables contain all of the information necessary
to properly value a pitcher’s contribution to run prevention. However, it is useful
to know that pitchers may have some small skill in affecting fielder-dependent
outcomes. This skill just happens to be captured by strikeouts.
THE LABOR MARKET FOR PITCHERS
If it is true that pitchers’ defense-independent performance metrics are the
best predictors of future performance, then it is useful to know if the market for
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626
JOURNAL OF SPORTS ECONOMICS / December 2007
TABLE 5: Determinants of Pitcher BABIP (1980-2004)
Variable
Strikeouts
Walks
Home runs
BABIP
Team BABIP
Age
Age2
National League
Year effects
Observations
Number of players
R2
Estimate Type
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
Marginal effect
Elasticity
z statistic
671
1
BABIP
Current
−0.00022
−0.00442
0.64
0.00141
0.01519
2.59∗∗
−0.00096
−0.00309
0.61
0.35570
0.35847
8.58∗∗
0.00074
0.07596
0.66
−1.026E −05
−0.03186
0.57
−0.00179
−0.00303
1.75y
Yes
2,565
671
.14
2
3
BABIP
Current
−0.00007
−0.00147
0.21
0.00146
0.01580
2.67∗∗
−0.00046
−0.00147
0.29
BABIP
Lagged
−0.00184
−0.03794
4.84∗∗
0.00007
0.00078
0.12
−0.00201
−0.00619
1.11
−0.05842
−0.05784
2.79∗∗
0.36910
0.37127
8.05∗∗
−0.00017
−0.01754
0.12
1.648E −06
0.00527
0.08
−0.00158
−0.00267
1.38
Yes
2,174
551
.14
−0.00302
−0.00147
2.92∗∗
Yes
2,565
551
.11
4
BABIP
Lagged
−0.00177
−0.03649
4.77∗∗
0.00014
0.00150
0.23
−0.00192
−0.00591
1.08
0.38120
0.38352
8.47∗∗
−0.00038
−0.03939
0.30
5.754E −06
0.01841
0.29
−0.00120
−0.00202
1.10
Yes
2,174
.16
Note: BABIP = batting average allowed on balls in play. z statistics are absolute value.
y
Significant at 10%. ∗ Significant at 5%. ∗∗ Significant at 1%.
pitching talent recognizes this phenomenon. Furthermore, if the labor market for
players values performance in DIPS and BABIP according to their usefulness to
predict run prevention, then this lends support to the previous results. Therefore,
I examine the impact of the metrics on compensation for starting pitchers
included in the sample from 1986 to 2004—years for which salary data are
available in the Lahman Database (The Baseball Archive, 2005). I focus on starters because the run-prevention models are based on pitchers who pitched many
innings.
I separately estimate Equation 3 for each year using ordinary least squares.
I independently analyze the seasons to identify any changes in the valuation of
these skills over time.9
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Bradbury / PITCHERS IN THE BASEBALL LABOR MARKET
627
Ln(S)it = lPit1 + βBABIPit1 + gXit + yCit + The model is similar to the above equations, therefore I highlight only the differences here. S is the annual salary of pitcher i in year t. Vector C includes variables important to the determinant of player salaries resulting from the collectively
bargained labor classification of each player. The variables are indicators for
nonarbitration and arbitration-eligible players and the time of service in the major
leagues (estimated quadratically).10 Following Hakes and Sauer (2006), I employ
1-year lags of pitcher performance to proxy expected performance because it is a
reasonable expectation of what a player will produce in the future.
Table 6 reports the results for strikeouts, walks, home runs, hit batters, and
BABIP. The compensation to pitchers estimated from their previous performances
in the metrics is consistent with the metrics’ estimated impacts on run prevention.
The three main DIPS—strikeouts, walks, and home runs—are statistically significant predictors of pitcher salaries, at the 5% level, for 16, 5, and 6 years of the
sample. The lag of BABIP is a statistically significant predictor of salaries in 3
seasons.
Next, I estimate pitcher salaries with using a model of the traditional ‘‘triple
crown’’ of pitching categories—strikeouts, ERA, and wins—instead of the DIPS.
Strikeouts, which are also important components of the DIPS model, are normalized on a per-nine-innings basis. Wins are normalized for opportunities, which
generates a winning percentage. Table 7 displays the results. As expected, strikeouts are statistically significant in 11 years. ERA and winning percentage are
statistically significant in 3 years.11 The mean fit of the model is the same as the
DIPS model, but the included coefficients appear to be less important.
In summary, the evidence from the labor market indicates that the participants value the consistent predictors of run prevention and ignore the less
important factors of hit batters, BABIP, ERA, and wins. Because the scarcity of
these skills is not known for any year, the exact efficiency of the market is not
quantifiable. However, it is important to note that the market does show a general tendency to value the skills it should. The average ratio of the coefficients
in the salary regressions in Table 6 are similar to the coefficient ratios in ERARA regressions in Table 4. The ratio of the coefficients on strikeouts to walks is
1.25 in the salary regressions and 1.29 in the ERA-RA regressions. The ratio of
the coefficients on strikeouts to home runs is 0.32 in the salary regressions and
0.71 in the ERA-RA regressions. Thus, the market for pitchers valued strikeouts
and walks similar to their values in preventing runs while overvaluing home run
prevention by a small margin. This lends further support to the argument that
pitcher estimates of MRP should not include metrics that include joint product
estimates of run prevention.
Also, the market appears to have solved the problem of estimating pitcher MRPs
in team production well before McCracken published his findings in 2001. This
finding mirrors Hakes and Sauer (2006), who find that the baseball labor market
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628
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0.102
0.071
0.145
0.142
0.123
0.183
0.180
0.097
0.082
0.146
0.158
0.106
0.087
0.140
0.107
0.110
0.116
0.112
0.233
0.128
16
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
M
Year significant (5%)
Strikeout/(variable)
ratio (salary)
Strikeout/(variable)
ratio (earned run average)
0.71
1.25
2.50∗
0.94
0.92
1.43
0.26
1.40
0.29
0.94
2.39∗
0.51
0.49
2.63∗
2.44∗
0.50
0.23
2.60∗
1.76
0.37
0.16
0.32
−0.152
−0.081
−0.074
−0.197
−0.018
−0.152
−0.023
−0.064
−0.217
−0.057
−0.045
−0.177
−0.210
0.046
0.024
−0.206
−0.237
−0.075
0.021
−0.100
5
2.23∗
1.32
2.95∗∗
3.04∗∗
2.69∗∗
3.13∗∗
3.43∗∗
2.03∗
1.68
2.42∗
3.09∗∗
2.49∗
2.15∗
3.21∗∗
2.36∗
3.15∗∗
2.63∗
1.84
3.57∗∗
t
1.29
Coeff.
t
Walkst-1
−0.242
0.144
−0.363
−0.012
0.305
−0.347
−0.774
−0.677
−1.026
−0.104
−0.432
−0.098
−0.412
−0.406
−0.716
−0.646
−0.076
−1.341
−0.399
−0.401
6
Coeff.
1.11
0.45
2.40∗
0.05
0.96
0.95
2.45∗
2.00∗
3.28∗∗
0.33
1.50
0.51
1.50
1.42
1.84
2.39∗
0.25
3.30∗∗
1.00
t
Home Runst-1
0.041
−0.579
−0.208
0.115
−0.611
−0.826
−0.396
0.662
−1.095
−0.007
−0.531
−0.478
0.071
0.201
−0.516
−0.120
−0.052
0.412
0.158
−0.198
1
Coeff.
0.10
1.07
0.54
0.26
1.22
1.15
0.76
1.37
2.82∗∗
0.01
1.14
1.67
0.13
0.48
0.94
0.34
0.12
0.41
0.20
t
Hit Batterst-1
−4.440
2.552
0.018
−1.684
−5.106
−0.180
−2.449
−6.590
−4.558
−9.338
0.205
−5.072
0.641
−6.366
−3.481
−2.029
−3.045
2.564
−6.915
−2.909
3
Coeff.
t
2.08∗
0.83
0.01
0.57
2.53∗
0.05
0.84
1.56
1.36
2.66∗
0.06
1.86
0.20
1.70
0.76
0.46
0.79
0.28
1.12
BABIPt-1
Note: BABIP = batting average allowed on balls in play; DIPS = defense-independent pitching statistics. t-statistics are robust.
∗
Significant at 5%. ∗∗ Significant at 1%.
Coeff.
Year
Strikeoutst-1
TABLE 6: Determinants of Pitcher Salaries, DIPS Model (1986-2004)
72
64
64
70
71
71
71
77
71
67
75
71
84
87
70
61
54
47
53
68
Observations
.61
.70
.81
.50
.75
.70
.83
.78
.77
.71
.76
.83
.78
.68
.58
.57
.54
.53
.77
.69
R2
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629
0.614
0.385
1.439
1.039
0.132
−0.084
0.504
1.130
−0.362
1.722
0.612
0.930
0.733
1.910
1.781
1.111
1.340
2.501
−0.060
−0.060
0.866
3
Note: t-statistics are robust.
∗
Significant at 5%. ∗∗ Significant at 1%.
Year
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
M
Year significant (5%)
0.95
0.57
2.50∗
1.18
0.26
0.11
0.76
1.54
0.52
2.27∗
0.73
1.20
0.88
2.73∗∗
1.32
1.15
1.26
1.73
0.05
0.05
−0.303
−0.018
−0.106
−0.046
−0.053
−0.155
−0.186
−0.177
−0.162
−0.054
−0.046
−0.244
−0.241
−0.065
−0.109
−0.209
−0.101
−0.074
−0.165
−0.165
−0.134
3
3.54∗∗
0.12
1.46
0.37
0.85
1.44
1.82
1.20
1.45
0.51
0.40
2.83∗∗
2.08∗
0.60
0.82
1.32
0.69
0.29
0.93
0.93
t
Coeff.
Coeff.
t
Earned Run Averaget-1
Winning Percentaget-1
TABLE 7: Determinants of Pitcher Salaries, Traditional Model (1986-2004)
0.060
0.049
0.137
0.111
0.114
0.167
0.192
0.089
0.053
0.116
0.159
0.057
0.027
0.106
0.038
0.045
0.064
0.067
0.205
0.205
0.103
11
Coeff.
t
1.59
0.93
3.20∗∗
2.41∗
2.31∗
2.74∗∗
5.19∗∗
2.38∗
0.89
2.17∗
3.22∗∗
1.38
0.56
2.45∗
0.56
1.14
1.64
0.96
3.28∗∗
3.28∗∗
Strikeoutst-1
72
64
64
70
71
71
71
77
71
67
75
71
84
87
70
61
54
47
53
53
68
Observations
.65
.69
.83
.50
.73
.68
.82
.78
.70
.71
.75
.82
.78
.70
.58
.55
.53
.47
.76
.76
.69
R2
630
JOURNAL OF SPORTS ECONOMICS / December 2007
corrected its misvaluation of on-base percentage and slugging percentage before it
became public knowledge in Michael Lewis’s (2003) bestseller Moneyball.
DISCUSSION AND CONCLUSION
Valuing pitcher contributions to run prevention is difficult because pitchers
jointly produce defense with their fielders. Fielder contributions and randomness
pollute common measures of run prevention, such as ERA. In this article, I find
that areas where pitchers prevent runs without the help of fielders provide a
more accurate measure of pitcher skill in run prevention than does ERA. In
addition, the labor market for pitchers appears to reward pitchers on the basis of
individual run prevention and ignore defensive output produced jointly with
fielders. Researchers using measures of pitcher skill as control variables in
regression analysis ought to proxy pitcher skill with defense-independent metrics (or DIPS)—strikeouts, walks, and home runs—rather than metrics that
include jointly produced outcomes with fielders. Even other more-sophisticated
measures of pitcher performance, such as WHIP (walks plus hits per inning) and
component ERA (a regression-based estimate of ERA), are polluted by their
reliance on pitcher performance on balls in play.
As a practical matter, these results ought to be of interest for player agents,
general managers, and arbitrators, all of whom benefit from properly valuing
player contributions. And the results indicate that labor-market participants are
aware of the factors that are important for imputing pitcher MRPs despite being
clouded by team production.
NOTES
1. Bradbury and Drinen (in press) demonstrate that although player skills in hitting do spill over
to other teammates, the magnitude of the externality is so small that it is not practically relevant.
2. Batters do sometimes hit inside-the-park home runs, and some fielders do make spectacular
plays to prevent short home runs from going over the fence. These are rare events that should not
greatly bias the assumption of the defense independence of home runs. I also exclude outcomes such
as balks, catcher interference, and so on because of their rarity.
3. Data are from the Lahman Baseball Database, Version 5.2 (The Baseball Archive, 2005).
I exclude observations for pitchers who pitched for more than one team in the same season.
4. RA includes earned and unearned runs. The Lahman method for calculating park factor corrections is derived from run production at and away from a given park. The correction is based on
a 3-year average of the differences. This method is not perfect, as parks may have different ways
of affecting runs (e.g., home runs, extra-base hits, etc.), but these outcome-specific corrections are
not publicly available.
5. I also estimated models that normalized these statistics by batters faced and used the strikeout-to-walk ratio instead of separately using the strikeouts and walks. The results were not meaningfully different.
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Bradbury / PITCHERS IN THE BASEBALL LABOR MARKET
631
6. Because the estimates are generated from a random effects model, R2 refers to the ‘‘overall’’
R2 , which is the weighted average of ‘‘within’’ and ‘‘between’’ R2 values.
7. These percentages are slightly higher than the weights assigned in Bill James’s Win Shares
system (70% and 30%). Thanks to an anonymous referee for suggesting this comparison.
8. See Albert (1994) and Albert and Bennett (2001) for discussions of this method.
9. Estimating the model in a single pooled time-series equation is problematic because years,
age, and service times are such major determinants in the change of player salaries over time. The
coefficients on the performance variables are swamped by these other factors.
10. Blass (1992) finds that Major League Baseball hitters receive compensation for experience
even after controlling for on-field productivity.
11. The lack of importance for wins is not surprising. A pitcher who starts the game is credited
with a win if he pitches five or more innings and his team holds the lead until the end of the game.
The pitcher’s job in wining a baseball game is very simple: prevent runs. The value of a pitcher
should be based solely on his contribution to run prevention, not on his performance relative to his
team’s offense. Whether or not he succeeds according to this arbitrary benchmarks should be irrelevant to the valuation of pitchers in the labor market. A pitcher who earns many wins because he
plays on an excellent offensive team will not be valued by teams with poor offenses. What is important to the labor market is how a pitcher achieves those benchmarks via preventing runs.
REFERENCES
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Bradbury, J. C., & Drinen, D. J. (in press). Pigou at the plate: Externalities in Major League Baseball.
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JOURNAL OF SPORTS ECONOMICS / December 2007
John Charles Bradbury is an associate professor of health, physical education, and sport science
at Kennesaw State University. He has a PhD in economics from George Mason University and a
BA from Wofford College. His research interests include public economics and the economics of
sports. He is the author of The Baseball Economist: The Real Game Exposed (Dutton/Penguin
2007).
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