I. INTRODUCTION
Are you seriously going to throw at somebody when you're
facing Randy Johnson?
--Curt Schilling (1)
In 1973, amid waning fan interest in baseball, the American League
(AL) of Major League Baseball (MLB) instituted the designated hitter
rule as an experiment. The stated goal of this rule change was to boost
offensive output by increasing the talent pool of batters in the lineup.
Traditionally, the competing teams field nine players who must play
defense in the field and bat. Because of the importance of the pitcher,
who is responsible for putting every ball in play, teams rely on
pitching ability and ignore the hitting ability when choosing the
pitcher in the lineup. Therefore, pitchers tend to be very poor hitters.
By allowing teams to substitute a player of greater hitting ability
known as the designated hitter (DH)--to bat for the pitcher the total
offensive output increases. The experiment has since grown into an
institution in the AL that differentiates it from the National League
(NL), where all players must bat and play in the field.
The DH succeeded in turning the AL into the "power
league" as intended, but an unintended consequence of the rule
change is that the AL now has more batters hit by pitches than the NL.
Traditional baseball lore holds that the lack of retaliatory punishment
in the AL for hitting batters is the cause of this phenomenon. Veteran
NL manager Dusty Baker describes the deterrent impact from a
pitcher's point of view, "You can be bold in (the American)
League and get away with [hitting batters]. It's different in our
league where you have to hit." (2) Pitchers who do not have to bat
(where they might face retaliation) are more willing to risk hitting
batters than pitchers who do bat.
Given that the rules of the game in both leagues are identical
except for the use of the DH, MLB created ideal conditions for a natural
experiment to examine the impact of the DH on hit batters in a
controlled setting. (3) Several economists have looked at the issue and
found that there is a statistically significant relationship between the
DH and hit batters. However, the reason for this difference is subject
to much debate. It is possible for the hit batter differential to exist
without the deterrent effect of retaliation. The rulebook punishment for
hitting a batter--awarding the hit batter first base makes retaliatory
enforcement costly for teams to employ. Pitchers are typically poor
hitters who rarely reach base via hitting, while batters who are DHs are
typically good hitters. The fewer hit batters in the NL may reflect the
lineup composition, in which the pitcher must bat. NL teams will try to
avoid plunking pitchers because they are relatively less likely to reach
base than non-pitchers, while AL teams do not have this easy out in
their batting lineups.
A problem with previous studies of the subject is their reliance on
yearly aggregate data. Hit batters are rare events--approximately 1% of
all plate appearances result in a hit batter--that occur in the course
of game where other incentives are quite relevant. This means that
identifying small changes in pitcher behavior from specific factors will
be difficult to identify with aggregate data. Differentiating between
the two competing explanations for the hit batter differential between
leagues deterrence and lineup composition--requires micro-level data
where we can control for in-game strategic incentives for hitting
batters.
Using a unique play-by-play data set that allows us to control for
specific factors that affect hit batters, we find that pitchers are
still more likely to hit batters with a DH in the lineup than without.
And though pitchers are hit more rarely than other players, pitchers do
experience retaliation for hitting batters. Retaliation against pitchers
who plunk batters, which was not found in earlier studies, is needed to
generate an effective deterrent for pitchers in the NL. These findings
provide support for the deterrence hypothesis that the threat of
retaliation against pitchers who hit batters does impact the probability
that a pitcher will hit a batter and demonstrate the importance of
informal enforcement mechanisms in deterring criminal behavior.
Furthermore, we show that it is likely that the addition of formal
administrative punishments for hitting batters by MLB may, in fact, have
increased the incidence of hit batters in both leagues. The remainder of
the paper is organized as follows. Section II reviews the previous
literature, concentrating on the empirical problems with these studies.
Section III discusses the strategic incentives for hitting batters.
Section IV presents the empirical model with section V discussing the
findings. Section VI discusses a peculiar deviation in the pattern of
hit batters in the 1990s. Section VII concludes the paper.
II. A REVIEW OF PREVIOUS STUDIES
Goff, Shughart, and Tollison (1997, hereafter, GST) first examined
the hypothesis that the cost differential to pitchers for hitting
batters induced by the DH is the cause of the interleague difference in
hit batsmen. Using annual league time series data from 1901 to 1990, GST
analyzes changes in the difference in hit batsmen between leagues before
and after the implementation of the DH. The results indicate that,
controlling for several factors, the introduction of the DH raised the
level of hit batsmen in the AL 15% higher than the NL, consistent with
the hypothesis that the DH removes an effective criminal deterrent.
However, though the evidence is clear that the DH is associated with an
increase in hit batsmen, it is not necessarily a consequence of the
lesser deterrent to hitting batters in the AL. Trandel, White, and Klein
(1998, hereafter, TWK) and Levitt (1998) are skeptical of the
interpretation of GST on two grounds. First, adding the DH raises the
marginal benefit of hitting batters due to the existence of an
additional good batter in the lineup. Because pitchers are poor hitters,
few teams want to risk hitting the other pitcher. Replacing the pitcher
with the DH places a batter more worthy of plunking in the lineup. As
TWK state, "the difference [in hit batsmen] is largely because the
AL batters are (on average) better hitters, and are thus less costly and
more beneficial to hit." Therefore, the aggregate increase in hit
batsmen in the AL over the NL may be attributed to increased rewards
rather than the lowered punishment for hitting batters. (4) Second, the
deterrence story seems implausible because pitchers are rarely hit, and
therefore, the probabilistic penalty of retaliation for hitting batters
is too small to have any real effect in a pitcher's decision
calculus. Hitting the pitcher in retaliation may actually reward the
instigator by putting the weak-hitting pitcher on base. Given that
pitchers know this, it is unlikely that pitchers consider reciprocal
retaliation to be a cost. As evidence, Levitt (1998) finds that there is
no correlation between pitchers hitting batters and pitchers being hit
themselves, and pitchers are hit so rarely that they would have to be
hypersensitive to the relative price change induced by the DH. (5)
Trandel (2004) finds similar results for the 1974-1977 seasons using the
same test and finds little evidence of retaliation against any pitcher.
All of these studies conclude that the increase in the frequency of hit
batsmen in the AL likely reflects changes in the batting lineup
composition and not a deterrent response by pitchers. (6)
The crux of the problem in identifying what factors influence the
difference in hit batters across leagues lies with aggregate data, with
which researchers can observe only the increase in the frequency of hit
batsmen with the DH, a result that both competing hypotheses predict.
Aggregate data, though informative, only reveal a quantity hit without
regard to different situations where strategic incentives vary. A
retaliatory plunking war in one game may be hidden within yearly
statistics from a 162-game season, even though such an event may signal
a credible threat of retaliation that persists into the future. As a
result, the differing hypothesized effects are hard to disentangle from
aggregate data. To remedy this we examine the costs and benefits of
hitting any particular batter at the time the pitcher chooses a pitch.
This allows us to examine pitcher decisions as the strategic incentives
for hitting batters vary.
Readers familiar with the previous economics literature on this
topic will recall that the earlier studies debate the cause of the
DH-hit batter relationship as a moral hazard problem. In the AL,
pitchers are actors who are improperly "monitored" by the
opposition and therefore are more likely to engage the undesirable
behavior of hitting batters than NL pitchers. The manger of the pitcher,
in addition to the opposing team, may suffer as a consequence of their
shirking agent, creating the potential for moral hazard. In this paper,
we focus on the strategic incentives of pitchers as they impact pitcher
behavior and shift the debate away from relying on moral hazard as the
disputed explanation. The central debate has to do with a behavioral
response to the cost of hitting batters. Is requiring pitchers to bat a
real deterrent against hitting batters, or is the observed league
difference in hit batsman a product of differing lineup compositions in
the leagues? That pitchers might shirk in their duty to the manager is a
possibility, but it is largely irrelevant to the debate and nearly
impossible to identify empirically. Pitchers can still be perfect agents
of their managers and act in accordance with their managers' wishes
to hit more batters with a DH and fewer batters without a DH. Managers
certainly have reason to fear that a pitcher who hits batters may end up
injured, suspended, etc. Therefore, even without moral hazard, the cost
differential of hitting batters in the leagues is sufficient to explain
the league difference in hit batters.
III. THE COSTS AND BENEFITS OF HITTING BATTERS
Getting hit by a pitch is a painful, and sometimes dangerous, event
in baseball. (7) To deter the pitcher from accidentally or purposely
hitting batters the hit batter is awarded first base. Given this
statutory constraint, we know the benefits and costs of hitting a
batter. The benefits include preventing a batter from hitting the ball,
which might generate more runs than simple base advancement; inflicting
injury on a competitor; or decreasing the opposing team's
willingness to stand close to the plate to hit outside pitches. The
costs include putting a runner on base, which increases the chance of
the opposing team scoring; ejections, fines, and suspensions to the
pitcher or manager; physical retaliation via assault; retribution
against the teammates of the pitcher by plunking them when they bat; and
direct reciprocal retribution in the form of the current pitcher being
intentionally plunked by the opposing pitcher.
It is this last cost which is the main subject of discussion. AL
and NL pitchers bear identical costs and benefits when facing batters
except for the reciprocal retribution. AL pitchers do not bat and
therefore bear a lower cost for hitting a batter than NL pitchers. GST
hypothesizes that this relative price difference induces AL pitchers to
hit more batters than NL pitchers hit. (8) This is not to say that any
pitcher actively seeks to consume hit batsmen purposely (at least not
most of the time). Instead pitchers engage in riskier behavior (e.g.,
throwing inside, faster) when DHs bat in their place, which results in a
greater number of hit batsmen. Cy Young award--winning pitcher Randy
Johnson, who has played in both leagues, explains, "If you're
the pitcher and you're playing in the American League, then you may
have a tendency to throw inside a little bit more knowing when that
ninth hole comes up, you won't be hitting. You're protected in
that regard." (9) This is a behavioral response similar to
automobile drivers in Peltzman (1975), which documents seat belt laws
inducing motorists to engage in riskier behavior that leads to car
accidents. Lowering the negative consequences of an action leads people
to take more risks that result in the negative outcome.
However, the critics of the deterrent hypothesis propose that the
expected punishment for plunking is too minor to have much, if any,
effect on an NL pitcher's decision when he pitches to batters. On
average, hitting the pitcher is not a good idea. If retaliation does
provide a deterrent, pitchers would have to be extremely sensitive to
that threat. However, circumstances arise where the benefits of hitting
a pitcher exceed the costs. This may occur in the course of the same
game in which a pitcher hits a batter, or it may occur in some future
game. (10) Though pitchers are hit less than other position players, it
is possible that pitchers may be hit more than they ought to be, given
their hitting abilities. Ultimately, this is an empirical question.
Using the data we describe in the following section, we can answer the
questions central to the analysis.
IV. EMPIRICAL MODEL
A data-gathering project known as Retrosheet has carefully
reconstructed baseball play-by-play data for many seasons. (11) Using a
computer program, we extracted data by plate appearance from the
Retrosheet data. From this we can observe the exact game situation when
a player is hit or not hit; thereby, we can control for the costs and
benefits of hitting any particular player during a plate appearance.
(12) We use a predictive model to estimate the likelihood that a batter
is hit given five categories of influences on hitting batters:
deterrence (DH), batter quality (BQ), pitcher quality (PQ), retaliation
(R), and game situation (GS). Thus,
[HBP.sub.j] = [[alpha].sub.j] + [beta][DH.sub.j] +
[lambda][BQ.sub.j] + [gamma][PQ.sub.j] + [phi][R.sub.j] +
[psi][GS.sub.j] + [eta][YR.sub.j] + [[epsilon].sub.j],
where HBP is a dummy variable equal to one when a pitcher hits a
batter and zero otherwise. Subscript j represents a plate appearance,
[alpha] is the constant, [epsilon] is the error term, and YR is the
year. We estimate the equation using both logit and probit estimation
techniques.
The variable DH is a dummy equal to one when the DH rule is in
effect. According to baseball's conventional wisdom, it is the
lower deterrence induced by the DH that explains the hit batsmen
differential between leagues. If, after accounting for the many factors
we include, the DH coefficient remains positive, it is likely that the
deterrent effect of requiring the pitcher to bat explains some of the
difference. If it is insignificant when controlling for other factors,
it is likely that the deterrence hypothesis is incorrect.
The BQ vector includes two batter quality variables that effect the
cost-benefit calculation of hitting batters. Better hitting batters that
replace pitchers in the batting order ought to be hit more frequently
than pitchers; therefore, we include the season OPS of the batter and a
dummy equal to one if a pitcher is hitting. OPS is the sum of the
slugging average and on-base percentage. (13) A batter with a higher OPS
is more likely to generate offense and is therefore more beneficial to
hit than a player with a lower OPS. Even when controlling for OPS,
pitchers may be less desirable batters to hit relative to teammates,
which is why we also include the pitcher dummy. These variables are
important in determining whether composition of the lineup explains the
hit batsmen differential.
Though it has not been discussed much in this literature, hit
batsmen are largely accidental. Even pitchers who do not mean to brush a
player back or pitch on the inside of the plate may accidentally hit
batters. The variables in PQ control for the pitcher's propensity
to hit batters accidentally. Pitchers who are more likely to hit batters
mistakenly are also likely to make mistakes in the form of placing
hittable balls in the strike zone when compared to other pitchers. These
pitchers will generate more offense for opposing teams relative to more
skilled pitchers. We use the pitcher's OPS allowed to hitters as a
proxy for pitcher skill. Also, pitchers with less control are more
likely to issue walks than pitchers with good control. Therefore, we
also include the walk rate of the pitcher to control for pitcher
quality. Both of these measures ought to be positively related to hit
batsmen.
At the heart of this paper is the issue of using the pitcher to
retaliate against the other team for hitting batters. This retaliation
may be reciprocal, pitcher hitting pitcher, or pitchers may hit
teammates of the pitcher. Trandel (2004) notes that observing
retaliation in the data is of fundamental importance to this debate.
(14) We have the ability to detect retaliation using the variables in
vector R. There are several reasons pitchers retaliate against the other
team through plunking, but we will focus on two common reasons that we
can capture in the data. If a batter on the current pitcher's team
was hit in the previous half-inning, this may provoke a retaliatory
plunking of any player on the opposing team. We include a dummy variable
equal to one if this occurs. Also, we test specifically for reciprocal
retaliation against pitchers. We create a dummy for a pitcher appearing
at the plate when a batter was hit in the previous half-inning. If
retaliation does occur through pitchers hitting pitchers, this variable
should be positive. Also, it is a baseball tradition to hit a batter
following a home run, on occasion. We include a dummy equal to one if
the previous batter hit a home run.
Finally, we include vector GS of many possible game situations
affecting the cost-benefit calculation. The score, inning, number of
outs, and base runners threatening to score all affect the costs and
benefits of hitting a batter at the particular moment. The following
example from an altercation between the Houston Astros and Chicago Cubs
in 2004 demonstrates the role of the game situation in the decision to
plunk a batter.
Both benches cleared briefly in the second inning of Friday's
game between the Houston Astros and the Chicago Cubs when Cubs catcher
Michael Barrett began jawing with Astros pitcher Roy Oswalt, 5 days
after Oswalt hit him in the back with a pitch. Barrett said after that
game that he "thought he [Oswalt] was better than that" and
warned: "We're going to see him again." With Wood on the
mound Friday in another matchup with Oswalt, Barrett and Oswalt
exchanged words when the Houston pitcher came to the plate to lead off
the second with the Astros leading 4-2. After the brief altercation,
Oswalt grounded out and the two again exchanged a few words after
Barrett had run down the first-base line to back up the throw. In the
top of the sixth, Oswalt again came up as the leadoff hitter, with the
Astros leading 8-4, and he was hit in the thigh by the first pitch from
Cubs reliever Kent Mercker. (15)
Score differential and whether a team is winning or losing
certainly impact the strategic incentives. A large absolute score
difference means there is a low marginal impact of runs. When the score
differential becomes large both teams may be more willing to engage in a
plunking war than when the game is tight. However, because the costs of
retaliation fall as the differential rises, pitchers may be extra
careful as the likelihood of retaliation increases. Also, it may be the
case that a big loser is more willing to plunk batters. As the score
differential grows the losing team may feel the opponent is
"rubbing it in," and thus may start plunking the winning team.
It is unclear if batters are more likely to be hit early as opposed to
later in a game. Plunking early may send a message to players not to
"crowd" the inside of the plate throughout the game. However,
if retaliation is an ex post enforcement mechanism to prevent plunking,
later in the game teams have more incentive to renege on tacit
agreements not to hit each others' players. The number of outs
affects the probability that any base runner will score. A batter put on
base with no outs has a better chance of scoring than a batter who
reaches first with two outs. Finally, the number and positioning of base
runners can also affect the costs and benefits. The specific predictions
between differing runner configurations is a bit complicated and largely
irrelevant to the discussion here. Generally, the more runners on base
and the further the runners are around the bases, the greater the
offensive damage a batter can do by putting a ball in play. Therefore,
the seven of eight possible runner configurations included (we exclude
empty bases for comparison) should be positively related to hit batsmen.
We also include year effects to control for unobservable differences in
hit batsmen that may change from year to year. Table 1 lists the summary
statistics for the variables in both of our data sets.
V. RESULTS AND DISCUSSION
Retrosheet provides play-by-play data for both leagues from 1972 to
1992 and for the 1969 season. From this data, we extract two four-season
data sets--the earliest and most recent available years--to estimate the
empirical model. For each plate appearance, we extract data on the
specific game situation and the seasonal performance of the players
participating in the event. Initially, we focus on the four most recent
years of available data, 1989-1992.
Table 2 lists the results of the logit and probit estimations of
coefficients and z statistics. For ease of interpretation, we also
include the odds ratio (logit) and marginal probability (probit)
calculations for each variable. Most of the variables are significant
and of the expected sign. Of particular interest, the DH variable is
positive and significant when controlling for all other factors,
including the lineup composition batter quality variables. When the DH
is in effect pitchers are 15%-17% more likely to hit batters than when
the DH is not in effect. Consistent with the lineup composition
hypothesis, batter quality is positively related with hit batsmen, and
pitchers are about 55% less likely to be hit than other batters. Also,
pitcher quality is negatively related to hit batsmen. Both proxies for
lack of pitch control are positively associated with a greater
likelihood of hitting a batter; however, pitcher OPS is not
statistically significant.
The retaliation variables tell an interesting story. Preceding
events likely to provoke retaliation all tend to increase the likelihood
that a pitcher hits a batter. A batter who appears at the plate
following a home run is 32% more likely to be hit than when the
preceding batter did not hit a home run. In response to hit batters,
pitchers are more likely to hit batters the half-inning after the
opposing pitcher hits a current pitcher's teammate. Though the
results are not significant for players in general, a pitcher is four
times more likely to be hit when an opposing player was hit in the
previous half-inning. This variable, which is significant, is very
important for the deterrence hypothesis. We now observe retaliation
against pitchers who hit batters. This is a phenomenon previously
unidentified in the aggregate data. Though pitchers are hit less
frequently than other players on average, pitchers are more likely to be
hit after plunking an opposing player. Therefore, pitchers do bear a
very real cost to hitting batters, which is necessary to provide a
deterrent to pitchers.
For the game situation variables, outs and innings seem to be
relatively unimportant. Though the absolute score differential is
unimportant, the relative score differential from the offense to the
defense has a small but significant effect on the incidence of hit
batsmen. The base runner composition variables appear to be important
and consistent with our predictions.
Over this sample, the AL hit batsmen rate is 26% higher than the
NL. Controlling for all of the above factors, including batter quality,
the DH rule dummy explains approximately 60% of this difference. It is
now clear that something other than the lineup composition created by
the DH is responsible for the increase in hit batsmen differential
between leagues. The most plausible explanation for this difference is
the removal of a credible threat of ex post punishment of pitchers in
the AL. However, it is possible that some yet unidentified factors
unique to the AL may explain the sign and significance of the DH dummy
since the DH occurs only in this league. For example, differences in
strike zones, stadium configurations, league traditions, etc. between
leagues are competing but less satisfying explanations. To be thorough,
we examine a different data set that includes the 1969 and 1972-1974
seasons. (16) This is the earliest available data in the Retrosheet
archives, plus this period includes some observations of the AL without
the DH rule. We are slightly less confident in this data than our more
recent data for a few reasons. First, the only two seasons available
prior to the introduction of the DH are the noncontiguous years 1969 and
1972. Second, the late 1960s and early 1970s were low offense years for
baseball. The DH was the last of several rules instituted to
"fix" baseball, which was losing fans. The league responded in
1969 by lowering the pitchers mound, shrinking the strike zone to make
it more hitter friendly, and adding two new teams to each league.
Luckily, the exogenous events other than the DH apply to both leagues;
therefore, we feel the data are useful in isolating the effect of the DH
rule on hit batsmen, given that we acknowledge the deficiencies.
We apply the same model for the previous sample to this data,
except that the DH variable is now coded zero for some observations in
the AL, when the DH was not in effect. Therefore, the DH should now
reflect the change in the costs of hitting batters induced by the DH
rule itself. The results in Table 3 are quite similar to estimates of
the more recent data. For this sample, when the DH is in effect pitchers
are 11%-12% more likely to hit batters than without the DH rule, ceteris
paribus. These results differ only slightly in magnitude from our
previous estimates. We also observe pitchers, as well as position
players, being hit in retaliation for hit batters in this sample. Most
of the other factors are of similar magnitude and size, though some
measures are no longer statistically significant. In the years following
the DH, AL pitchers hit batters at a rate 14% higher than NL pitchers;
thus, the DH rule dummy explains approximately 80% of the interleague
difference in hit batsmen in this sample. Therefore, the results
indicate that the removal of the threat of retaliation by the DH rule,
not unobserved league-specific factors, is the likely cause.
VI. THE PROBLEM OF THE 1990s
Figure 1 shows the fluctuation in the rate of hit batsmen from 1921
to 2003. It is evident from the figure that the introduction of the DH
in 1973 coincides with the AL's continued higher rate of hit
batsmen as compared to the NL. From the introduction of the DH until the
present, the AL's average yearly hit batsmen rate has exceeded the
NL rate by 15%. From the beginning of the modern era of baseball until
the 1970s, the hit batsmen rates varied closely, yet randomly, across
leagues. For the next 21 years the AL rate exceeded the NL rate every
year, which is consistent with both the deterrence and lineup
composition hypotheses. But in the mid-1990s, just as economists began
to study this issue and the public availability of play-by-play data
ceased, a deviation in this pattern emerged. In 1994, the NL hit batsmen
rate rose above the AL rate for the first time since the implementation
of the DH, and the leagues' hit batter rates began to fluctuate
more closely than in the past. Why was there such a dramatic shift and
how does this shift impact the perceived relationship between the DH and
hit batsmen? There are two important factors that contributed to this
change: league expansion and a rule change in the punishment for
pitchers hitting batters.
In response to criticism over the recent events of the 1990s, Goff,
Shughart, and Tollison (1998) postulates that the NL expansion in 1993
diluted the talent pool of players increasing the number of accidental
hit batsmen. We believe the evidence supports this contention. Fringe
pitchers and hitters are more apt to make mistakes by hitting batters or
getting hit by pitches. (17) In 1993, the NL hit batsmen rate fell to
only 10% of the AL rate, while the average difference over the preceding
2 decades was 20%. Additionally, the mid-1990s corresponded with a
dramatic increase in hit batsmen in both leagues, doubling over the
decade. The expansion hypothesis is consistent with both the change in
the difference between leagues and the rise in hit batters overall. In
the two rounds of expansion, three of the four expansion teams joined
the NL with one existing AL team (Milwaukee) shifting to the NL. But
more importantly, the asymmetric expansion draft rules in 1993 favored
expansion players coming from NL rosters. Therefore, the expansion
diluted the talent pool of both leagues but affected NL rosters to a
greater degree than AL rosters. (18) From 1993 to 1997, as the expansion
players eased into the league, the NL rate exceeded the AL rate in 3 of
the 5 years, with the AL rate being 2% lower than the NL rate, on
average. But in 1998, when both leagues added a team, there was no
asymmetry between leagues in drafting expansion players. Interestingly,
the disruption to the previous pattern was noticeably smaller. Since the
last round of expansion in 1998, only once (2000) has the NL rate
exceeded the AL rate, with the AL rate exceeding the NL rate by an
average of 6.5%.
[FIGURE 1 OMITTED]
The second factor was an important rule change in the punishment
for hitting batters that significantly altered the cost of retaliating
against pitchers who hit batters. In 1994, MLB adopted the
"double-warning" rule, which authorized umpires to warn both
teams if an umpire judges that a pitcher intentionally hits or attempts
to hit a batter. (19) Once the umpire issues a warning, retaliation
results in the immediate expulsion of the current pitcher and manager of
the offending team, accompanied by monetary fines. This statutory
constraint significantly raised the cost of retaliation, which, in turn,
lowered the probability of punishment to pitchers for initially hitting
batters. With the double-warning rule, pitchers can take risks that are
more likely to result in hit batters than without the rule because
pitchers know the opposition will be less likely to retaliate due to the
increased penalty after the umpire issues a warning. The relative rise
in the NL rate of hit batsmen in the 1990s is consistent with the
deterrence hypothesis and therefore is expected. NL pitchers are now
more protected from retaliation than before the double-warning rule,
thereby inducing NL pitchers to behave more like their counterparts in
the AL. A similar phenomenon occurred in Japanese professional baseball.
The Nippon Professional Baseball League, which also has the DH in only
one league, experienced a similar convergence of hit batsmen after
several years of excessive hit batsmen in the DH league. Kawaura and La
Croix (2002) find that this convergence correlates with a rule change
that increased the penalty for intentionally hitting batters. Thus, the
statutory constraint designed to limit hit batters likely had the
unintended consequence of doing the opposite.
Finally, using game-level (not play by play) data from 1973 to
2003, Bradbury and Drinen (forthcoming) find that games in which the DH
is allowed are associated with more hit batters than non-DH games,
controlling for many relevant factors. Over the entire 31-year history
of the DH, the 4 years in which the NL rate exceeded the NL rate appear
to be exceptions rather than the rule. When relevant historical facts
are included in the analysis, it is clear that the 1990s actually lend
support to, rather than cast doubt upon, the deterrence explanation for
differences in hit batsmen between leagues. The most recent history of
hit batsmen rates is indicative of a return to the pre-1990s league
differences in hit batsmen, with a tempering of the difference by the
double-warning rule.
VII. CONCLUSION
Competing economic theories predict that DH rule is responsible for
raising the rate of hit batsmen in the AL above the NE. As Figure 1
illustrates, for the 3 decades following the introduction of the DH the
AL hit batsmen rate remained higher than the NL rate for all but 4
years. However, there is less agreement regarding the cause of this
difference. While the lower cost of hitting batters for AL pitchers, who
do not have to bat and face reciprocal retaliation, is a likely
explanation, it is not the only explanation. An alternate hypothesis is
that the DH increases the incidence of hit batters by altering the
composition of the batting lineup. Replacing a poor-hitting pitcher with
a good-hitting DH raises the marginal benefit to hitting an additional
batter in the lineup in the AL. Additionally, the retaliation threat to
pitchers may be too small to be relevant. If retaliation is not likely,
there is no cost differential to pitchers between leagues to explain the
hit batsmen difference.
Past empirical analyses of the competing hypotheses to explain the
hit batsmen differential have relied on yearly aggregate data. However,
the explicit cost-benefit analysis of the pitcher at the time of a pitch
is not observable with aggregate data. Using two new unique data sets we
have been able to observe the costs and benefits of hitting batters
during individual plate appearances. Therefore, we isolate the predicted
effects of the competing hypotheses and determine the impact of many
relevant factors that influence the pitcher's consumption of risk
in hitting a batter every time a hitter steps to the plate. Controlling
for variables that proxy batter quality, pitcher quality, retaliation,
and game situation, we find that the DH rule increases the likelihood
that any batter will be hit during a plate appearance between 11% and
17%. This explains approximately 60%-80% of the hit batsmen rate
differential between leagues. Furthermore, we observe retaliation
against plunking pitchers, which is necessary for the deterrent
explanation. In total, the findings support the fact that requiring
pitchers to bat deters them from hitting batters. Though other factors
are important in the economics of plunking, the threat of retaliation
plays a nontrivial role. Players really do "take care of it"
themselves through an informal enforcement mechanism, while official
enforcement penalties may have, in fact, exacerbated the problem of hit
batters.
ABBREVIATIONS
AL: American League
DH: Designated Hitter
MLB: Major League Baseball
NL: National League
OPS: On-Base Percentage Plus Slugging percentage
doi:10.1093/ei/cb1014
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Batsmen: A Comment on Goff et al. and Trandel et al." Manuscript,
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283-6.
(1.) The quotation is from Rosenthat (2002).
(2.) The quotation is from Morgan (2002).
(3.) The controlled environment of sports has become a popular
arena for testing economic hypotheses. Some examples include Duggan and
Levitt (2002) on identifying corruption in sumo wrestling: Goff,
McCormick, and Tollison (2002) on racial integration and innovation as
measured by winning in baseball and basketball: McCormick and Tollison
(1984) and Heckelman and Yates (2003) on crime and enforcement in
basketball and hockey: and Sobel and Nesbitt (2004) on offsetting
behavior in response to safety regulations in National Association for
Stock Car Auto Racing.
(4.) In reply Goff, Shughart, and Tollison (1998) responds to the
criticisms by referring to the control variables (batting and pitching
statistics) in previous and revised regressions that control for this
factor.
(5.) This mirrors Levitt's critique on the deterrent effect of
capital punishment in Katz, Levitt, and Shustorvich (2003).
(6.) These studies also extend the data into the 1990s, in which
the difference in hit batsmen between leagues becomes less stable.
However, there are several plausible explanations for the change that we
discuss in Section VI.
(7.) Pitches hitting batters have ended several professional
baseball careers; seven players (only one in MLB) have died from their
injuries. For a sample of serious injuries resulting from players hit by
pitches see James (1985).
(8.) Two other unpublished studies of the relationship between the
DH and hit batsmen also find support for the deterrence hypothesis.
Using differences in hit batsmen between relievers (who rarely bat in
the NL) and starting pitchers (who do bat) who switch leagues, Rupert
and Stephenson (2002) find some support for the deterrence explanation.
Kawaura and La Croix (2002) replicate the GST and TWK estimations on
Japanese professional baseball, which also has the DH in only one
league. The results are consistent with Goff, Shughart. and Tollison
(1998) in support of the deterrence hypothesis.
(9.) The quotation is from Rosenthal (2002).
(10.) A well-documented case of how long teams will wait to
retaliate against a pitcher occurred in 2002. Shawn Estes of the New
York Mets threw at (and missed) Roger Clemens in retaliation for hitting
Mets' star Mike Piazza two seasons prior. Mets' manager Bobby
Valentine clearly ordered the retaliation because Estes was not a Met at
the time Clemens struck Piazza.
(11.) As a condition of using this data, we must include the
following statement. The information used here was obtained free of
charge from and is copyrighted by Retrosheet. Interested parties may
contact Retrosheet at 20 Sunset Rd., Newark, DE 19711. Turocy (2005)
uses Retrosheet play-by-play data to test game-theoretic predictions
regarding stolen bases.
(12.) We use baseball designation "plate appearance" as
opposed to "at bats," because several results of plate
appearances (including being hit by a pitch) do not count as at bats.
(13.) Baseball fans may wonder why we chose this measure as opposed
to batting average. Though batting average is positively correlated with
offensive output, OPS is a better predictor of run production.
(14.) Trandel (2004) states, "While retaliation is widely
believed to exist ... it is now clear that any attempt to debate the
method of retaliation should be postponed. Rather, the attention of
interested researchers should be focused on finding a way in which
retaliation (to the extent that it exists) can be detected."
(15.) Description from ESPN.com (2004).
(16.) A few games in the Retrosheet data are missing for the 1972
and 1973 seasons.
(17.) See Gould (1996) for an interesting theory of how the
dispersion of talent causes the best players to excel and the worst
players to suffer. Schmidt and Berri (2003) find some support for
Gould's hypothesis in regards to the influx of new talent into MLB.
(18.) In the 1993 expansion. AL teams were allowed to protect more
players on their rosters than N L teams. See Pappas (1997) for a
description of expansion draft rules.
(19.) In December 1993, MLB adopted the On-Field Behavior Policy,
which, along with several new policies, created the double-warning rule
according to the N.A.P.B.L. Umpire Manual (1996). We would like to thank
Jim Porter for identifying the exact timing of this rule change.
JOHN CHARLES BRADBURY and DOUGLAS J. DRINEN *
* An earlier version of this paper circulated under the title
"Identifying Moral Hazard: A Natural Experiment in Major League
Baseball." Thanks to David Smith and the volunteers of the
Retrosheet organization for compiling and sharing the play-by-play data.
We also thank seminar participants at Clemson University, session
participants at the annual meeting of the American Mathematical Society
and the Mathematical Association of America, Kevin Holman, and Jim
Porter for helpful comments and suggestions.
Bradbury: Associate Professor, Department of Health, Physical
Education, and Sport Science, Kennesaw State University, 1000 Chastain
Road #0202, Kennesaw, GA 30144-5591. E-mail jbradbu2@kennesaw.edu
Drinen: Assistant Professor, Department of Mathematics &
Computer Science, Sewanee: The University of the South, 735 University
Avenue, Sewanee, TN 37383-1000. Phone 1-931-598-3370, E-mail ddrinen@
sewanee.edu
TABLE 1
Summary Statistics
1989-1992
Standard
Variable Mean Deviation Minimum Maximum
Hit by pitch 0.005528 0.074145 0 1
DH 0.54037 0.498368 0 1
Batter OPS 0.702851 0.126917 0 3
Pitcher hitting 0.029663 0.169656 0 1
Pitcher OPS 0.705841 0.089025 0 4
Pitcher walk rate 0.087155 0.027912 0 0.5
Batter hit in last 0.022312 0.147695 0 1
half-inning
Pitcher hitting after 0.00056 0.023647 0 1
batter hit
Previous batter hit 0.019982 0.139937 0 1
home run
Relative score (offense -0.04484 2.959261 -20 20
to defense)
Absolute relative score 2.017926 2.164995 0 20
Inning 5.035247 2.6935 1 22
Outs 0.977866 0.81623 0 2
Man on first 0.179398 0.383686 0 1
Man on second 0.08862 0.284194 0 1
Man on third 0.031418 0.174445 0 1
Men on first and second 0.068588 0.252753 0 1
Men on first and third 0.032199 0.176528 0 1
Men on second and third 0.022048 0.14684 0 1
Bases loaded 0.022591 0.148594 0 1
1969,1972-1974
Standard
Variable Mean Deviation Minimum Maximum
Hit by pitch 0.005394 0.073247 0 1
DH 0.253612 0.435078 0 1
Batter OPS 0.687984 0.142806 0 4
Pitcher hitting 0.05493 0.227845 0 1
Pitcher OPS 0.690408 0.079808 0 2.5
Pitcher walk rate 0.08878 0.027886 0 1
Batter hit in last 0.021249 0.144212 0 1
half-inning
Pitcher hitting after 0.001058 0.032515 0 1
batter hit
Previous batter hit 0.019453 0.138112 0 1
home run
Relative score (offense -0.04525 2.924196 -19 19
to defense)
Absolute relative score 1.96396 2.166984 0 19
Inning 5.067495 2.735999 1 25
Outs 0.977184 0.816156 0 2
Man on first 0.188647 0.391228 0 1
Man on second 0.083079 0.276003 0 1
Man on third 0.027007 0.162104 0 1
Men on first and second 0.071399 0.25749 0 1
Men on first and third 0.031505 0.174679 0 1
Men on second and third 0.020134 0.140458 0 1
Bases loaded 0.02336 0.151045 0 1
TABLE 2 Estimates of Hit Batsmen, 1989-1992
Category Variable Logit
Deterrence DH dummy Coefficient 0.162214
Odds ratio 1.176112
z statistic 4.63 **
Batter Batter OPS Coefficient 0.614065
quality Odds ratio 1.847929
z statistic 3.93 **
Pitcher hitting Coefficient -0.81375
dummy Odds ratio 0.443191
z statistic -4.52 **
Pitcher Pitcher OPS Coefficient 0.235353
quality Odds ratio 1.265355
z statistic 1.24
Pitcher walk Coefficient 2.893827
rate Odds ratio 18.06231
z statistic 4.89 **
Retaliation Hit batter in Coefficient 0.073132
previous Odds ratio 1.075873
half-inning z statistic 0.65
Pitcher hitting Coefficient 1.447219
after hit in Odds ratio 4.251276
previous half- z statistic 2.36 **
inning
Previous batter Coefficient 0.283919
hit home run Odds ratio 1.328325
z statistic 2.68 **
Game Relative score Coefficient 0.042483
situation differential of Odds ratio 1.043399
offense to z statistic 7.02 **
defense
Absolute relative Coefficient -0.0117
score Odds ratio 0.988371
z statistic -1.38
Inning Coefficient -0.01545
Odds ratio 0.984668
z statistic -2.31 *
Outs Coefficient -0.01707
Odds ratio 0.983078
z statistic -0.8
Man on first Coefficient 0.048279
Odds ratio 1.049463
z statistic 1.03
Man on second Coefficient 0.075331
Odds ratio 1.078241
z statistic 1.23
Man on third Coefficient 0.278385
Odds ratio 1.320995
z statistic 3.14 **
Men on first and Coefficient 0.135049
second Odds ratio 1.144593
z statistic 2.02 *
Men on first and Coefficient 0.197402
third Odds ratio 1.218234
z statistic 2.19 *
Men on second Coefficient 0.251846
and third Odds ratio 1.286398
z statistic 2.4 **
Bases loaded Coefficient 0.132466
Odds ratio 1.14164
z statistic 1.21
Year Year 1990 Coefficient 0.050283
dummies Odds Ratio 1.051568
z statistic 1.02
Year 1991 Coefficient 0.096062
Odds Ratio 1.100827
z statistic 1.97 *
Year 1992 Coefficient 0.189908
Odds Ratio 1.209139
z statistic 3.97 **
Goodness Observations 641640
of fit Log-likelihood -21841.72
Likelihood ratio- 264.99
[chi squared]
Category Variable Probit
Deterrence DH dummy Coefficient 0.056729
Marginal 0.000864
probability
z statistic 4.65 **
Batter Batter OPS Coefficient 0.215086
quality Marginal 0.003293
probability
z statistic 3.95 **
Pitcher hitting Coefficient -0.26391
dummy Marginal -0.00297
probability
z statistic -4.6 **
Pitcher Pitcher OPS Coefficient 0.086929
quality Marginal 0.001331
probability
z statistic 1.3
Pitcher walk Coefficient 1.033456
rate Marginal 0.015822
probability
z statistic 4.92 **
Retaliation Hit batter in Coefficient 0.023006
previous Marginal 0.000362
half-inning probability
z statistic 0.58
Pitcher hitting Coefficient 0.485283
after hit in Marginal 0.013967
previous half- probability
inning z statistic 2.18 *
Previous batter Coefficient 0.099798
hit home run Marginal 0.001729
probability
z statistic 2.62 **
Game Relative score Coefficient 0.01472
situation differential of Marginal 0.000225
offense to probability
defense z statistic 7.05 **
Absolute relative Coefficient -0.00368
score Marginal -5.60 x [10.sup.-5]
probability
z statistic -1.26
Inning Coefficient -0.0055
Marginal -8.40 x [10.sup.-5]
probability
z statistic -2.36 **
Outs Coefficient -0.00581
Marginal -8.90 x [10.sup.-5]
probability
z statistic -0.78
Man on first Coefficient 0.016536
Marginal 0.000257
probability
z statistic 1.01
Man on second Coefficient 0.026281
Marginal 0.000414
probability
z statistic 1.23
Man on third Coefficient 0.098077
Marginal 0.00169
probability
z statistic 3.1 **
Men on first and Coefficient 0.047716
second Marginal 0.00077
probability
z statistic 2.03 *
Men on first and Coefficient 0.068936
third Marginal 0.001147
probability
z statistic 2.15 *
Men on second Coefficient 0.08975
and third Marginal 0.001534
probability
z statistic 2.4 **
Bases loaded Coefficient 0.045277
Marginal 0.000733
probability
z statistic 1.17
Year Year 1990 Coefficient 0.017926
dummies Marginal 0.000278
probability
z statistic 1.05
Year 1991 Coefficient 0.033389
Marginal 0.000522
probability
z statistic 1.97 *
Year 1992 Coefficient 0.066534
Marginal 0.001064
probability
z statistic 3.99 **
Goodness Observations 641640
of fit Log-likelihood -21841.24
Likelihood ratio- 265.96
[chi squared]
Notes: Constants not reported.
* Statistical significance at the 5% level.
** Statistical significance at the 1% level.
TABLE 3 Estimates of Hit Batsmen, 1969, 1972-1974
Category Variable Logit
Deterrence DH Dummy Coefficient 0.116442
Odds ratio 1.123492
z statistic 2.25 *
Batter Batter OPS Coefficient 1.415542
quality Odds ratio 4.118717
z statistic 10.07 **
Pitcher hitting Coefficient -0.45747
dummy Odds ratio 0.632884
z statistic -3.68 **
Pitcher Pitcher OPS Coefficient 0.708161
quality Odds ratio 2.030253
z statistic 3.2 *
Pitcher walk rate Coefficient 3.173758
Odds ratio 23.89712
z statistic 5.16 **
Retaliation Hit batter in Coefficient 0.334874
previous half-inning Odds ratio 1.397764
z statistic 3.04 **
Pitcher hitting Coefficient 1.630977
after batter hit in Odds ratio 5.108862
previous half-inning z statistic 4.57 **
Previous batter hit Coefficient 0.172655
home run Odds ratio 1.188456
z statistic 1.51
Game Relative score Coefficient 0.046296
situation differential of Odds ratio 1.047385
offense to defense z statistic 7.22 **
Absolute relative Coefficient 0.006134
score Odds ratio 1.006153
z statistic 0.7
Inning Coefficient -0.01564
Odds ratio 0.984482
z statistic -2.26 *
Outs Coefficient 0.020185
Odds ratio 1.02039
z statistic 0.89
Man on first Coefficient -0.06239
Odds ratio 0.939517
z statistic -1.25
Man on second Coefficient 0.144596
Odds ratio 1.155572
z statistic 2.29 *
Man on third Coefficient 0.09539
Odds ratio 1.100088
z statistic 0.91
Men on first and Coefficient 0.072292
second Odds ratio 1.074969
z statistic 1.04
Men on first and Coefficient -0.09798
third Odds ratio 0.906663
z statistic -0.92
Men on second and Coefficient 0.05883
third Odds ratio 1.060595
z statistic 0.48
Bases loaded Coefficient -0.05206
Odds ratio 0.949273
z statistic -0.43
Year Year 1969 Coefficient 0.191714
dummies Odds ratio 1.211324
z statistic 3.41 **
Year 1972 Coefficient 0.168274
Odds ratio 1.18326
z statistic 2.89 **
Year 1973 Coefficient -0.05735
Odds ratio 0.944265
z statistic -1.11
Goodness Observations 584886
of fit Log-likelihood -19436.32
Likelihood 373.84
ratio-[chi square]
Category Variable Probit
Deterrence DH Dummy Coefficient 0.039419
Marginal 0.000596
probability
z statistic 2.19 *
Batter Batter OPS Coefficient 0.509973
quality Marginal 0.007512
probability
z statistic 9.87 **
Pitcher hitting Coefficient -0.14043
dummy Marginal -0.00177
probability
z statistic -3.41 **
Pitcher Pitcher OPS Coefficient 0.266846
quality Marginal 0.003931
probability
z statistic 3.33 *
Pitcher walk rate Coefficient 1.150442
Marginal 0.016947
probability
z statistic 5.16 **
Retaliation Hit batter in Coefficient 0.120795
previous half-inning Marginal 0.002068
probability
z statistic 3.06 **
Pitcher hitting Coefficient 0.581011
after batter hit in Marginal 0.018297
previous half-inning probability
z statistic 4.24 **
Previous batter hit Coefficient 0.06083
home run Marginal 0.000966
probability
z statistic 1.48
Game Relative score Coefficient 0.016223
situation differential of Marginal 0.000239
offense to defense probability
z statistic 7.31 **
Absolute relative Coefficient 0.0027
score Marginal 3.98 x [10.sup.-5]
probability
z statistic 0.89
Inning Coefficient -0.00546
Marginal -8.10 x [10.sup.-5]
probability
z statistic -2.27 *
Outs Coefficient 0.00656
Marginal 9.66 x [10.sup.-5]
probability
z statistic 0.83
Man on first Coefficient -0.02133
Marginal -0.00031
probability
z statistic -1.24
Man on second Coefficient 0.050283
Marginal 0.000782
probability
z statistic 2.25 *
Man on third Coefficient 0.034457
Marginal 0.000529
probability
z statistic 0.93
Men on first and Coefficient 0.024472
second Marginal 0.00037
probability
z statistic 1
Men on first and Coefficient -0.03147
third Marginal -0.00045
probability
z statistic -0.85
Men on second and Coefficient 0.021674
third Marginal 0.000328
probability
z statistic 0.5
Bases loaded Coefficient -0.0202
Marginal -0.00029
probability
z statistic -0.48
Year Year 1969 Coefficient 0.066753
dummies Marginal 0.001027
probability
z statistic 3.4 **
Year 1972 Coefficient 0.05901
Marginal 0.000905
probability
z statistic 2.91 **
Year 1973 Coefficient -0.02012
Marginal -0.00029
probability
z statistic -1.13
Goodness Observations 584886
of fit Log-likelihood -19434.23
Likelihood 378.01
ratio-[chi square]
Notes: Constants not reported.
* Statistical significance at the 5% level.
** Statistical significance at the 1$ level.