Hitting Is Contagious in Baseball: Evidence from Long
Hitting Streaks
Joel R. Bock1*, Akhilesh Maewal1, David A. Gough2
1 Scalaton, La Mesa, California, United States of America, 2 Department of Bioengineering, University of California San Diego, La Jolla, California, United States of America

Abstract
Data analysis is used to test the hypothesis that ‘‘hitting is contagious’’. A statistical model is described to study the effect ofa hot hitter upon his teammates’ batting during a consecutive game hitting streak. Box score data for entire seasonscomprising 28 streaks of length L§30 games, including a total 4,496 observations were compiled. Treatment and control
sample groups (n~151) were constructed from core lineups of players on the streaking batter’s team. The percentile
method bootstrap was used to calculate 95% confidence intervals for statistics representing differences in the mean
distributions of two batting statistics between groups. Batters in the treatment group (hot streak active) showed statisticallysignificant improvements in hitting performance, as compared against the control. Mean BA for the treatment group was
found to be 1:6 to 20 percentage points higher during hot streaks (mean difference increased 11:1 points), while the batting
heat index Q introduced here was observed to increase by 32 points. For each performance statistic, the null hypothesis was
rejected at the a~0:05 significance level. We conclude that the evidence suggests the potential existence of a ‘‘statisticalcontagion effect’’. Psychological mechanisms essential to the empirical results are suggested, as several studies from thescientific literature lend credence to contagious phenomena in sports. Causal inference from these results is difficult, but wesuggest and discuss several latent variables that may contribute to the observed results, and offer possible directions for
future research.
Citation: Bock JR, Maewal A, Gough DA (2012) Hitting Is Contagious in Baseball: Evidence from Long Hitting Streaks. PLoS ONE 7(12): e51367. doi:10.1371/
journal.pone.0051367
Editor: Andrew R. Dalby, University of Westminster, United Kingdom
Received February 14, 2012; Accepted November 7, 2012; Published December 12, 2012
Copyright: ß 2012 Bock et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: The authors have no support or funding to report.
Competing Interests: The authors have declared that no competing interests exist. The authors are affiliated with a small startup company, ‘‘Scalaton’’. This
company is developing ideas and designs for cloud-based computing systems. The authors declare that they intend to adhere to all PLOS ONE policies on sharing
data and materials.
* E-mail: sauerkraut@gmail.com

Introduction

Previous Work
Streakiness in sports. Are sports streaks real phenomena, or
merely views of random sequences of events misinterpreted by adesire to detect temporal patterns? The ‘‘hot hand’’ has been abountiful topic for sports-related statistical research.
Streakiness has been studied in connection to many different
sports. In a 2006 review, Bar-Eli et al. [1] surveyed a large numberof studies providing both support and non-support for the belief
that ‘‘success breeds success and failure breeds failure’’ in diverse
sports. They concluded that most of the empirical research on hot
hand effects supported an earlier conclusion by Gilovich et al. [2],namely that the probability of a successful shot in basketball was
independent of the outcomes on previous shots. Hoewever,simulation studies in different sports [1] suggested that rates ofsuccess are non-stationary over time, providing evidence in favorof the hot hand.
Subsequent to the Bar-Eli review [1], reports have appeared in
the literature that quantify possible hot hand effects in several
sports. Raab and co-workers [3] found evidence for streakiness insome volleyball players’ hit-and-miss patterns; scoring a point
made a player more likely to score another in future chances.
Moreover, when players were ‘‘on a roll’’ this was detected by theirteammates, who were found more likely to pass the ball to thestreaking player. In cricket, Ribeiro et al. [4] found long-term
memory effects by analysis of event-wise scoring in over 2000

Baseball folklore has long included the belief that hitting iscontagious, meaning that when an individual batter’s hit production
rate increases over some period (i.e., in a single game, or aconsecutive sequence of games), this enhanced facility spreads likean infectious disease to other batters in the lineup. Despite only
anecdotal evidence, the idea persists that a hot hitter can transmit
this exceptionally difficult mechanical skill to his teammates.
Hot hitting is a transient phenomenon, inherently related to an
observation interval. An archetype of unusually hot hitting inbaseball is the individual consecutive game batting streak. In
particular, streaks of 30 or more games’ duration are rare–only 46
such streaks have been recorded in the Modern Era from 1901 to
the present.
The question examined here is whether or not hitting iscontagious. The infrequent, long hitting streak provides a modelsituation to study this question. However, the methods and resultsof this research have broader implications. If empirical evidence
for a contagion effect in baseball were shown to exist, it could
provide insights into the psychology of motivation in other teamsports, and perhaps more generally into the dynamics ofpropagation of positive behaviors in sociological, organizational
management or economic studies.

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Hitting Is Contagious in Baseballpeople tend to ‘‘catch’’ others’ emotions, and cite literature from awide spectrum of fields in support of this conclusion.
Barsade [13] conducted experiments on different aspects ofmood propagation amongst groups, and concluded that emotional
contagion does exist within groups. Positive emotional contagion
was correlated with better cooperation, reduced conflict, andenhancements in perceived task performance. In the sportingworld, Moll and investigators [14] uncovered association between
team celebrations after successful soccer penalty kicks and theultimate outcome of a penalty shootout. This was attributed to the
spread of a positive attitude throughout the team during thesequence of shots. The opposite effect was seen on the opposing
team–after a successful kick, the opponents’ next try was more
likely to result in a miss if certain behaviors were exhibited by theprevious, successful kicker. On the cricket pitch, Totterdell [15]found evidence for what he called ‘‘mood linkage’’ on sports
teams, which contributed to correlation between a positive overall
team mood and a players’ mood as well as self-appraisal of his
performance. Experiments reported by Lee et al. [16] showed that
golfers who believed they were using a club previously used by aprofessional golfer realized improved putting performance. Specifically, subjects perceived that the golf cup itself had increased inphysical dimension. The authors [16] assigned this to a positive
contagion effect from using the pro golfer’s equipment.
There may be a neurobiological mechanism explaining suchobservations, suggesting a connection between observation ofsports behavior and its propagation to observers of that action.
Rizzolati et al. [17] reviewed a large number of ‘‘mirror
neuron’’-related studies, which show that simple conceptualizationof limb movements produces activity in the same brain areas thatare involved in producing the actual movements themselves. The
ventral premotor cortex has both cognitive (space perception,action understanding and imitation) and motor functions, thelatter of which transform object properties into hand actions, andspatial locations into head and arm actions. Cross and co-workers[18] found experimental evidence for a common neural substrate
for both observational and physical learning. The authors
concluded that it is possible to achieve new action learning frompassive observation.
Gray and Beilock [19] reported on a simulation experiment on
the psychological mechanism of ‘‘action induction’’, whereby
observation of the actions of a hot hitter in turn improve thebatting performance of the observer. While real game data was notpart of this study, action induction was proposed as a sensorimotor
explanation for the belief that hitting is contagious.
Homophily or social influence. It is important to recognize
the potential impact of unobserved variables before declaring thata causal relationship is fundamental in any contagious hitting
effect. The work of Shalizi and Thomas [20] suggests that ingeneral, it is virtually impossible to distinguish between influenceand ‘‘latent homophily’’ in social networks. Under social influence(or contagion), The diffusion of behaviors corresponds to the ideaof contagion, as behaviors change in order to be more similar toothers in the group. Homophily, on the other hand, suggests theformation of social connections due to pre-existing similar
attributes among individuals. As applied to the present study,
important analogic incongruities are present. Unlike online social
networks, in the baseball setting, the population on each team issmall and fixed; associations are controlled by the manager who
constructs the lineup. Baseball teams don’t self-organize; baseballownership draft or trade for players based on economics andskillset requirements at different positions. The effect of location in
the batting order is the closest conceptual analog to a linkagechange in a dynamic social network; however, this change ismatches. They concluded that a hot hand phenomena exists incricket, and that this diffusion-like process may unfold over a very
long temporal scale. Recently, Yaari and Eisenmann [5] analyzed
a large dataset of sequential success/failure rates on free throwattempts documented in NBA basketball. They reported evidence
for a hot hand effect, as the probability of success on a free throwimproved by 1:4{4:6% on the second attempt, conditioned on
the fact that the first attempt was successful. This was interpreted
as strong evidence for a hot hand effect in free throws by NBA
players [5].
Baseball hitting streaks were studied by Albright [6], where runs
tests and logistic regression models were used to evaluate theexistence of batting streakiness. Four years’ Major League batting
results were analyzed; the author concluded that batting performance is better explained by a model of randomness, as opposed
to objective evidence in support of prevalence in streaky hitting.
Albert [7] proposed a consistent-p model assuming that for each atbat during the 2005 Major League season, the probability of that
player successfully getting a hit was constant; it was further
assumed that outcomes for different at-bats were independent.
Using various metrics, players were evaluated and ranked bystreakiness with respect to hits/outs, strikeouts, and home runs.
The model in [7] was shown to explain most of the intra-seasonalvariation in streaky hitting. Quintana et al. [8] developed Bayesianmodels to investigate sequential hitting success (incorporating hits,
walks and sacrifices) spanning four complete seasons. They did not
find evidence that streakiness of individual players persisted fromseason-to-season. The most important covariates with situational
hitting success were found to include: (1) the number of outs attime of plate appearance; (2) the number of runners on base; and(3) game location at batter’s home field; and (4) the earned run
average (ERA) of the opposing pitcher [8].
Previous studies of statistical contagion. These investigations applied statistical methods to analyze an individual streaky
player, or that of aggregate behavior. The identification ofcontagion effects requires consideration of a streak’s effect as it
spreads to teammates. The metaphor of contagion suggests
utilizing analytical methods developed in epidemiology as aframework for scientific investigation.
The first Surgeon General’s report in 1964 [9] established the
U.S. government’s position that scientific evidence suggested acausal relationship between cigarette smoking and lung cancer.
This report advanced a number of criteria to identify causal
relationships between variables, including: consistency (reproducibility over time and location), strength of association, specificity of
association, temporality (cause precedes effect), and coherence(concurrence of collective evidence). These criteria for evaluationof either an association or true causative effect between
environmental feature A and a consequent event B were reviewed
extensively by Hill [10]. In a recent study of epidemiologicalliterature, Parascandola et al. [11] found that strength andcoherence were most often used in practice to establish causal
inference; consistency was moderately used, and temporality andspecificity were not applied at all in some cases. This suggests thatover time, scientific approaches to causal inference in an
epidemiological setting have a reduced emphasis on temporality
as an essential prerequisite to statistical demonstration of causality.
Contagious feelings in social groups have been widely studied.
Hatfield et al. [12] described the process of emotional contagion as
one in which ‘‘…people nonconsciously and automatically mimic
their companions’ fleeting expressions of emotion…people canand do`feel themselves into’ the emotional landscapes inhabited bytheir partners.’’ They concluded that from moment-to-moment,

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Hitting Is Contagious in Baseballcontrolled by the manager, not the players, precluding theapplication of statistical tests to discriminate homophily versus
influence (for example, see [21] and [22]). Despite these
discrepancies in analogy, we recognize that unobserved covariates
may be important in shaping the observed results. Our discussion
considers a number of possible latent factors, including battingorder position, opposing pitching quality, latency in streak
recognition, and overall team skill level.
Contribution of this research. The purpose of this study
was to examine the hypothesis that ‘‘hitting is contagious’’ inbaseball. A retrospective analysis was undertaken on box scoresfrom 28 entire seasons during which long hitting streaks wereaccomplished. An hypothesis test was formulated to investigate thetreatment effect of the hot hitter on his teammates. Results
obtained from the aggregated sample (n~151) suggest thedemonstration of a ‘‘statistical contagion effect’’. This work offersa contribution to the literature where investigators found evidence
for positive contagion in other sports, such as soccer [14], cricket[15] and golf [16].
There appear to exist no previous empirical studies within theframework of confirmatory data analysis to quantify the spread of
hot hitting in baseball. This approach appears to be novel, andcould be applied to studies of performance enhancement in otherteam sports, or extended to sociological, organizational andeconomic investigations.

Table 1. Hitting streaks of length Lw~30 games since 1945.

Methods
Population and Sample
The implied population for the present study is the set of all
Major League Baseball (MLB) players active since 1945. The
experimental sample culled from this population comprises players
who were teammates of one of the players achieving a consecutive
game batting streak of length Lw~30 games spanning one or two
seasons. In order to perform meaningful inference, we select only
those players within this sample whose average number of at-bats
per game exceeded a threshold value t~AB=gamew~2. Werefer to this subsample as the ‘‘core lineup’’ for each hitting streakunder consideration. The reader will note that our specific interest
is on at-bats versus plate appearances, the latter of which may
include walks, hit-by-pitch, sacrifices, or other outcomes notindicative of hot hitting.
We partition the sample into two groups: a treatment group Gt
and a control group Gc . The same individuals are observed bothduring the hot hitter’s streak (treatment) and when the streak is not
active (control) in the context of a season. Inclusion of the same
individuals within each group in the sample design reduces thepotential for selection bias [23].
A sufficiently randomized sample is achieved by collecting datafrom both Major Leagues, over many seasons, thereby mitigating
undue influence of potential sample biasing factors including: (a)the raised mound and expanded strike zone (ca. 1963–1968) which
tended to favor pitchers; (b) the ‘‘steroid era’’ (approx. 1988–2010)
which favored batters using performance-enhancing substances;and (c) subjective differences in strike zones between the two
leagues favoring pitchers (National League: low zone) and batters(American League: high zone), respectively [24].
Finally, our sample streaks postdate the Lively Ball Era (1920–1945) where batters were at a distinct advantage.

PlayerTeam

Year

Finish L

1

T. Holmes

BOS Braves

1945

6/8

37 4

2

D. DiMaggio

BOS Red Sox

1949

2/8

34 7

3

S. Musial

STL Cardinals

1950

5/8

30 6

4

V. Pinson

CIN Reds

1965(6)1

4/10

31 6

5

W. Davis

LA Dodgers

1969

4/6

31 6

6

R. Carty

ATL Braves

1970

5/6

31 5

7

R. LeFlore

DET Tigers

1975(6)1

6/6

31 5

8

P. RoseCIN Reds

1978

2/6

44 5

9

G. Brett

KC Royals

1980

1/7

30 9

10

K. Landreaux

MIN Twins

1980

3/7

31 7

11

B. Santiago

SD Padres

1987

6/6

34 6

12

P. Molitor

MIL Brewers

1987

3/7

39 6

#CL

13

J. Walton

CHI Cubs

1989

1/6

30 5

14

H. Morris

CIN Reds

1996(7)1

3/5

32 4

15

N. Garciaparra

BOS Red Sox

1997

4/5

30 7

16

S. Alomar, Jr.

CLE Indians

1997

1/5

30 7

17

E. Davis

CIN Reds

1998

4/6

30 6

18

L. Gonzalez

ARI Diamondbacks

1999

1/5

30 5

19

V. Guerrero

MON Expos

1999

4/5

31 4

20

L. Castillo

FLA Marlins

2002

4/5

35 5

21

A. Pujols

STL Cardinals

2003

3/6

30 4

22

J. Rollins

PHI Phillies

2005(6)1

2/5

38 6

23

C. Utley

PHI Phillies

2006

2/5

35 4

24

W. Taveras

HOU Astros

2006

2/6

30 7

25

M. Alou

NY Mets

2007

2/5

30 5

26

R. Zimmerman

WSH Nationals

2009

5/5

30 3

27

A. Ethier

LA Dodgers

2011

3/5

30 4

28

D. Uggla

ATL Braves

2011

2/5

33 4

#CL is the size of the core lineup that in total constitutes the sample
population for this study.
1
In streaks spanning two seasons, only the season with the majority of games
comprising the streak is considered.
doi:10.1371/journal.pone.0051367.t001

the post-WWII era as listed in Table 1. Season-long data for thebatting streaks subject to investigation represented in total 4,496
observations.
Raw box scores were downloaded manually in commaseparated value (CSV) format. These files were annotatedaccording to the dates of activity of the associated hitting streak;this annotation formed the basis for partitioning the batters into
the two sample groups. The aggregate sample sizes for each groupwere identical (nt ~nc ~151, the total of the core lineup column inTable 1).
This database of box score data was subsequently analyzed
using the statistical methods that are described in the section on
Analysis.

Analysis
Hot hitting statistics. How shall we define ‘‘hotness’’? Ourmodel situation for studying the contagion of hot hitting is theconsecutive game hitting streak. By definition, it is the length of thestreak itself that is the primary distinguishing factor. The batting
average, the ratio of number of hits H to at-bats AB,

Box Scores Database
The box score data analyzed in the present study were obtained
from the online resource Baseball-Reference.com (http://www.
baseball-reference.com). Our analysis centers on 28 long streaks in
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Hitting Is Contagious in Baseball

BA~

H
AB

Comparative distributions of raw numerical values for thesestatistics for the two groups are presented in Figures 1 and 2.
These figures display, side-by-side, distributions of the hot hitting
statistics between groups. These are the original sample data
representing the population from which resampled statistics are
drawn, and ultimately used to construct bootstrap distributions
and confidence intervals. They provide a visual description therelative distributions of values of the statistics between groups.
In the next section, we describe hypothesis tests applied to the
distributional differences between groups based on this sampling of
the population.
Hypothesis tests. Let us define hitting statistics for thedifferences in group wise means of the distributions of batting
average and batting heat index:

ð1Þ

is the most widely understood and fundamental measure of hit
production by a player. According to MLB rules, just a single base
hit per game (with at least one qualifying at-bat) is enough toperpetuate a consecutive game hitting streak. While virtuallyunobserved historically, it is possible under the rules to post a low
batting average during a long (Lw~30) game streak.
By extension, in the putative measurement of hot hitting
contagion throughout the dugout, it is possible that the batting
average statistic alone may not be a sufficiently sensitive indicator.
Long runs of consecutive games with at least one hit are notrealized by the streaking batters’ teammates; otherwise they would
constitute noteworthy streaks in and of themselves. However, shortbursts of ‘‘microstreaks’’ coincident with the hot batter’s streak areobserved and can be quantified.
To assess offensive production by the core lineup players
constituting each sample group, we propose a statistic that
expresses both microstreak length (run length of consecutive
games with H§1) and batting average to express the quality ofbatting performance. Let us define a batting heat index over thekth microstreak by the ith core lineup member as
qik ~lkiBAik
1zBAikTBA ~DmBA ~mBA,t {mBA,c

ð5Þ

TQ ~DmQ ~mQ,t {mQ,cð6Þ

The null hypothesis H0 assumed no difference between groups.
In this investigation, the interpretation of the null hypothesis wasthat hitting is not contagious. The alternative hypothesis HA wasthat hitting is contagious. Symbolically, these hypotheses are
written
ð2Þ

H0 : DmBA ~0

where lk is the run length in games, and BAik is the player’s batting
average for games occurring over this interval. For runs lk where
no hits are produced, the value of qk ~0, precluding heataccumulation over hitless microstreaks. The core lineup batter
realizes many such clusters (total K) of short-term streaks within
the course of the hot hitter’s streak, which lasts for L games. The
overall heat index for this player is compiled and normalized as

HA : DmBA =0ð7Þ

H0 : DmQ ~0

i

QiL ~

K
2X
qi ,
L k~1 k0ƒQiL ƒ1:

ð3ÞThe heat index of Eqn. 3 represents both the persistence anddensity of hit production by the core lineup player over theinterval L.
As an illustration, consider sequences of hits per game as
produced by two different hitters. Suppose that for a notional 13
game interval, each player records 4 at-bats per game. The hit
totals for each player are, respectively,
S1 ~ð1,1,1,1,1,1,1,1,1,1,1,1,1Þ;
S2 ~ð3,2,3,0,0,0,0,1,1,1,1,1,0Þ

ð4Þ

The first hitter’s 13-game hitting streak yields statistics
Q1L ~0:400, BA1 ~0:250; the second hitter’s statistics over thisinterval are Q2L ~0:338, BA2 ~0:250. The batting averages are
identical. As measured by Q, the second player’s ephemeral
hotness as compared to the streak hitter can be quantified,although his 2 microstreaks are not extraordinary events.
The statistics BA and Q were computed from box score data forthe core lineup players comprising each sample group (treatment [streak active; control [ streak inactive).
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Figure 1. Distribution of BA statistic for sample groups. Original
sample data representing the population from which resampled
statistics are drawn, and ultimately used to construct bootstrap
distributions and confidence intervals.
doi:10.1371/journal.pone.0051367.g001

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Hitting Is Contagious in Baseball

2. Compute statistics (TBA , TQ ) from these resamples;
3. Repeat B~2,000 times;
4. For each statistic, construct sampling distributions and estimate
95% confidence intervals.

Results
The main results of the experiments are summarized in Figures 3
and 4.
The bootstrap distribution for batting average difference
between groups TBA (Eqn. 5) is displayed in Fig. 3. The estimatedlimits of the 95% confidence interval for this statistic are(0:0016,0:020) around a mean difference of TBA ~0:011. CI
limits are shown in blue in the figure. The dashed line marks thelocation of the mean of the distribution under the null hypothesis.
For the batting ‘‘heat index’’ metric, bootstrap distribution
results for differences between the treatment groups (Eqn. 6)
appear in Fig. 4. The 95% CI calculated for TQ is (0:0157,0:047),
centered about a mean difference TQ ~0:032.

Discussion
Our results show that for the batting average, the null
hypothesis of ‘‘no difference between groups’’ is rejected at thea~0:05 level. We submit that this suggests the existence of astatistical contagion effect for hot hitting. The aggregate (n~151) BA
was seen to increase by 1:6 to 20 points (average of 11 percentage
points) for the treatment group during a teammate’s hitting streak.
The null hypothesis is also rejected for the heat index statistic Q.
This provides additional evidence in support of the conjectured
alternative hypothesis, according to the methods and assumptionsof this study. The mean value of Q improved by 32 points relative
to the control group. The Q effect is apparently more pronounced
than that seen for BA, as indicated by the location of the
distributional mean under the null hypothesis in Fig. 4 relative tothe confidence interval.
We reject the null hypothesis. However, this does not prove thetruth of the alternative hypothesis; that is, we cannot claim to have

Figure 2. Distribution of Q statistic for sample groups. Original
sample data representing the population from which resampled
statistics are drawn, and ultimately used to construct bootstrap
distributions and confidence intervals.
doi:10.1371/journal.pone.0051367.g002

HA : DmQ =0

ð8Þ

for the batting average and heat index tests, respectively.
Bootstrap confidence intervals. The null hypothesis wastested using bootstrap resampling to calculate nonparametricconfidence intervals (CIs) around the statistics for the differences ingroup wise means, TBA (Eqn. 5) and TQ (Eqn. 6).
Efron introduced bootstrap methods [25], which have beenshown to be useful for a large variety of statistical estimation
problems. Here, bootstrapping is used to esimate the value of astatistic describing a population by repeated resampling of theoriginal sample representing the population, computing thestatistic for each replicate, and finally constructing a ‘‘bootstrap
distribution’’–an approximation of the shape, variance and bias ofthe sampling distribution of the sample statistic.
In principle the distribution of nearly any real-valued statistic
may be examined using the bootstrap procedure. The statistics
TBA and TQ express the difference in means of distributions for thetreatment and control groups. We used the percentile method [26]with B~2,000 bootstrap replicates to estimate empirical distributions of the resampled statistics; the 2:5 and 97:5 percentiles ofthese distributions were taken to constitute the limits of the 95%
CIs. Analysis of bootstrap differences in means between the sample
groups was carried out using the simpleboot package [27] within
the R statistical computing environment [28].
Locations of the values of the statistics observed from theoriginal sample were compared to these CIs in order to infer thepresence or absence of a significant (a~0:05)‘‘treatment effect’’ ofstreaky hitters upon their teammates.
Our two-sample bootstrap procedure is described by thefollowing steps [29]:Figure 3. Bootstrap distribution for for difference in groupwise means, TBA. Blue lines denote 95% confidence interval BA ~0:011, or 11 percentage(0:0016,0:020) around a mean difference T
points. Sample size n~151, B~2000 replicates.
doi:10.1371/journal.pone.0051367.g003

1. Draw distinct resamples of size nt , nc with replacement fromtreatment and control samples, respectively;
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Hitting Is Contagious in BaseballFigure 4. Bootstrap distribution for difference in group wisemeans, TQ. Blue lines denote 95% confidence interval (0:0157,0:047)
 Q ~0:032. Sample size n~151, B~2000
around mean difference T
replicates.
doi:10.1371/journal.pone.0051367.g004

Figure 6. Mean Q versus relative lineup position. Offensive
statistics for players in each sample group as a function of battingorder. Negative values along the abscissa correspond to batting before
the streak hitter.
doi:10.1371/journal.pone.0051367.g006

demonstrated a direct causal relationship between a hot hitter’s
streak and improved hitting performance of his team.
The observed results may be generated by any number of latent
factors. Some of these are discussed below.

LOESS curves with a first degree polynomial have been overlayed
as a visual aid.
Consider Figure 5. It is apparent that batting averages tend tobe higher the earlier in the lineup that a player is positioned(negative values along the abscissa correspond to batting before thestreak hitter). The general decrease in BA from top to bottom of
the order is observed for both treatment and control groups; this is
as expected, as managers devise their lineups to increase plate
opportunities for more productive hitters, in an average sense.
Similar trends are seen in terms of the heat index Q, shown in
Figure 6. For both groups, the average value of this indicator
declines as a function of position in the batting order, and this may
be again attributed as per design by the team manager.
We conclude that batting order position is not an explanatory
factor in the hitting contagion phenomenon.

Batting Order Position
A player’s position in the batting order relative to that of thestreak hitter might correlate with the quality of pitching heexperiences, thereby contributing to the observed effect. To study
this variable, mean values for offensive statistics posted by players
in each sample group were associated with their average relative
lineup position for the games under consideration.
The results are summarized in Figures 5 and 6 for BA and Q,
respectively. In each figure, due to large variance in the data,

Streak Recognition Delay
One of the criteria for causal infererence that was identified in
the Surgeon General’s report [9] was temporality, or establishingthat the cause precedes the effect. Hill noted [10] that this criterion
is important in the spread of diseases which are slow to develop.
Parascandola et al. [11] later found that the scientific literatureoften ignored the criterion of temporality when making the casefor epidemiological causality.
In terms of the present study, a reasonable question is whether
the streaking batter’s teammates notice a change in behavior in theearly games of a nascent hot streak. We wondered if the contagion
effect would manifest as statistical improvement after some periodof latency following the official onset of the hitting streak.
The procedure followed to partition the sample groups in thisinvestigation assumed that the treatment group immediately
recognizes that their teammate is ‘‘hot’’. In practice, a hot batting
streak in baseball usually eludes diffuse media attention before
having progressed for at least 5 or 10 games.
To simulate this situation, we carried out the bootstrap
resampling procedure and computed 95% confidence intervals
for the distributions of the differences in means between groups, asdetailed in the Section Hypothesis tests. For this analysis, theassignment of the ‘‘treatment’’ effect was delayed by several games

Figure 5. Mean BA versus relative lineup position. Offensive
statistics for players in each sample group as a function of battingorder. Negative values along the abscissa correspond to batting before
the streak hitter.
doi:10.1371/journal.pone.0051367.g005

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Hitting Is Contagious in Baseball(Dg[f1,3,5,7g) after the streak actually began. Because termination of a long streak is obvious, in this model the treatment effectends in coincidence with the end of the streak.
The results of this analysis are compiled in Table 2. Mean BAvalues of the bootstrapped group wise differences in means (Tand TQ ) are listed in the table, alongside the corresponding
decision to accept or reject the null hypothesis H0 which states thatthat hitting is not contagious. For reference, the results for a zerogame recognition lag (Dg~0) are included in the table in the firstdata row.
For the BA statistic, a recognition time delay of any number ofgames results in failure to reject H0 at the a~0:05 significancelevel. This is true even for a single game delay Dg~1, as the
distribution represented in Figure 3 shifts to the left enough suchthat the H0 mean falls within the bootstrapped confidence interval.
The BA contagion effect disappears when there is a delay inidentification of the streak on the part of the team.
A different result is seen for the heat index Q within the delayed
recognition model. In terms of this statistic, the contagious effectpersists up to a lag of Dg~5 games. One interpretation of thisobservation is that when recognition latency is present, the heatindex is more sensitive at detecting the spread of hot hitting
throughout the lineup (as compared to BA). The association
between cause and presumed effect is stronger according to thismetric.

Table 3. Batting statistics for the streak hitters of this study.

ID

Player

Year

DBA

DQ

1

T. Holmes

1945

0.08980.1491

2

D. DiMaggio

1949

0.05820.0516

3

S. Musial

1950

0.05430.1432

4

V. Pinson

1965

0.08030.0972

5

W. Davis

1969

0.16540.3488

6

R. Carty

1970

0.1116

0.2635

7

R. LeFlore

1976

0.09750.18608

P. Rose1978

0.11680.19309

G. Brett

1980

0.10630.3332

10

K. Landreaux1980

0.14970.2982

11

B. Santiago

1987

0.05600.1456

12

P. Molitor

1987

0.09570.3035

13

J. Walton

1989

0.06390.2546

14

H. Morris

1996

0.07290.155815

N. Garciaparra 1997

0.09750.147016

S. Alomar, Jr.

1997

0.13290.239217

E. Davis

1998

0.10190.2651

18

L. Gonzalez

1999

0.08480.0684

Opposing Pitching Quality

19

V. Guerrero

1999

0.08770.1541

The quality of opposing pitching facing the sample groups is
another variable potentially influencing the results of this study.
Although unlikely over the course of a 30z game streak, it ispossible that collective pitching performance faced by thetreatment sample is somehow inferior in contrast to the control.
Analysis of the isolated importance of ‘‘pitching quality’’ would
be complicated. One difficulty lies in the task of separating
pitching from hitting–the two factors are clearly not independentof one another. As baseball philosopher Casey Stengel once
remarked, ‘‘Good pitching will always stop good hitting and vice-versa’’(http://www.baseball-almanac.com/quotes/quosteng.shtml).
Including pitching quality as an essential variable was deemedbeyond the scope of the present investigation. Future research into
the role of pitching to suppress hot hitting may be informed by thefollowing notes.

20

L. Castillo

2002

0.13030.1642

21

A. Pujols

2003

0.03890.022122

J. Rollins

2005

0.11720.2016

0

0.011

Y

0.032

Y

1

0.009

N

0.025

Y

3

0.005

N

0.018

Y

5

0.005

N

0.018

Y

7

0.000

N

0.011

N

Reject H0?

QT

Reject H0?

Mean values of bootstrapped group wise mean differences for various streak
recognition delays Dg.
doi:10.1371/journal.pone.0051367.t002

PLOS ONE | www.plosone.org

2006

0.12600.2107

W. Taveras

2006

0.09770.230225

M. Alou

2007

0.10150.3384

26

R. Zimmerman 2009

0.11450.183127

A. Ethier2011

0.12230.2675

28

D. Uggla

2011

0.18380.2547requirement for an average, minimum number of at-bats as
imposed here. This might reduce the sample size considerably.
2. Owing to the fact that a large number of different pitchers areseen by a team over course of a season, an important design
parameter would be to establish rational criteria for a requisite
number of pitchers’ innings. Managers can always bring in
fresh arms from the bullpen when necessary.
3. A more general view might be accomplished by theformulation of a composite Earned Run Average (ERA)
realized against both hitting groups. However, the ERA
statistic includes many means to reach base and ultimately
score (walks, hit batters, sacrifices) not accounted for using thepresent hot hitting statistics; this would still be problematic fordrawing inference from pitching as a factor. One of many otherquality statistics that might be considered is the so-called‘‘Pitcher Dominance Factor’’ proposed by former MLB pitcher
Curt Schilling [30].
4. The conditional dependence of hitting and pitching could bepartially mitigated through the implementation of a Nave
Bayes computational approach, for example, as discussed in
Duda and Hart [31].

Table 2. Effect of streak recognition delay.

 BAT

C. Utley

24

Values are expressed as differences in/out of their streaks (see Table 1). Thesehitters were excluded from the sample population.
doi:10.1371/journal.pone.0051367.t003

1. A detailed perspective could be obtained by expanding thepresent analysis to consider the individual batter versus pitcher
matchups for each at-bat. This type of information is available
from at least two readily accessible resources (www.baseballreference.com, and www.retrosheet.org). The constitution of
the core lineups would probably be changed, because of the

Dg

23

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Hitting Is Contagious in Baseballdemonstrated a positive contagion effect on golfers who erroneously thought they were using putters belonging to highly skilled
golf professionals.

Overall Team Skill
It is conceivable that the observed hot hitting results might bedue to a greater concentration of skilled players on certain teams
relative to the competition. This relates to the dilemma of
discerning homophily from influence [20]; better hitters might
already have coalesced onto certain teams, and the contagious
hitting is due to this structural grouping as opposed to a diffusive
effect. If some teams were generally more highly skilled, we would
expect that teams with players achieving long hitting streaks would
dominate, and routinely finish at or near the top of their respective
divisions at the conclusion of the streak seasons.
As an indicator of overall team skill, we considered the final
standings for each team in the present study. These standings arelisted in the Finish column of Table 1. The first number is thenumeric standing (lower numbers mean a higher finish), and total
number of teams in that division is shown after the backslash.
The mean finishing position for the streak teams was 3:2 out of
6:03 teams/division, or slightly worse than the middle of the packin the division. All other factors being equal, this implies that theseteams did not possess uncommonly talented players as comparedto their competition. Good, mediocre and bad teams experience
hot hitting streaks. Therefore, overall team skill level is ruled out as
an explanation for the observed contagion effect.

Concluding Remarks
A fascination with statistics is one of the hallmarks of fans ofAmerican baseball. Several interesting extensions to the present
work can be envisioned.
Other statistics indicative of hot hitting might be used toaugment those used here (BA and the heat index Q). For example,
the on-base plus slugging percentage (OPS) might be incorporated
to provide information on different aspects of offensive output(walks and power hitting) by core lineup players during a hot
streak.
Supplemental studies might investigate the time course of a hot
hitting ‘‘epidemic’’ as a streak extends in duration, perhaps
carrying the metaphor forward by employing analytical methods
from epidemiology to the extent that additional insight may beachieved into the mechanisms of transduction.
Finally, it is of interest to note how the streaking battersthemselves performed using our statistical indicators during theirlong hitting streaks. In Table 3, we present data summarizing
differences DBA and DQ for the model streaks considered in thecurrent investigation. These batters were not included in thesample groups subjected to hypothesis testing.

Mechanisms of Contagion
We observed evidence of a statistical contagion effect. The
preceding discussion considered a number of possible latent
external covariates that might account for our observed results. If
hitting contagion does have a concrete basis, it is likely be
motivated internally; some neurobiological or psychologicalmechanisms then would translate the identification and observation of hot hitting by the streak hitter into an improvement inhitting performance by the observer.
We briefly point to four distinct studies from the scientific
literature that attempt to explain mechanisms of the transductionof observation into performance by the observer.
In a study particulary germane to our investigation, Gray and
Beilock [19] advanced the idea of the mechanism of ‘‘action
induction’’ to explain hot hitting contagious effect. In action
induction, observers of the hot hitter tended to imitate performance of others’ actions that were recently observed. An
experimental study by Cross et al. [18] identified a neurologicalpathway that associates new action learning from passive
observation; the implications for the present work are immediateand obvious. Rizzolati et al. [17] summarize many studies on
mirror neurons that fire in the mind of an observer watchingothers perform physical activities; these same neurons areassociated with limb movements used in actual performance of
this activity. Finally, the work of Lee and co-workers [16]Supporting Information
The hitting streak box scores data are provided in Dataset S1.

Supporting Information
Dataset S1 Box score data used in this research. The archive filecontains one folder for each of the 28 batting streaks, named
according to streak batter, year and length of the streak. Individual
game box score filenames indicate date of occurrence relative tothe streak (beginning with characters ‘‘B’’ for before streak, ‘‘A’’
for after streak). Raw data were obtained from www.baseballreference.com.
(ZIP)

Acknowledgments
The authors would like to thank the editor and anonymous reviewers fortheir insightful comments on the original manuscript.

Author Contributions
Conceived and designed the experiments: JB. Performed the experiments:
JB. Analyzed the data: JB AM. Wrote the paper: JB DG.

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