PERSONNEL PSYCHOLOGY 2012, 65, 79–119 THE BEST AND THE REST: REVISITING THE NORM OF NORMALITY OF INDIVIDUAL PERFORMANCE ERNEST O’BOYLE JR. Department of Management College of Business and Economics Longwood University HERMAN AGUINIS Department of Management and Entrepreneurship Kelley School of Business Indiana University We revisit a long-held assumption in human resource management, organizational behavior, and industrial and organizational psychology that individual performance follows a Gaussian (normal) distribution. We conducted 5 studies involving 198 samples including 633,263 re- searchers, entertainers, politicians, and amateur and professional ath- letes. Results are remarkably consistent across industries, types of jobs, types of performance measures, and time frames and indicate that in- dividual performance is not normally distributed—instead, it follows a Paretian (power law) distribution. Assuming normality of individual performance can lead to misspecified theories and misleading practices. Thus, our results have implications for all theories and applications that directly or indirectly address the performance of individual workers in- cluding performance measurement and management, utility analysis in preemployment testing and training and development, personnel selec- tion, leadership, and the prediction of performance, among others. Research and practice in organizational behavior and human resource management (OBHRM), industrial and organizational (I-O) psychology, and other fields including strategic management and entrepreneurship ul- timately build upon, directly or indirectly, the output of the individual worker. In fact, a central goal of OBHRM is to understand and predict the performance of individual workers. There is a long-held assumption in OBHRM that individual performance clusters around a mean and then fans out into symmetrical tails. That is, individual performance is assumed to follow a normal distribution (Hull, 1928; Schmidt & Hunter, 1983; A previous version of this paper was presented at the Annual Meetings of the Academy of Management, San Antonio, Texas, August 2011. We thank Wayne L. Winston for his insightful comments regarding data analysis issues. Correspondence and requests for reprints should be addressed to Herman Aguinis, De- partment of Management and Entrepreneurship, Kelley School of Business, Indiana Univer- sity, 1309 E. 10th Street, Suite 630D, Bloomington, IN 47405-1701; [email protected]. C 2012 Wiley Periodicals, Inc. 79
Transcript
PERSONNEL PSYCHOLOGY
2012, 65, 79–119
THE BEST AND THE REST: REVISITING THE NORM
OF NORMALITY OF INDIVIDUAL PERFORMANCE
ERNEST O’BOYLE JR.Department of Management
College of Business and EconomicsLongwood University
HERMAN AGUINISDepartment of Management and Entrepreneurship
Kelley School of BusinessIndiana University
We revisit a long-held assumption in human resource management,organizational behavior, and industrial and organizational psychologythat individual performance follows a Gaussian (normal) distribution.We conducted 5 studies involving 198 samples including 633,263 re-searchers, entertainers, politicians, and amateur and professional ath-letes. Results are remarkably consistent across industries, types of jobs,types of performance measures, and time frames and indicate that in-dividual performance is not normally distributed—instead, it followsa Paretian (power law) distribution. Assuming normality of individualperformance can lead to misspecified theories and misleading practices.Thus, our results have implications for all theories and applications thatdirectly or indirectly address the performance of individual workers in-cluding performance measurement and management, utility analysis inpreemployment testing and training and development, personnel selec-tion, leadership, and the prediction of performance, among others.
Research and practice in organizational behavior and human resourcemanagement (OBHRM), industrial and organizational (I-O) psychology,and other fields including strategic management and entrepreneurship ul-timately build upon, directly or indirectly, the output of the individualworker. In fact, a central goal of OBHRM is to understand and predictthe performance of individual workers. There is a long-held assumptionin OBHRM that individual performance clusters around a mean and thenfans out into symmetrical tails. That is, individual performance is assumedto follow a normal distribution (Hull, 1928; Schmidt & Hunter, 1983;
A previous version of this paper was presented at the Annual Meetings of the Academyof Management, San Antonio, Texas, August 2011. We thank Wayne L. Winston for hisinsightful comments regarding data analysis issues.
Correspondence and requests for reprints should be addressed to Herman Aguinis, De-partment of Management and Entrepreneurship, Kelley School of Business, Indiana Univer-sity, 1309 E. 10th Street, Suite 630D, Bloomington, IN 47405-1701; [email protected].
Figure 1: A Normal Distribution (Black) Overlaying a ParetianDistribution (Grey).
Tiffin, 1947). When performance data do not conform to the normal dis-tribution, then the conclusion is that the error “must” lie within the samplenot the population. Subsequent adjustments are made (e.g., dropping out-liers) in order to make the sample “better reflect” the “true” underlyingnormal curve. Gaussian distributions are in stark contrast to Paretian orpower law distributions, which are typified by unstable means, infinitevariance, and a greater proportion of extreme events. Figure 1 shows aParetian distribution overlaid with a normal curve.
The goal of our research is to revisit the norm of normality of individualperformance and discuss implications for OBHRM theory and research;methodology; and practice, policy making, and society. Our manuscriptis organized as follows. First, we describe the origins and document thepresence of the norm of normality regarding individual performance. Sec-ond, we discuss the Gaussian (i.e., normal) and Paretian (i.e., power law)distributions and key differences between them. Third, we describe fiveseparate studies involving 198 samples including 633,263 researchers,entertainers, politicians, and amateur and professional athletes. Resultsof each of these five studies are remarkably consistent and indicate thatindividual performance does not follow a normal distribution and, instead,
O’BOYLE JR. AND AGUINIS 81
it follows a power law distribution. Finally, we discuss implications of ourresults, including directions for future research.
The Norm of Normality of Individual Performance
The normal distribution has been used to model a variety of phenom-ena including human traits such as height (Yule, 1912) and intelligence(Galton, 1889), as well as probability distributions (Hull, 1928), economictrends such as stock pricing (Bronzin, 1908), and the laws of thermo-dynamics (Reif, 1965). Based on the normal distribution’s prevalenceacross scientific disciplines and phenomena, it has seemed reasonableto assume that normality would also be the distribution of individualperformance.
Although the assumption of individual performance normality is com-mon across most research domains in OBHRM, it seems to have orig-inated in the performance appraisal literature. More than half a centuryago, Ferguson (1947) noted that “ratings for a large and representativegroup of assistant managers should be distributed in accordance with thepercentages predicted for a normal distribution” (p. 308). The normalityassumption persisted through the years, and researchers began to not onlyassume job performance normality but forced it upon the observed dis-tributions regardless of the actual observed distributional properties. Forexample, in developing a performance appraisal system, Canter (1953)used “a forced normal distribution of judgments” (p. 456) for evaluatingopen-ended responses. Likewise, Schultz and Siegel (1961) “forced the[performance] rater to respond on a seven-point scale and to normalizeapproximately the distribution of his responses” (p. 138). Thus, if a su-pervisor rated the performance of her subordinates and placed most ofthem into a single category while placing only a small minority in thetop ranking, it was assumed that there was a severity bias in need of acorrection to normality (Motowidlo & Borman, 1977; Schneier, 1977).Moreover, the advice is that if an employee contributes a disproportion-ate amount of sales in a firm, he should be dropped from the data set orhave his sales statistically adjusted to a more “reasonable” value (e.g.,three standard deviations within the mean) before moving forward with atraditional analysis that assumes an underlying normal distribution. Bothdesign practices (i.e., forced-response formats) and statistical analyses(i.e., deletion or “correction” of outliers) in performance evaluation createa normal distribution in samples regardless of the shape of the underlyingpopulation distributions.
We readily acknowledge that some researchers and practitioners maynot believe that individual performance is normally distributed (e.g.,Bernardin & Beatty, 1984; Micceri, 1989; Murphy & Cleveland, 1995;
82 PERSONNEL PSYCHOLOGY
Saal, Downey, & Lahey, 1980; Schmidt & Johnson, 1973). However,the normality assumption is a convenient way of studying individualperformance—just like economists also make assumptions so that theirtheoretical models can be simplified. As noted by an anonymous reviewer,some may not put too much thought into the shape of the performancedistribution whereas others may believe that, with a sufficiently large num-ber of cases, individual performance is normally distributed. Regardlessof the actual beliefs, researchers and practitioners assume performanceis normally distributed and alter the distribution of scores through thedesign, training, and analysis of raters’ judgments. Specifically, whenperformance scores deviate from normality, the cause is attributed to le-niency bias, severity bias, and/or a halo error (Aguinis, 2009; Schneier,1977). Rating systems where most employees occupy the same categorywith only a few at the highest category are assumed to be indicative ofrange restriction and other “statistical artifacts” (Motowidlo & Borman,1977). In fact, Reilly and Smither (1985) provided an extensive critiqueof individual performance research that violates the normality assumptionand provided guidance on how to reestablish the normal and presumablycorrect distribution of performance.
The norm of normality of individual performance is also evident inmany other research domains in OBHRM. Consider the case of personnelselection that, similar to the prediction of performance and performancemeasurement/work outcomes category, is among the top five most pop-ular research domains based on articles published in Journal of AppliedPsychology and Personnel Psychology over the past 45 years (Cascio &Aguinis, 2008a). Utility analysis has allowed researchers and practition-ers to establish the financial value added of implementing valid personnelselection procedures, and all utility analysis approaches operate underthe normality assumption. For example, Schmidt, Hunter, McKenzie, andMuldrow’s (1979) linear homoscedastic model of work productivity “in-cludes the following three assumptions: (a) linearity, (b) equality of vari-ances of conditional distributions, and (c) normality of conditional distri-butions” (p. 615). In the same manner, Cascio and Ramos (1986) statedthat “[a]ssuming a normal distribution of performance, 55% equates toa Fisher z-value of .13, which translates back to a validity coefficient of.13 for the old selection procedure” (p. 25). More recently, Sackett andYang (2000) concluded that “[o]n the basis of the ordinate of the normalcurve at the point of selection, it is possible to infer the mean and varianceof the unrestricted distribution. Clearly, the use of such approaches reliesheavily on the normality assumption” (p. 115). The validity and accuracyof all utility analyses that rely on the assumed normality of individualperformance would be put into question if this assumption is actually nottenable.
O’BOYLE JR. AND AGUINIS 83
Summary
Although some have argued that performance may not be normallydistributed (Bernardin & Beatty, 1984; Murphy & Cleveland, 1995; Saalet al., 1980; Schmidt & Johnson, 1973), theory and application regard-ing individual performance are built around the assumption of normality.For example, theories on performance targeting the average worker, theimplementation of performance appraisal systems that include droppingoutliers, and the choice of analytic techniques point to an underlying as-sumption of normality. Moreover, we are not aware of influential theoret-ical developments or applications that explicitly assume that performancefollows a nonnormal distribution (Aguinis, 2009; Smither & London,2009b). So, although some may not believe in the normal distribution ofindividual performance, there is little evidence that this belief has affectedtheoretical developments or application in an influential way. Possiblereasons for why skepticism about normality has not affected theory andpractice may be the lack of empirical evidence negating the normal dis-tribution and the lack of proposed alternative distributions. But, what ifperformance does not conform to the Gaussian distribution? What if themeans are unstable and the variance of these distributions infinite? Quitesimply, if performance is not normally distributed, theories that directly orindirectly build upon individual job performance and its prediction mayneed to be revisited. In addition, popular practices (e.g., utility analysis ofpreemployment tests and training and development interventions), whichalso rely on the assumption of individual performance normality, wouldalso need to be revisited.
Next, we provide an alternative perspective, which draws mainly fromthe economics, mathematics, and statistics literatures, that challenges thenorm of normality and posits that individual performance conforms to apower law or Paretian distribution, which is typified by an unstable mean,infinite variance, and a greater number of extreme events (West & Deering,1995).
The Paretian Distribution and Individual Performance
The possibility of a nonnormal performance distribution of individ-ual performance has been proposed in the past but the normality as-sumption has remained the dominant approach. Jacobs (1974) arguedthat in sales industries (automotive, insurance, stock) performance is notnormal because a small group of incumbents who possess the exper-tise and salesmanship dominate activity. If performance output does notconform to a bell-shaped, normal distribution, then power law distribu-tions may apply (West & Deering, 1995). Power laws such as Pareto’s
84 PERSONNEL PSYCHOLOGY
(1897) Law produce fatter tails than those seen in a normal curve. Stateddifferently, Paretian probability distributions allow more extreme val-ues to be present (see Figure 1). Whereas a value exceeding three stan-dard deviations from the mean is often thought to be an outlier in thecontext of a normal curve (e.g., Orr, Sackett, & Dubois, 1991), a Pare-tian distribution would predict that these values are far more commonand that their elimination or transformation is a questionable practice.Paretian distributions are sometimes referred to as the 80/20 principle,which has been shown to apply to many contexts and research domainsoutside of OBHRM. For example, marketing researchers have reportedthat about 80% of a brand’s volume is purchased by about 20% of itsbuyers (Anschuetz, 1997) and sociology researchers have reported thatabout 80% of land is owned by about 20% of the population (Pareto,1897).
There are important differences between Gaussian and Paretian dis-tributions. First, Gaussian distributions underpredict the likelihood of ex-treme events. For instance, when stock market performance is predictedusing the normal curve, a single-day 10% drop in the financial mar-kets should occur once every 500 years (Buchanan, 2004). In reality,it occurs about once every 5 years (Mandelbrot, Hudson, & Grunwald,2005). Second, Gaussian distributions assume that the mean and stan-dard deviation, so central to tests of statistical significance and computa-tion of effect sizes, are stable. However, if the underlying distribution isParetian instead of normal, means and standard deviations are not stableand Gaussian-based point estimates as well as confidence intervals arebiased (Andriani & McKelvey, 2009). Third, a key difference betweennormal and Paretian distributions is scale invariance. In OBHRM, scaleinvariance usually refers to the extent to which a measurement instrumentgeneralizes across different cultures or populations. A less common op-erationalization of the concept of scale invariance refers to isomorphismin the shape of score distributions regardless of whether one is exam-ining an individual, a small work group, a department, an organization,or all organizations (Fiol, O’Connor, & Aguinis, 2001). Scale invariancealso refers to the distribution remaining constant whether one is lookingat the whole distribution or only the top performers. For example, theshape of the wealth distribution is the same whether examining the entirepopulation or just the top 10% of wealthy individuals (Gabaix, 1999). Re-lated to the issue of scale invariance, Gabaix, Gopikrishnan, Plerou, andStanley (2003) investigated financial market fluctuations across multipletime points and markets and found that data conformed to a power lawdistribution. The same distribution shape was found in both United States(U.S.) and French markets, and the power law correctly predicted both thecrashes of 1929 and 1987.
O’BOYLE JR. AND AGUINIS 85
Germane to OBHRM in particular is that if performance operatesunder power laws, then the distribution should be the same regardless ofthe level of analysis. That is, the distribution of individual performanceshould closely mimic the distribution of firm performance. Researcherswho study performance at the firm level of analysis do not necessarilyassume that the underlying distribution is normal (e.g., Stanley et al.,1995). However, as noted earlier, researchers who study performanceat the individual level of analysis do follow the norm of normality intheir theoretical development, research design, and choices regarding dataanalysis. These conflicting views, which may be indicative of a micro–macro divide in OBHRM and related fields (e.g., Aguinis, Boyd, Pierce,& Short, 2011), could be reconciled if individual performance is found toalso follow a power law distribution, as it is the case for firm performance(Bonardi, 2004; Powell, 2003; Stanley et al., 1995).
The Present Studies
We conducted five separate studies to determine whether the distri-bution of individual performance more closely follows a Paretian curvethan a Gaussian curve. In all studies, the primary hypothesis was thatthe distribution of performance is better modeled with a Paretian curvethan a normal curve. For each of the five studies, we used the chi-square(χ2) statistic to determine whether individual performance more closelyfollows a Paretian versus a Gaussian distribution. The chi-square is a“badness of fit” statistic because higher values indicate worse fit (Agui-nis & Harden, 2009). That is, the greater the degree of divergence of anempirically derived performance distribution from a Gaussian or Pare-tian distribution, the higher the chi-square. Accordingly, for each of thesamples we studied we first forced the data to conform to a normal distri-bution and then forced the same data to conform to a Paretian distribution.For each comparison, a smaller chi-square value indicates which of thetwo theoretical distributions describes the data better. To calculate thechi-square for each distribution, we used Decision Tools Suite add-on@Risk 5.5 (Palisades Corporation, 2009). This program operates withinMicrosoft Excel and provides estimates of fit for a variety of distributions,including normal and Paretian distributions.
The deficiency and contamination problems associated with perfor-mance measurement (collectively known as the criterion problem) are stillunresolved (Cascio & Aguinis, 2011; Murphy, 2008). Accordingly, givenour ambitious goal to challenge a long-held assumption in the field, we de-liberately conducted five separate studies including heterogeneous indus-tries and used a large number of performance operationalizations includingqualitative evaluations (e.g., award nominations in which raters propose
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the names of nominees), quantitative outcomes (e.g., number of publica-tions by researchers), and observed behavior based on specific events (e.g.,career homeruns of baseball players) or overall reputation (e.g., votes forpoliticians). Taken together, our five studies involve 198 samples andinclude 633,263 researchers, entertainers, politicians, and amateur andprofessional athletes.
Although we deliberately chose an eclectic and heterogeneous set ofperformance measures, they did share several features. First and most im-portant, each operationalization contained behaviors that directly affectedimportant outcomes such as compensation, bonuses, and promotions. Inother words, the performance measures included in our study are particu-larly meaningful for the individual workers because they have importantconsequences. Second, the outcomes we chose primarily reflect individualbehavior that is largely under an individual’s control (Aguinis, 2009). Thedeterminants of an individual’s performance are individual characteristics,the context of work, and the interaction between the two. Thus, even in in-dividual sports such as golf, other players influence each golfer’s behavior.However, we made efforts to minimize the effects of contextual factors onindividual performance. For example, the examination of baseball errorsin Study 5 was based on grouping players into their respective positions.This prevented right fielders that typically have fewer fielding opportuni-ties to be grouped with shortstops that have more fielding opportunities. Inaddition, when possible, we scaled the performance of each individual toa measurement period that was time bound. For example, in Study 4, weincluded career performance measures as well as single-season measuresand examined both single-season performance and career performance.
Our research deliberately excludes samples of individuals whose per-formance has been exclusively rated by a supervisor because such per-formance operationalizations include biases that would render addressingour research question impossible. Specifically, instructing raters to fol-low a bell curve, implementing rater error training programs, normalizingperformance ratings, and correcting for leniency or severity bias all helpto create a normal curve in a sample regardless of the true underlyingdistribution.
Study 1
Method
Overview. In Study 1, we tested whether a Paretian or Gaussian dis-tribution better fit the distribution of performance of 490,185 researcherswho have produced 943,224 publications across 54 academic disciplinesbetween January 2000 and June 2009.
O’BOYLE JR. AND AGUINIS 87
Procedure
We categorized academic disciplines using Journal Citation Reports(JCR), which provide impact factors in specific subject categories acrossthe physical and social sciences. In some cases, there were multiple sub-fields included within one JCR category. For instance, there are eightentries for material sciences (e.g., ceramics, paper and wood, compos-ites), but we identified authors across all material sciences so that authorspublishing in more than one area would have all their publications in-cluded. Our analyses included 54 academic fields (see Table 1). We usedimpact factors (also reported in JCR) from 2007 to identify the top fivejournals within each of the 54 fields. We chose field-specific journals toavoid having the search contaminated by authors from other sciences.For instance, Accounts of Chemical Research most likely only includesarticles related to chemistry, but this assumption cannot be made withan interdisciplinary journal such as Nature, which publishes chemistryresearch alongside other scientific research. We next used the Publishor Perish program (Harzing, 2008), which relies on Google Scholar, toidentify all authors who had published at least one article in one of thesejournals between January 2000 and June 2009. These procedures resultedin a total of 490,185 researchers who have produced 943,224 scholarlyjournal publications.
Operationalization of individual performance. Publication in top-tier journals is the most important antecedent of meaningful outcomes forfaculty including salary and tenure status (Gomez-Mejia & Balkin, 1992).Thus, in Study 1 we operationalized performance as research productivity,specifically as the number of articles published by an author in one of thetop five journals over the 9.5-year observation period. All authors of eacharticle were recorded, and no differentiation was made based on authorshiporder.
Results
Results reported in Table 1 show that the Paretian distribution yieldeda superior fit than the Gaussian distribution in every one of the 54 scien-tific fields. Recall that a larger chi-square value indicates worse fit and,thus, can be considered an index of badness of fit. As Table 1 shows,the average misfit for the Paretian distribution was 23,888 whereas themisfit of the normal distribution was larger than forty-four trillion (i.e.,44,199,201,241,681)—a difference in favor of the Paretian distribution inthe order of 1:1.9 billion. Figure 2a displays a histogram of the empiri-cally observed performance distribution of researchers. To interpret theseresults further, consider the field of Agriculture (see Table 1). A normal
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TABLE 1Distribution of Individual Performance of Researchers: Fit With Gaussian vs.
distribution and a sample size of 25,006 would lead to approximately 35scholars with more than 9.5 publications (three standard deviations abovethe mean). In contrast, our data include 460 scholars with 10 or morepublications. In other words, the normal distribution underestimates thenumber of extreme events and does not describe the actual distributionwell.
Discussion
We tested whether the distribution of research performance best fitsa Gaussian distribution or a Paretian distribution. Results based on chi-square statistics and a comparison of Figure 2a with Figure 1 provide evi-dence that the performance of researchers follows a Paretian distribution.
Study 2
Method
Overview. A potential limitation of Study 1 is that performance (i.e.,successful publication) was assessed by a single individual: a journal ed-itor. Even if editors rely heavily on the opinion of associate editors andreviewers, the decision to publish each article has been made by a verysmall number of individuals in each case (i.e., typically an action editorand two or three reviewers). Moreover, there is evidence regarding the lowreliability (i.e., consistency across reviewers) in the peer review process(Gilliland & Cortina, 1997). Therefore, it is possible that the job per-formance distribution of researchers is idiosyncratic enough to challenge
90 PERSONNEL PSYCHOLOGYP
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the notion that it generalizes to other types of workers. Accordingly, weconducted Study 2 to expand the generalizability of these findings andtest whether a different industry with different performance metrics andlarger number of raters involved would confirm results from Study 1. InStudy 2, we examined the performance of 17,750 individuals in the en-tertainment industry, with performance rated by a large voting body ormore objective performance measures such as the number of times anentertainer received an award, nomination, or some other indicator (e.g.,Grammy nominations, New York Times best-selling list).
Procedure. To capture the multifaceted nature of performance of en-tertainers, we completed the following steps. First, we generated a list ofthe different forms of entertainment and determined that motion pictures,music, literature, and theater would serve as the population of interestgiven the availability of data. Second, we consulted several individualswithin the film and music industries to help identify well-known (e.g., Os-cars, Grammys) as well as lesser-known and more industry-specific awards(e.g., Edgar Allen Poe Award for mystery writing). Third, we proceededwith data collection by searching Web sites for relevant data. When datawere not available online, we contacted the organization that distributesthe awards for more detailed information. We identified more than 100potential entertainment awards, but incomplete records and award limits(i.e., certain awards limit the number of times a recipient can win) reducedthe number of qualified groups. Because a small group of awardees coulddiverge from normality due to either sampling error or true divergencefrom normality, we stipulated that a group must consist of at least 100individuals in order to qualify for inclusion. Forty-two (42) awards andhonors met our inclusion criteria (see Table 2).
Operationalization of Individual Performance. Award nominations(Oscars, Emmys), expert rankings (Rolling Stone), and appearances ona best seller list such as the New York Times Best Seller List all servedas measures of individual performance. These types of performance mea-sures either are based on expert opinions (e.g., music critics) or peer voting(e.g., Oscars). Although the number of nominations a performer receivesis a count variable, these counts encapsulate ratings and may better con-form to traditional subjective ratings such as those most typically foundin traditional OBHRM research (Landy & Farr, 1980).
Results
Table 2 shows results that are very similar to those in Table 1: Thedistribution of individual performance is substantially closer to a Paretiandistribution than to a Gaussian distribution for each of the 42 samples.The average misfit of the Gaussian distribution was more than
92 PERSONNEL PSYCHOLOGY
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9E+
05
52
Rat
ing
sfo
rB
est
Mal
eor
Fem
ale
Vo
cali
stE
dgar
All
enP
oe
Aw
ards
nom
.121
15.0
710.4
01954–2009
147
53
Exper
tra
nkin
gs
inB
est
Novel
cate
gory
Em
my
nom
.A
ctor
685
2.8
62.7
41949–2009
5.4
9E+
07
173
Nom
inat
ion
toan
yca
tegory
and
anar
tist
Em
my
nom
.A
ctre
ss442
2.4
92.3
31949–2009
1.4
1E+
06
11
0ca
no
bta
inm
ult
iple
no
min
atio
ns
inth
eE
mm
ynom
.A
rtdir
ecti
on
866
1.8
22.3
71949–2009
4.2
6E+
10
1,0
97
sam
eyea
r.T
he
nom
inat
ion
pro
cess
Em
my
nom
.C
asti
ng
193
2.1
62.0
11949–2009
2.4
6E+
05
51
com
bin
esa
po
pu
lar
vote
wit
hvolu
nte
erE
mm
ynom
.C
hore
ogra
phy
127
1.7
11.5
41949–2009
4.9
3E+
05
140
judgin
gpan
els
Em
my
nom
.C
inem
atogra
phy
588
1.6
81.4
31949–2009
1.5
7E+
07
387
Em
my
nom
.D
irec
tion
395
1.9
52. 0
71949–2009
1.0
1E+
08
92
Em
my
nom
.E
dit
ing
942
1.8
91.7
71949–2009
3.8
3E+
13
614
Em
my
nom
.L
ighti
ng
131
3.0
23.5
51949–2009
2.5
1E+
05
29
Em
my
nom
.W
riti
ng
1,4
57
2.4
62.7
21949–2009
3.1
0E+
09
356
Gold
enG
lobe
nom
.ac
tor
392
2.0
72.0
21944–2009
2.3
8E+
09
111
Nom
inat
ion
toan
yca
tegory
and
anar
tist
Gold
enG
lobe
nom
.ac
tres
s415
2.0
52.0
61944–2009
2.1
4E+
08
12
3ca
no
bta
inm
ult
iple
no
min
atio
ns
inth
e
conti
nued
O’BOYLE JR. AND AGUINIS 93
TA
BL
E2
(co
nti
nu
ed)
Dat
aC
oll
ecti
on
Gau
ssia
nP
aret
ian
Per
form
ance
Op
erat
ion
aliz
atio
nan
dS
amp
leN
Mea
nSD
Tim
eF
ram
e(χ
2)
(χ2)
Com
men
ts
Gold
enG
lobe
nom
.dir
ecti
on
156
1.9
41.5
31944–2009
1.1
9E+
04
95
sam
eyea
r.T
he
Holl
yw
ood
Fore
ign
Gold
enG
lobe
nom
.T
Vac
tor
375
2.1
21.7
81944–2009
7.2
5E+
04
203
Pre
ssA
ssoci
atio
nra
tes
and
vote
son
the
Gold
enG
lobe
nom
.T
Vac
tres
s354
2.1
91.7
91944–2009
3.2
7E+
04
234
nom
inee
sG
ram
my
nom
.3313
2.0
22.7
81959–2009
3.8
2E+
12
1,3
07
Nom
inat
ion
toan
yca
tegory
Man
Booker
Pri
zeF
icti
on
nom
.283
1.3
5.8
41969–2009
3.6
2E+
05
2,0
18
Exper
tra
nkin
gs
inB
est
Novel
cate
gory
MT
VV
MA
nom
.561
3.9
85.5
81984–2009
1.3
7E+
07
78
Fan
voti
ng
and
indust
ryra
tings
NY
TB
est
Sel
ler
fict
ion
222
2.4
23.8
51950–2009
4.5
4E+
08
219
Eac
hap
pea
rance
on
the
New
York
Tim
es
NY
TB
est
Sel
ler
nonfi
ctio
n419
1.1
9.6
51950–2009
2.7
1E+
06
6.2
0E+
04
Bes
tsel
ler
list
Osc
arnom
.ac
tor
421
1.8
41.6
21927–2009
3.3
4E+
11
177
Nom
inat
ions
asdet
erm
ined
by
Aca
dem
yO
scar
nom
.ar
tdir
ecti
on
531
2.6
43.7
51927–2009
8.1
0E+
08
94
mem
ber
susi
ng
apre
fere
nti
al-v
oti
ng
Osc
arnom
.dir
ecti
on
199
1.9
71.6
01927–2009
1.5
7E+
06
76
syst
emfo
rbes
tdir
ecto
ran
dnom
inee
sO
scar
nom
.A
ctre
ss432
1.8
01.5
01927–2009
4.0
7E+
07
289
ina
pri
mar
yor
support
ing
acti
ng
role
Osc
arnom
.ci
nem
atogra
phy
159
1.9
11.5
61927–2009
5.6
7E+
06
84
PE
Naw
ard
voti
ng
125
14.5
511.4
51976–2009
2295
21
Nom
inat
ion
inan
yca
tegory
(e.g
.,dra
ma)
Puli
tzer
Pri
zenom
.dra
ma
121
1.2
6.7
51917–2009
2.0
0E+
06
3711
Sel
ecti
on
tofi
nal
ist
for
the
dra
ma
cate
gory
Roll
ing
Sto
ne
Top
500
album
s261
1.9
01.5
21940–2009
1.7
8E+
06
137
Num
ber
of
appea
rance
son
the
Top
500
Roll
ing
Sto
ne
Top
500
songs
247
2.0
22.1
91940–2009
1.2
7E+
08
75
list
asra
ted
by
contr
ibuto
rsan
dw
rite
rsT
ony
nom
.ac
tres
s583
1.5
91.1
81947–2009
3.9
1E+
08
817
Nom
inat
ions
det
erm
ined
by
apan
elof
Tony
nom
.ch
ore
ogra
phy
108
2.1
02.1
01947–2009
445
93
judges
from
ente
rtai
nm
ent
indust
ryT
ony
nom
.ac
tor
642
1.4
3.9
41947–2009
1.7
7E+
08
2,0
56
Tony
nom
.dir
ecto
r237
1.8
61.7
01947–2009
1.0
0E+
12
133
Wei
ghte
dave
rage
2,7
69,3
15,5
05,4
76
2,0
92
No
te.
AC
E=
Aw
ard
for
Cab
leE
xce
llen
ce,
AV
N=
Adult
Vid
eoN
ews,
MT
V=
Mu
sic
Tel
evis
ion
,P
EN
=p
oet
s,pla
yw
rig
hts
,es
say
ists
,ed
ito
rs,
and
novel
ists
,N
YT
=N
ewYo
rkT
imes
,T
V=
tele
vis
ion,nom
=nom
inat
ions.
94 PERSONNEL PSYCHOLOGY
1 billion times larger than the average misfit of a Paretian distribution(i.e., 2,769,315,505,476 vs. 2,092). To understand the nature of theseresults better, consider the Grammy nominations under an assumptionof normality. Of the 3,313 individuals nominated for a Grammy, only5 should be three standard deviations above the mean with more than10 nominations. In contrast, our data include 64 entertainers with morethan 10 nominations. As in Study 1, the normal curve does not describethe actual distribution well.
Discussion
Results of Study 2 closely matched those of Study 1. Entertainers’ per-formance better fits a Paretian distribution than a Gaussian distribution.These findings across a variety of entertainment industries and with mul-tiple performance operationalizations provides further evidence regardingthe robustness of the Paretian distribution as the better model of individ-ual performance compared to a normal distribution. As an illustration,Figure 2b displays the overall distribution of the largest sample of enter-tainers, Emmy nominees. This histogram illustrates that the empiricallyderived distribution aligns with a Paretian distribution (cf. Figure 1).
Study 3
Method
Overview. In Study 3, we examined the distribution of performanceof politicians. Study 3 includes a set of performance raters that is evenmore inclusive compared to those in Study 2: All citizens eligible to votein a given political jurisdiction. In Study 3 we examined the performanceof candidates (i.e., being elected or reelected) running for elective officesat the state (e.g., legislature of the state of Oregon in the U.S.) and na-tional levels (e.g., Dutch Parliament). We included the performance of42,745 candidates running for office in 42 types of elections in Australia,Canada, Denmark, Estonia, Finland, Holland, Ireland, New Zealand, theUnited Kingdom, and the U.S.
Procedure. We identified elected officials through national and stateWeb sites. We first constructed a list of 195 nations, 50 U.S. states, 10Canadian provinces, and 6 Australian territories to serve as potentialsources of data. The search began at the national level, and we eliminatednations without a democratic form of government such as absolute monar-chies (e.g., Saudi Arabia), theocracies (e.g., Vatican City), and one-partynations (e.g., Cuba). Next, offices with term limits or lifetime appoint-ments were excluded as the results would be artificially truncated at the
O’BOYLE JR. AND AGUINIS 95
maximum number of terms an individual could serve. For this reason,we eliminated most executive and judicial branches of government, thusleaving legislatures as the primary source of data. For the remaining po-tential data sources, we searched for a complete list of current and pastmembers in each country, state, and province. Lists of current memberswere available for nearly all governments, but relatively few governmentsmade past members or the dates that current members were first electedavailable. For example, the reporting of past members for the Australianlegislature was intermittent, therefore a complete list of members was notavailable. However, a complete list of present members and their originalelection to office, as well as a complete list of the most recent legislaturethat contained no current members (1969), were also available. Becausethese two groups had no overlap, we included them separately in thedatabase. As in Study 2, we limited our search to groups that containedat least 100 individuals. We identified 42 samples from state and nationalgoverning bodies. Table 3 includes descriptive information about each ofthese samples.
Operationalization of individual performance. As stated earlier,elected official performance was operationalized by an individual’s elec-tion to office. In most cases, this was established as the number of timesa person’s name appeared on each new session of the legislature. In caseswhere only the current legislature was available, the length of service wasrecorded (either days or years in office) and used as a measure of perfor-mance. Thus, this type of performance measure is essentially based onratings—those provided by eligible voters in any given political district.
Results
Results included in Table 3 indicate that the data fit a Paretian dis-tribution better than a Gaussian distribution for 31 of the 42 samples.The average fit strongly favored the Paretian (misfit of 8,692) versus theGaussian distribution (misfit of over one trillion). Using the U.S. Houseof Representatives as an example, the normal distribution suggests that ofthe 8,976 individuals to have served in the House, no more than 13 repre-sentatives should be three standard deviations above the mean (i.e., servemore than 13 terms). Contrary to the expectation based on the normalityassumption, 173 U.S. Representatives have served more than 13 terms.
Discussion
Results suggest that the individual performance of politicians fol-lows a Paretian distribution more closely than a normal distribution.Specifically, the data fit a Paretian distribution more closely than a normal
96 PERSONNEL PSYCHOLOGYT
AB
LE
3D
istr
ibuti
on
of
Indiv
idual
Per
form
ance
of
Poli
tici
ans:
Fit
Wit
hG
auss
ian
vs.
Pare
tian
Dis
trib
uti
ons
Dat
aco
llec
tio
nS
amp
leN
Mea
nSD
tim
efr
ame
Gau
ssia
n(χ
2)
Par
etia
n(χ
2)
Ala
bam
aL
eg.
104
11.4
38.4
72009
79
157
Aust
rali
aH
ouse
128
8.5
78.1
01969
22
164
Aust
rali
aH
ouse
153
10.4
66.8
42009
122
119
Can
adia
nL
eg.
4,0
59
2.6
51.8
71867–2009
1.0
6E+
07
1.0
5E+
04
Connec
ticu
tL
eg.
151
9.8
96.3
12009
28
249
Den
mar
kP
ar.
177
10.4
17.3
92009
167
354
Dutc
hP
ar.
150
5.3
23.9
02009
1.0
1E+
05
184
Est
onia
Par
.100
2.0
01.1
12009
225
167
Fin
land
Par
.200
9.3
97.7
42009
293
229
Geo
rgia
House
179
4.8
03.8
92009
333
96
Illi
nois
Leg
.120
9.9
66.4
82009
60
220
Iow
aL
eg.
100
6.7
44.8
92009
42
11
Irel
and
Par
.1,1
47
3.9
93.1
51919–2009
2970
1,4
43
Irel
and
Sen
ate
716
2.4
01.9
51919–2009
2.0
6E+
04
809
Kan
sas
House
5,6
75
2.7
22.9
42009
6.5
3E+
12
5,6
36
Kan
sas
Sen
ate
1,2
09
4.0
13.3
41812–2009
3.7
6E+
07
1,1
71
Ken
tuck
yL
eg.
100
5.0
64.0
42009
82
57
Louis
iana
House
3,4
68
1.9
31. 9
71812–2009
2.0
9E+
12
6,1
28
Mai
ne
Leg
.153
2.5
82.0
62009
2.4
4E+
09
24
Mar
yla
nd
Leg
.141
9.4
27.6
32009
212
165
Mas
s.H
ouse
160
9.8
26.8
82009
113
205
Min
nes
ota
House
134
4.3
13.6
62009
387
47
Mis
souri
Leg
.163
4.7
02.1
92009
921
571
New
Bru
ns.
Par
.1,1
36
2.2
41.5
21882–2009
7,9
33
2,8
55
conti
nued
O’BOYLE JR. AND AGUINIS 97
TA
BL
E3
(co
nti
nu
ed)
Dat
aco
llec
tio
nS
amp
leN
Mea
nSD
tim
efr
ame
Gau
ssia
n(χ
2)
Par
etia
n(χ
2)
New
York
Ass
oci
atio
n148
11.6
18.9
42009
76
193
New
Zea
land
Leg
.122
8.0
57.4
92009
120
126
N.
Car
oli
na
Ass
oci
atio
n124
4.6
33.3
82009
68
141
Nova
Sco
tia
Leg
.414
3.0
11.2
61867–2009
2,0
96
539
Okla
hom
aL
eg.
101
4.7
02.6
72009
98
254
Onta
rio
Leg
.1,8
79
4.5
63.3
01867–2009
1.6
2E+
05
5,5
39
Ore
gon
Leg
.377
4.4
73.8
11858–2009
2654
108
Ore
gon
Sen
ate
161
5.4
54.4
41858–2009
1597
94
Pen
nsy
lvan
iaH
ouse
200
10.7
69.1
82009
269
141
Queb
ecL
eg.
399
3.5
22.4
01867–2009
697
583
S.
Car
oli
na
House
125
8.2
36.4
42009
87
118
Tas
man
iaA
sso
ciat
ion
54
23.1
12.3
51856–2009
4742
442
Ten
nes
see
House
100
5.2
24.1
02009
134
63
UK
Par
.7,2
14
3.4
12.5
91801–2009
4.3
2E+
09
1.7
0E+
04
US
House
8,9
76
3.4
23.2
31789–2009
6.3
9E+
08
1.4
3E+
04
US
Sen
ate
1,8
40
9.1
47.7
91789–2009
2.4
2E+
04
3,2
64
Vir
gin
iaA
ssoci
atio
n100
11.0
98.2
62009
497
96
Wis
consi
nL
eg.
100
8.1
16. 9
92009
309
89
Wei
gh
ted
ave
rage
1,0
37,3
89,9
25,0
13
8,6
92
No
te.
UK
=U
nit
edK
ingdom
,U
S=
Un
ited
Sta
tes,
Bru
ns
=B
runsw
ick,
Leg
=L
egis
latu
re,
Mas
s=
Mas
sach
use
tts,
Par
=P
arli
amen
t,S
=S
outh
,N
=N
ort
h.
98 PERSONNEL PSYCHOLOGY
distribution in 74% of the samples we studied. Figure 2c illustrates theshape of the observed performance distribution for the largest sample inStudy 3, the U.S. House of Representatives. One reason why the superiorfit for a Paretian distribution was not seen in all samples may be that the es-tablished frequency of elections prevents superstar performers to emergein the same way as they do in other industries like those we examined inStudies 1 and 2. We speculate that this may be a result of the measure ofperformance not being as sensitive and discriminating regarding variouslevels of performance compared to the measures of performance we usedin Studies 1 and 2. Performance in Study 3 was binary with the legisla-tor either returning to office with a simple majority vote or being oustedby another also by a simple majority vote. Therefore, an incumbent whodoes just enough to be reelected (e.g., victory margin of 1%) receives thesame performance “score” as an extraordinary incumbent (e.g., victorymargin of 25%). Nevertheless, on average, the difference in fit favored theParetian distribution in the order of 1:119 million.
Study 4
Method
Overview. In Study 4 we investigated the performance of athletes incollegiate and professional sports. Study 4 presents additional evidenceto supplement Studies 1–3 because many of the measures of performanceare more objective, they rely more heavily on measures of physical per-formance, and depend more strongly on the individual (see Table 4).
Procedure. We compiled a list of individual and team sports at thecollegiate and professional levels. We accessed each Web site that hostedthe sport (e.g., MLB.com) and downloaded the necessary statistics fromeach database. In all cases, we were able to find the necessary data for thechosen sports for at least one complete season. In most cases, we collecteddata from multiple years, and we were able to record all players, but insome cases, only the top players were available (e.g., only the top 1,000MLB pitchers were available).
Operationalization of individual performance. We attempted to iden-tify the most individual-based measures of performance. For instance, runsbatted (RBI) in baseball are both a function of a hitter’s prowess and theability of those batting before him. Therefore, a less contaminated measurefor baseball is home runs. For individual sports such as golf and tennis,we chose the total numbers of wins, but team sports required a differentoperationalization. For sports such as soccer and hockey, we used goalsor points as the performance metric, and for position-oriented sports likeU.S. football we used receptions, rushing yards, and touchdowns.
O’BOYLE JR. AND AGUINIS 99
TA
BL
E4
Dis
trib
uti
on
of
Posi
tive
Indiv
idual
Per
form
ance
of
Ath
lete
s:F
itW
ith
Gauss
ian
vs.
Pare
tian
Dis
trib
uti
ons
Dat
aco
llec
tio
nG
auss
ian
Par
etia
nP
erfo
rman
ceo
per
atio
nal
izat
ion
and
Sport
NM
ean
SD
tim
efr
ame
(χ2)
(χ2)
com
men
ts
ML
Bca
reer
stri
ke
outs
1,0
01
1103.6
7563.2
61900–2006
6.0
0E+
11
91
Avar
iety
of
met
rics
of
po
siti
ve
ML
Bca
reer
HR
1,0
04
174.0
0109.4
41900–2006
4850
89
beh
avio
rsfo
rpla
yer
san
dm
anag
ers
ML
Bca
reer
mgr
win
s647
301.0
2450.9
01900–2006
3630
480
NC
AA
Div
1-1
/ER
A516
.25
.07
2009
5.2
6E+
09
59
Avar
iety
of
met
rics
of
po
siti
ve
NC
AA
Div
1-H
R548
11.5
73.7
62009
959
211
beh
avio
rsfo
rbas
ebal
lpla
yer
sonly
NC
AA
Div
2-1
/ER
A300
.31
.11
2009
2770
17
NC
AA
Div
2-H
R383
10.2
63.6
62009
5.0
8E+
03
92
NC
AA
Div
3-1
/ER
A500
.31
.12
2009
9.6
9E+
07
25
NC
AA
Div
3-H
R424
7.2
72.9
12009
5.0
8E+
06
87
NC
AA
pas
s.T
Ds
193
11.6
510.4
12009
279
171
Avar
iety
of
met
rics
of
posi
tive
NC
AA
rush
ing
529
407.5
6444.6
82009
788
958
beh
avio
rsfo
rfo
otb
all
pla
yer
sonly
NC
AA
WR
yd.
798
299.0
9294.0
32009
1100
649
NC
AA
TE
yd.
297
146.8
4190.7
32009
1.2
0E+
06
301
NC
AA
sack
s992
2.5
52.2
32009
5.8
5E+
04
1081
Cri
cket
runs
252
4279.4
82205.7
71909–2009
239
52
Top
200
cric
ket
ers
inru
ns/
wic
ket
sC
rick
etw
icket
s150
201.5
5117.8
41909–2009
1830
15
EP
Lgoal
s1,5
21
10.9
019.7
21992–2009
1.1
7E+
12
96
Num
ber
of
goal
ssc
ore
dN
BA
coac
hes
win
s258
183.1
5263.7
31946–2009
9.5
7E+
05
14
7A
var
iety
of
met
rics
of
po
siti
ve
NB
Aca
reer
poin
ts3,9
32
2670.9
14308.4
41946–2009
2.6
2E+
12
3517
beh
avio
rsfo
rpla
yer
san
dm
anag
ers
PG
Aca
reer
win
s200
14.0
512.6
21916–2009
2.0
8E+
04
34
All
tim
eto
urn
amen
tw
ins
Men
’ssw
imm
ing
654
1.7
81.3
81896–2009
8.0
8E+
07
681
Gold
,si
lver
,or
bro
nze
med
alac
ross
anW
om
en’s
swim
min
g538
1.7
51.3
91896–2009
1.1
9E+
06
773
enti
reca
reer
Men
’str
ack
981
1.3
4.7
61896–2009
4.4
2E+
09
5058
conti
nued
100 PERSONNEL PSYCHOLOGYT
AB
LE
4(c
on
tin
ued
)
Dat
aco
llec
tio
nG
auss
ian
Par
etia
nP
erfo
rman
ceo
per
atio
nal
izat
ion
and
Sport
NM
ean
SD
tim
efr
ame
(χ2)
(χ2)
com
men
ts
Wom
en’s
trac
k437
1.4
5.9
41896–2009
1.4
1E+
08
943
Men
’sal
pin
e167
1.4
6.9
41896–2009
1.1
0E+
08
265
Wom
en’s
alpin
e148
1.6
4.9
81896–2009
791
198
PB
Ati
tles
20
04.9
56.7
01959–2009
1.4
3E+
06
47
All
tim
eto
urn
amen
tw
ins
NA
SC
AR
poin
ts125
1138.4
11410.4
72009
262
119
Poin
tsea
rned
inth
eS
pri
nt
Cup
seri
esN
FL
coac
hes
win
s413
31.2
546.6
41999–2009
1.1
9E+
07
10
4A
var
iety
of
met
rics
of
po
siti
ve
NF
Lkic
kre
turn
yd.
250
3238.4
31698.9
51999–2009
2.6
7E+
06
29
beh
avio
rsfo
rpla
yer
san
dm
anag
ers
NF
LT
Dre
cepti
ons
253
50.9
220.5
91999–2009
2.2
9E+
08
41
NF
Lfi
eld
goal
s252
110.6
1108.6
91999–2009
683
118
NF
Lsa
cks
251
59.3
828.4
31999–2009
9240
37
NF
Lru
shin
gyd.
250
5611.0
12708.4
61999–2009
127
20
NF
Lpas
sing
yd.
250
16897.2
011431.1
01999–2009
312
112
NH
Ldef
ense
assi
sts
1,5
33
107.1
2165.4
81917–2009
4.9
6E+
09
909
Poin
tssc
ore
dfo
ral
lN
HL
pla
yer
sN
HL
cente
rspoin
ts1,2
13
191.5
5300.8
71917–2009
3.6
4E+
05
708
acro
ssth
eir
care
ers
NH
Lri
ght
win
gpoin
ts1,0
73
162.3
6246.8
21917–2009
5.1
1E+
07
537
NH
Lle
ftw
ing
poin
ts1,1
02
141.8
1210.3
61917–2009
2.3
2E+
06
640
NH
Lgoal
ies
saves
392
3497.9
94848.0
21917–2009
1650
526
Men
’ste
nnis
146
2.9
42.8
01877–2009
1080
41
Gra
nd
Sla
mto
urn
amen
tw
ins
acro
ssan
enti
reca
reer
Wom
en’s
tennis
110
3.6
84.3
71877–2009
1140
29
NC
AA
bas
ket
bal
l100
615.2
175.0
22009
142
8P
oin
tssc
ore
dfo
ra
single
seas
on
Wei
ghte
dave
rage
502,1
93,9
74,1
89
1,0
76
No
te.E
PL
=E
ng
lish
Pre
mie
rL
eag
ue,
ER
A=
Ear
ned
run
aver
age,
HR
=H
om
eruns,
ML
B=
Maj
or
Lea
gu
eB
aseb
all,
NA
SC
AR
=N
atio
nal
Ass
oci
atio
nfo
rS
tock
Car
Auto
Rac
ing,
NB
A=
Nat
ion
alB
asket
bal
lA
sso
ciat
ion
,N
CA
A=
Nat
ion
alC
oll
egia
teA
thle
tic
Ass
oci
atio
n.
NF
L=
Nat
ion
alF
oo
tbal
lL
eague,
NH
L=
Nat
ional
Hock
eyL
eague,
PB
A=
Pro
fess
ional
Bow
ling
Lea
gue,
PG
A=
Pro
fess
ional
Golf
Ass
oci
atio
n,T
D=
touch
dow
ns,
yd
=yar
ds.
O’BOYLE JR. AND AGUINIS 101
Results
Results summarized in Table 4 indicate that the distribution of indi-vidual performance follows a Paretian distribution more closely than aGaussian distribution. In addition, we examined the distribution of per-formance within teams and for a more limited time period rather thanacross organizations and careers. This helps rule out the possibility thatour results are due to analyses across organizations and careers that mayaccentuate the preponderance of outliers. We examined the most recentseason (2009–2010) for teams in the English Premier League (goals),Major League Baseball (homeruns and strikeouts), and National HockeyLeague (points). The 94 samples (N = 1,797) for these analyses are consid-erably smaller, ranging from 9 to 30 athletes, thus making sampling errora limitation. However, in 84 of these 94 comparisons, chi-square statisticsprovided evidence regarding the superior fit of the Paretian distribution.
Discussion
Across a variety of sports, nationalities, and levels of play, the Paretiandistribution yielded a significantly better fit than the Gaussian distribution.In all but one sample, the performance distribution favored a power lawmore strongly than a normal distribution. Moreover, the sports and typesof athletic performance included in Study 4 vary regarding the extent towhich an individual performer participated in a team or individual sport,and we also conducted within-team and within-season analyses. The over-all weighted mean chi-square statistic for the Paretian distribution is about466 million times smaller (i.e., indicating better fit) compared to a Gaus-sian distribution. Figure 2d illustrates these results in a histogram of Study4’s largest sample: National Basketball Association (NBA) career points.
Study 5
Method
Overview. Studies 1–4 focused on positive performance (e.g., pub-lications, awards). However, the Paretian distribution possesses a greaterfrequency of extreme values at both ends of the distribution. If individualperformance is truly Paretian, then both sides of the performance dis-tribution should contain a disproportionate number of individuals. Ourdecision to conduct Study 5 focusing on negative performance was alsomotivated by an increased interest in counterproductive work behaviors(CWBs), such as abusive supervision (Tepper, Henle, Lambert, Giacalone,
The challenge to investigating the negative performance distributionis that, unlike positive performance, negative performance is often covert.Even in industries where performers are under constant scrutiny, a con-siderable number of negative behaviors occur without the knowledge ofothers. A researcher that forges his data, an actor hiding a drug addiction,and a politician accepting bribes are all behaviors that certainly qualify asnegative, but quantifying their frequency is difficult. Complicating mattersfurther, negative performance can be done intentionally (e.g., consumingalcohol while working) or unintentionally (e.g., accidentally breaking theoffice printer).
Procedure. To identify the distribution of negative performance, weused samples from collegiate and professional sports. We examined thedistribution of negative performance such as English Premier League yel-low cards, NBA career turnovers, and Major League Baseball first-baseerrors. The negative performance behaviors vary in their intent, severity,and frequency, but they are similar in that they are all detrimental to theorganization. Using samples from sports allows for an objective examina-tion of negative performance that would be virtually impossible to capturein industries in which performance is not measured so systematically andwith more ambiguous definitions of what constitutes positive and nega-tive performance. Study 5 included 17 types of negative performance of57,300 individual athletes in six sporting disciplines (see Table 5).
Operationalization of individual performance. We attempted to iden-tify negative behaviors that were primarily attributable to an individualperformer. For instance, an incomplete pass in U.S. football can be eithera failure of the quarterback or a failure of the receiver, but an interceptionis primarily viewed as a quarterback error. We identified four sports forwhich negative performance can largely be attributed to one individual.We contacted several individuals that currently or formerly participatedin these sports at an elite level (received an NCAA scholarship or playedprofessionally) to serve as subject matter experts and ensure that ourclassifications were acceptable. When possible, we divided the sport intoindividual positions. This was done because some negative performancebehaviors are more likely due to the role the player has on the team.For example, shortstops are most likely to have a baseball hit to them,thus they have a greater chance of being charged an error. In keepingwith our focus on performance measures that lead to important outcomes,we chose negative performance that is most likely to result in meaningfulconsequences for the athlete (e.g., fines, suspensions, losing sponsorships,being cut from a team).
O’BOYLE JR. AND AGUINIS 103
TA
BL
E5
Dis
trib
uti
on
of
Neg
ati
veIn
div
idual
Per
form
ance
of
Ath
lete
s:F
itW
ith
Gauss
ian
vs.P
are
tian
Dis
trib
uti
ons
Dat
aco
llec
tio
nG
auss
ian
Par
etia
nP
erfo
rman
ceo
per
atio
nal
izat
ion
Sam
ple
NM
ean
SD
tim
efr
ame
(χ2)
(χ2)
and
com
men
ts
ML
Bhit
bat
ters
ina
single
seas
on
1,007
51.5
426.4
61900–2006
1.0
2E+
05
65
Err
ors
assi
gned
for
ML
Bpla
yer
s
ML
B1B
erro
rsin
asi
ngle
seas
on
5,933
5.6
65.7
51900–2006
2.4
1E+
06
4,0
97
ML
B2B
erro
rsin
asi
ngle
seas
on
6,400
8.0
58.7
41900–2006
2.3
2E+
06
1,5
34
ML
B3B
erro
rsin
asi
ngle
seas
on
7,099
8.0
18.5
51900–2006
1.5
3E+
07
3345
ML
BC
erro
rsin
asi
ngle
seas
on
6,276
5.4
64.7
31900–2006
4.5
9E+
09
6973
ML
BO
Fer
rors
ina
single
seas
on
13,721
4.2
73.8
11900–2006
6.5
7E+
11
2.3
6E+
04
ML
BS
Ser
rors
ina
single
seas
on
6,456
11.9
813.5
51900–2006
5.1
9E+
06
3043
EP
Lyel
low
card
s1,876
9.7
812.2
61992–2009
4.7
3E+
06
44
2Y
ello
wca
rds
adm
inis
tere
dN
BA
care
ertu
rnover
2,691
427.9
4604.0
21946–2009
3.1
5E+
07
24
87
Avar
iety
of
met
rics
of
neg
ativ
eN
BA
care
erte
ch,
flag
,an
dej
ecti
ons
432
8. 8
410.3
32009
1.9
6E+
09
109
beh
avio
rsfo
rpla
yer
s
conti
nued
104 PERSONNEL PSYCHOLOGY
TA
BL
E5
(co
nti
nu
ed)
Dat
aco
llec
tio
nG
auss
ian
Par
etia
nP
erfo
rman
ceo
per
atio
nal
izat
ion
Sam
ple
NM
ean
SD
tim
efr
ame
(χ2)
(χ2)
and
com
men
ts
NF
Lfu
mble
s251
55.2
823.1
91999–2009
2030
26
Avar
iety
of
met
rics
of
neg
ativ
eN
FL
inte
rcep
tions
253
102.7
460.7
61999–2009
141
72
beh
avio
rsfo
rpla
yer
sN
HL
def
ense
pen
alty
min
ute
s1,5
05
368.6
7460.3
11917–2009
7.4
9E+
06
15
80
Pen
alty
min
ute
sre
ceiv
edfo
ral
l
NH
Lce
nte
rspen
alty
min
ute
s1,1
29
216.8
4329.9
91917–2009
8.3
8E+
06
546
NH
Lpla
yer
sac
ross
thei
rca
reer
s
NH
Lri
ght
win
gp
enal
tym
inu
tes
1,0
15
288.8
9466.3
91917–2009
9.0
2E+
07
567
NH
Lle
ftw
ing
pen
alty
min
ute
s1,0
53
286.6
1449.4
11917–2009
7.1
3E+
11
605
NC
AA
thro
wn
inte
rcep
tio
ns
202
7.0
24.6
12009
97
45
Quar
terb
acks
only
Wei
ghte
dave
rage
170,9
51,4
62,7
85
7,9
75
No
te.
1B
=fi
rst
bas
emen
,2B
=se
cond
bas
emen
,3B
=th
ird
bas
emen
,C
=ca
tch
ers,
EP
L=
En
gli
shP
rem
ier
Lea
gu
e,O
F=
outfi
elder
s,M
LB
=M
ajo
rL
eag
ue
Bas
ebal
l,N
BA
=N
atio
nal
Bas
ket
bal
lA
sso
ciat
ion
,NF
L=
Nat
ion
alF
oo
tbal
lL
eag
ue,
NC
AA
=N
atio
nal
Co
lleg
iate
Ath
leti
cA
sso
ciat
ion
,te
ch/fl
ag=
tech
nic
alor
flag
rant
foul,
NH
L=
Nat
ional
Hock
eyL
eague,
PG
A=
Pro
fess
ional
Golf
Ass
oci
atio
n,
SS
=sh
ort
stops.
O’BOYLE JR. AND AGUINIS 105
Results
Results regarding the distribution of negative performance of athletesare included in Table 5. Each of the samples fitted a Paretian distributionbetter than a Gaussian distribution. The average misfit of the Paretiandistribution was only 7,975 whereas the average misfit of the normaldistribution exceeded 170 billion. Similar to Study 4, we conducted within-team, within-season analyses to rule out a potential longevity confoundingeffect. We used EPL yellow cards, MLB hit batters, and NHL penaltyminutes for the 2009–2010 season. This included 67 teams (N = 1419),of which 52 better conformed to a Paretian distribution.
Discussion
Results of Study 5 closely match those regarding positive performancedistributions investigated in Studies 1–4. The distribution of negative per-formance more closely resembles a power law compared to a normaldistribution. We found this same result regarding every one of the 17samples including a variety of negative performance behaviors and acrossseveral types of sports including baseball, hockey, basketball, and non-U.S. football. As an illustration, Figure 2e includes a histogram for Study5’s largest sample: MLB errors. The within-team, within-season analysesfurther supported the Paretian distribution of performance output.
General Discussion
Theories and practices about performance, personnel selection, train-ing, leadership, and many other domains in OBHRM are firmly rooted inthe “norm of normality” where individual performance follows a normaldistribution and deviations from normality are seen as “data problems”that must be “fixed.” Although some may be skeptical regarding this normof normality, there is little evidence that this belief has affected theoret-ical developments or application in an influential way. This norm hasdeveloped many decades ago and, to our knowledge, has not been testedsystematically and comprehensibly. Individual performance serves as abuilding block not only for OBHRM and I-O psychology but for mostorganizational science theories and applications. Thus, understanding thedistribution of individual performance is a key issue for organizationalscience research and practice.
Our central finding is that the distribution of individual performancedoes not follow a Gaussian distribution but a Paretian distribution. Ourresults based on five separate studies and involving 198 samples in-cluding 633,263 researchers, entertainers, politicians, and amateur and
106 PERSONNEL PSYCHOLOGY
professional athletes are remarkably consistent. Of a total of 198 samplesof performers, 186 (93.94%) follow a Paretian distribution more closelythan a Gaussian distribution. If, as our results suggest, most performanceoutcomes are attributable to a small group of elite performers, then boththeory and practice must adjust to the substantial role played by theseindividuals. Next, we discuss implications of our findings for theory andsubstantive research; research methodology; and practice, policy making,and society.
Implications for Theory and Substantive Research
Our results have important implications for past and future researchin substantive domains in OBRHM, I-O psychology, and other fieldsconcerned with individual performance (e.g., strategy, entrepreneurship).We limit our discussion to key areas identified as being among the mostpopular in OBHRM over the past 45 years (Cascio & Aguinis, 2008a):performance measurement and management, utility analysis in preem-ployment testing and training and development, leadership and teamwork,and the understanding and prediction of performance.
Regarding performance measurement and management, the currentzeitgeist is that the median worker should be at the mean level of per-formance and thus should be placed in the middle of the performanceappraisal instrument. If most of those rated are in the lowest category,then the rater, measurement instrument, or both are seen as biased (i.e.,affected by severity bias; Cascio & Aguinis, 2011 chapter 5). Performanceappraisal instruments that place most employees in the lowest categoryare seen as psychometrically unsound. These basic tenets have spawneddecades of research related to performance appraisal that might “improve”the measurement of performance because such measurement would resultin normally distributed scores given that a deviation from a normal dis-tribution is supposedly indicative of rater bias (cf. Landy & Farr, 1980;Smither & London, 2009a). Our results suggest that the distribution ofindividual performance is such that most performers are in the lowestcategory. Based on Study 1, we discovered that nearly two thirds (65.8%)of researchers fall below the mean number of publications. Based on theEmmy-nominated entertainers in Study 2, 83.3% fall below the mean interms of number of nominations. Based on Study 3, for U.S. representa-tives, 67.9% fall below the mean in terms of times elected. Based on Study4, for NBA players, 71.1% are below the mean in terms of points scored.Based on Study 5, for MLB players, 66.3% of performers are below themean in terms of career errors. Moving from a Gaussian to a Paretianperspective, future research regarding performance measurement wouldbenefit from the development of measurement instruments that, contrary
O’BOYLE JR. AND AGUINIS 107
to past efforts, allow for the identification of those top performers who ac-count for the majority of results. Moreover, such improved measurementinstruments should not focus on distinguishing between slight perfor-mance differences of non-elite workers. Instead, more effort should beplaced on creating performance measurement instruments that are able toidentify the small cohort of top performers.
As a second illustration of the implications of our results, consider theresearch domain of utility analysis in preemployment testing and train-ing and development. Utility analysis is built upon the assumption ofnormality, most notably with regard to the standard deviation of individ-ual performance (SDy), which is a key component of all utility analysisequations. In their seminal article, Schmidt et al. (1979) defined SDy
as follows: “If job performance in dollar terms is normally distributed,then the difference between the value to the organization of the prod-ucts and services produced by the average employee and those producedby an employee at the 85th percentile in performance is equal to SDy”(p. 619). The result was an estimate of $11,327. What difference would aParetian distribution of job performance make in the calculation of SDy?Consider the distribution found across all 54 samples in Study 1 and theproductivity levels in this group at (a) the median, (b) 84.13th percentile,(c) 97.73rd percentile, and (d) 99.86th percentile. Under a normal distri-bution, these values correspond to standardized scores (z) of 0, 1, 2, and3. The difference in productivity between the 84.13th percentile and themedian was two, thus a utility analysis assuming normality would useSDy = 2.0. A researcher at the 84th percentile should produce $11,327more output than the median researcher (adjusted for inflation). Extendingto the second standard deviation, the difference in productivity betweenthe 97.73rd percentile and median researcher should be four, and this ad-ditional output is valued at $22,652. However, the difference between thetwo points is actually seven. Thus, if SDy is two, then the additional outputof these workers is $39,645 more than the median worker. Even greaterdisparity is found at the 99.86th percentile. Productivity difference be-tween the 99.86th percentile and median worker should be 6.0 accordingto the normal distribution; instead the difference is more than quadru-ple that (i.e., 25.0). With a normality assumption, productivity amongthese elite workers is estimated at $33,981 ($11,327 × 3) above the me-dian, but the productivity of these workers is actually $141,588 above themedian. We chose Study 1 because of its large overall sample size, butthese same patterns of productivity are found across all five studies. Inlight of our results, the value-added created by new preemployment testsand the dollar value of training programs should be reinterpreted froma Paretian point of view that acknowledges that the differences betweenworkers at the tails and workers at the median are considerably wider than
108 PERSONNEL PSYCHOLOGY
previously thought. These are large and meaningful differences suggestingimportant implications of shifting from a normal to a Paretian distribu-tion. In the future, utility analysis should be conducted using a Paretianpoint of view that acknowledges that differences between workers at thetails and workers at the median are considerably wider than previouslythought.
Our results also have implications for OB domains. For example,consider the case of leadership research that, similar to other OB domains(e.g., work motivation, job satisfaction, organizational commitment), hastraditionally focused on the “average worker” and how best to improvea group’s mean performance. Leadership theories grounded in Gaussianthinking focus on the productivity of the majority of workers rather thanthe workers responsible for the majority of productivity. Given a normaldistribution, 68% of output should derive from the individuals locatedbetween the 16th percentile and 84th percentile. With so much of the totaloutput produced by workers around the median, it makes sense for leadersto focus most of their energy on this group. However, if performancefollows a Paretian distribution similar to that found in Study 1, only 46%(vs. 68%) is produced by this group. If we extend this illustration further,we expect approximately 95% of the output to be produced by workersbetween the 2.5th and 97.5th percentiles in a normal distribution. However,using the distribution found in Study 1, only 81% of output comes fromthis group of workers. With less output from the center of the distribution,more output is found in the tails. Ten percent of productivity comes fromthe top percentile and 26% of output derives from the top 5% of workers.Consequently, a shift from a normal to a Paretian distribution points to theneed to revise leadership theories to address the exchanges and influenceof the extreme performers because our results demonstrate that a small setof followers produces the majority of the output. Leadership theories thatavoid how best to manage elite workers will likely fail to influence the totalproductivity of the followers in a meaningful way. Thus, greater attentionshould be paid to the tremendous impact of the few vital individuals.Despite their small numbers, slight percentage increases in the output oftop performers far outweigh moderate increases of the many. New theoryis needed to address the identification and motivation of elite performers.
In addition to the study of leadership, our results also affect researchon work teams (e.g., group empowerment, shared efficacy, team diver-sity). Once again, our current understanding of the team and how groupsinfluence performance is grounded in an assumption of normality. Thecommon belief is that teamwork improves performance through increasedcreativity, synergies, and a variety of other processes (Mathieu, Maynard,Rapp, & Gilson, 2008). If performance follows a Paretian distribution,then these existing theories are insufficient because they fail to address
O’BOYLE JR. AND AGUINIS 109
how the presence of an elite worker influences group productivity. Wemay expect the group productivity to increase in the presence of an eliteworker, but is the increase in group output negated by the loss of individ-ual output of the elite worker being slowed by non-elites? It may also bethat elites only develop in interactive, dynamic environments, and the iso-lation of elite workers or grouping multiple elites together could hampertheir abnormal productivity. Once again, the finding of a Paretian distribu-tion of performance requires new theory and research to address the elitenested within the group. Specifically, human performance research shouldadopt a new view regarding what human performance looks like at thetails. Researchers should address the social networks of superstars withingroups in terms of identifying how the superstar emerges, communicateswith others, interacts with other groups, and what role non-elites play inthe facilitating of overall performance.
At a more fundamental level, our understanding of job performanceitself needs revisiting. Typically, job performance is conceptualized asconsisting of three dimensions: in-role or task behavior, organizationalcitizenship behavior (OCB), and CWB (Rotundo & Sackett, 2002). CWB(i.e., harmful behaviors targeted at the organization or its members) hasalways been assumed to have a strong, negative relation with the other twocomponents, but it is unclear if this relationship remains strong, or evennegative, among elite performers. For example, the superstars of Study 4often appeared as supervillains in Study 5. Do the most productive workersalso engage in the most destructive behavior? If so, future research shouldexamine if this is due to managers’ fear of reprimanding a superstar, thesuperstar’s sense of entitlement, non-elites covering for the superstar’smisbehavior out of hero worship, or some interaction of all three.
Finally, going beyond any individual research domain, a Paretian dis-tribution of performance may help explain why despite more than a centuryof research on the antecedents of job performance and the countless theo-retical models proposed, explained variance estimates (R2) rarely exceed.50 (Cascio & Aguinis, 2008b). It is possible that research conducted overthe past century has not made important improvements in the ability to pre-dict individual performance because prediction techniques rely on meansand variances assumed to derive from normal distributions, leading togross errors in the prediction of performance. As a result, even models in-cluding theoretically sound predictors and administered to a large samplewill most often fail to account for even half of the variability in workers’performance. Viewing individual performance from a Paretian perspec-tive and testing theories with techniques that do not require the normalityassumptions will allow us to improve our understanding of factors thataccount for and predict individual performance. Thus, research addressingthe prediction of performance should be conducted with techniques thatdo not require the normality assumption.
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Implications for Research Methodology
What are the consequences of using traditional Gaussian-based tech-niques with individual performance data that follow a Paretian distribu-tion? A basic example is a test of differences in means (e.g., independentgroup t-test) for some intervention where individuals are randomly as-signed to groups. The assumption is that, given sufficient group sizes, noone individual will deviate from the mean enough to cause a significantdifference when there is none or vice versa (Type I and Type II errors).However, random assignment will only balance the groups when the dis-tribution of the outcome is normally distributed (when the prevalenceof outliers is low). In the case of Paretian distributions, the prevalenceof outliers is much higher. As a result, a single high performer has animportant impact on the mean of the group and ultimately on the sig-nificance or nonsignificance of the test statistic. Likewise, the residualcreated by extreme performers’ distance from a regression line widensstandard errors to create Type II errors. Interestingly, the wide standarderrors and unpredictable means caused by extreme performers should re-sult in great variability in findings in terms of both statistical significanceand direction. This may explain so many “inconsistent findings” in theOBHRM literature (Schmidt, 2008). Based on the problems of applyingGaussian techniques to Paretian distribution, our first recommendationfor researchers examining individual performance is to test for normality.Paretian distributions will often appear highly skewed and leptokurtic. Inaddition to basic tests of skew and kurtosis, additional diagnostics suchas the chi-square test used in the present studies should be incorporatedin the data screening stage of individual performance.
Along with testing for normality, our results also suggest that themethodological practice of forcing normality through outlier manipula-tion or deletion may be misguided. Dropping influential cases excludesthe top performers responsible for the majority of the output, and doingso creates a sample distribution that does not mirror the underlying popu-lation distribution. As such, sample statistics will bear little resemblanceto population parameters. Samples that exclude outliers generalize onlyto those individuals around the median of the distribution. Therefore, oursecond recommendation for research methodology is to shift the burdenof proof from outlier retention to outlier deletion/transformation. That is,influential cases should be retained in the data set unless there is clear evi-dence that their value is incorrect (e.g., typographical error) or belongto a population to which the researcher does not wish to generalize.Regardless, the handling of influential cases should always be reported.
An additional implication our findings is that ordinary least squaresregression, ANOVA, structural equation modeling, meta-analysis, and all
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techniques that provide accurate estimates only under a normal distribu-tion assumption should not be used when the research question involvesindividual performance output. If researchers find that their data are notnormally distributed, and they do not artificially truncate the distributionthrough outlier deletion, then this leaves the question of how to proceedwith analysis. Paretian distributions require analytic techniques that arenot common in OBHRM but nonetheless are readily available. Techniquesexist that properly and accurately estimate models where the outcome isParetian. Poisson processes are one such solution, and although not wellestablished in OBHRM research, they do have a history in the naturalsciences (e.g., Eliazar & Klafter, 2008) and finance (e.g., Embrechts,Kluppelberg, & Mikosch, 1997). In addition, agent-based modeling(ABM) is an inductive analytic tool that operates without the theoreti-cal assumptions that our results debunk (see Macy & Willer, 2002 fora review of ABM). ABM can be used to develop and test theories ofsuperstars in the more fundamental context of autonomous agents inde-pendently and in conjunction with others, making decisions based on verysimple rules (Bonabeau, 2002). The result is an understanding of perfor-mance based on dynamism instead of equilibrium, interdependent agentsinstead of independent automatons, and nonlinear change instead staticlinearity.
In addition, Bayesian techniques are likely to provide the greatestapplicability to the study of superstars. Beyond moving away from nullhypothesis significance testing, Bayesian techniques provide the addi-tional benefit of dealing with the nonlinearity introduced by influentialcases because they allow the underlying distribution to be specified a priori(Beyth-Marom & Fischhoff, 1983). Thus, a researcher can test hypotheseswithout having to assume normality or force it upon the data (Kruschke,Aguinis, & Joo, unpublished data). For example, one can specify that per-formance follows a Paretian distribution. Bayesian techniques are slowlybeing adopted in OBHRM and related disciplines (Detienne, Detienne,& Joshi, 2003; Nystrom, Soofi, & Yasai-Ardekani, 2010; Somers, 2001).Regardless of the specific data-analytic approach, our final methodolog-ical recommendation is the use of techniques that do not rely on thenormality assumption.
Implications for Practice, Policy Making, and Society
Our results lead to some difficult questions and challenges in termsof practice, policy making, and societal issues because they have im-plications for discussions around equality and merit (Ceci & Papierno,2005). There are several areas within OBHRM such as employee train-ing and development and compensation that rely on the assumption that
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individual performance is normally distributed, and any intervention orprogram that changes this distribution is seen as unnatural, unfair, or biased(Schleicher, & Day, 1998). In evaluation, interventions are deemed suc-cessful to the extent that all those who go through them experience im-proved performance. But, if training makes the already good better andleaves the mediocre and poor performers behind, then this is usually seenas an indication of program faultiness. The Matthew effect (Ceci & Pa-pierno, 2005; Merton, 1968) states that those already in an advantageousposition are able to leverage their position to gain disproportionate re-wards. It is disproportionate because the perception is that their inputsinto a system do not equal the outputs they receive. Training programsthat especially benefit elite performers are seen as unfair because theyartificially alter the normal curve that is the “natural” distribution of per-formance. The Matthew effect has been found in a variety of settings(e.g., Chapman & McCauley, 1993; Judge & Hurst, 2008; Sorenson &Waguespack, 2006). Likewise, compensation systems such as pay for per-formance and CEO compensation are an especially divisive issue, withmany claiming that disproportionate pay is an indicator of unfair practices(Walsh, 2008). Such differences are seen as unfair because if perfor-mance is normally distributed then pay should be normally distributed aswell.
Our results put the usual conceptions and definitions of fairness andbias, which are based on the norm of normality, into question and lead tosome thorny and complicated questions from an ethical standpoint. Howcan organizations balance their dual goals of improving firm performanceand also employee performance and well-being (Aguinis, 2011)? Is itethical for organizations to allocate most of their resources to an elite groupof top performers in order to maximize firm performance? Should separatepolicies be created for top performers given that they add greater value tothe organization than the rest? Our results suggest that practitioners mustrevisit how to balance the dual goals of improving firm performance andemployee performance and well-being as well as determine the properallocation of resources for both elites and nonelites.
Beyond concepts of ethics and fairness, a Paretian distribution of per-formance has many practical implications for how business is done. Aswe described earlier, a Pareto curve demonstrates scale invariance, andthus whether looking at the entire population or just the top percentile, thesame distribution shape emerges. For selection, this means that there arereal and important differences between the best candidate and the secondbest candidate. Superstars make or break an organization, and the abilityto identify these elite performers will become even more of a necessity asthe nature of work changes in the 21st century (Cascio & Aguinis, 2008b).Our results suggest that practitioners should focus on identification
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and differentiation at the tails of the distribution so as to best identifyelites.
Organizations must also rethink employment arrangements with su-perstars, as they will likely be very different from traditional norms interms of starting compensation, perquisites, and idiosyncratic employ-ment arrangements. Superstars perform at such a high level that makesthem attractive to outside firms, and thus even in a recession these individ-uals have a high degree of job mobility. In an age of hypercompetitiveness,organizations that cannot retain their top performers will struggle to sur-vive. At present, we know very little about the motivations, traits, andbehaviors of elite performers. Our work indicates that superstars exist butdoes not address the motivations, behaviors, and individual differencesof the superstar. We see the emerging literature on I-Deals (Rousseau,Ho, & Greenberg, 2006) and core-self-evaluations (Judge, Erez, Bono,& Thoresen, 2003) as potentially fruitful areas of managing and retain-ing superstars and encourage practitioners to incorporate these literaturestreams into their work.
Potential Limitations and Suggestions for Future Research
We attempted to establish the shape of the individual performance dis-tribution across a variety of settings and industries. Although we analyzedmultiple industries and a variety of performance operationalizations, it isstill possible that these samples do not generalize to other occupations.In addition, for the reasons described earlier, most of the data we useddo not include performance measures as typically operationalized in I-Opsychology research. We expand on these issues next.
Our results clearly support the superiority of the Paretian distributioncompared to the Gaussian distribution to model individual performance.In Studies 1, 2, 4, and 5, we found only one sample (NCAA rushing)for which individual performance was better modeled with a Gaussiandistribution than a Paretian distribution. However, in Study 3 we found11 samples favoring a Gaussian model. Note that given a total of 42 sam-ples in Study 3, results still heavily favor a Paretian distribution (i.e., 74%of samples favored a Paretian distribution). However, a closer examinationof results from Study 3 may provide some insights regarding conditionsunder which Gaussian distributions are likely to be found. We acknowl-edge the speculative nature of the material that follows, and we emphasizethat, rather than conclusions, these should be seen as hypotheses and re-search questions that need to be addressed by future research.
Consider two measurement-related reasons for the potential betterfit of a Gaussian distribution. First, a measure of performance may betoo coarse to capture differences between superstars and the “simply
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adequate” (Aguinis, Pierce, & Culpepper, 2009). Specifically, in Study 3,performance was measured as whether an official was elected or not, andthe measure did not capture differences among performers such as by howmany votes an individual won or lost an election. So, industries and typesof jobs for which performance is measured with coarse scales may leadto observed distributions that are Gaussian rather than Paretian. Second,consider situations in which there are constraints imposed on the ratingsof performance. As described earlier, ratings of performance, particularlysupervisory ratings, are one of the most popular ways to operationalizeperformance in I-O psychology research. These constraints can distortthe shape of the underlying performance distribution when normalityis introduced by the scale or rater evaluation training. In these cases,normality is likely to emerge in the observed data regardless of the trueshape of the performance distribution.
Now, consider three situations and reasons why the underlying perfor-mance distribution, not just observed performance scores, may actually fita Gaussian as opposed to a Paretian model. First, it may be the case that, incertain industries and certain job types, superstars simply do not emerge.For example, the manufacturing economy of the 20th century strove notonly for uniformity of product but also uniformity of worker. Quotas,union maximums, assembly lines, and situational and technological con-straints all constrained performance to values close to the mean. Evenin jobs without these formal constraints, informal barriers (i.e., norms)existed in ways that limited the emergence of superstars. Productivitynorms such as those found in the Hawthorne studies (Roethlisberger &Dickson, 1939) support a normal distribution of performance dependenton informal corrective actions of coworkers. Workers violating the es-tablished productivity norms were chastised, bullied, and ostracized intoconforming to prescribed output levels. Hence, even organizations outsideof the manufacturing sector where there are limited formal constraints toproductivity may still fail to see the emergence of superstars and Paretiandistributions.
In government, as is the case for the Study 3 samples, similar normsmay lead to the curtailment of outliers, resulting in an observed distributionthat is Gaussian rather than Paretian. Second, we also speculate that com-pared to the participants in the other studies, government officials as wehad in Study 3 have fewer direct ties between performance and compensa-tion. Pay raises in legislatures are generally voted on and applied equallyacross all members. Therefore, if a representative in the Alabama legis-lature wished to receive higher rewards (e.g., money, fame, power), shewould either need to increase the compensation of all her fellow represen-tatives or run for a more prestigious office. For samples in Study 3, all butone of those favoring a Gaussian distribution (the Danish Folketing) were
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lower houses of the legislative branch. Thus, superstar representatives mayhave quickly moved on to occupy higher-level and more prestigious po-sitions such as becoming senators or governors. Finally, given the natureof work and organizations in the 21st century (Cascio & Aguinis, 2008b),we believe that the Paretian distribution will apply to an increasingly highnumber of industries, occupations, and jobs. However, industries and or-ganizations that rely on manual labor, have limited technology, and placestrict standards for both minimum and maximum production are likelyto lead to normal distributions of individual performance. As we moveinto the 21st century, software engineers, consultants, healthcare workers,and educators make up an increasingly large part of the economy; but, forthe foreseeable future, farmers, factory workers, and construction crewswill continue to play an important role, and these types of jobs may bestbe modeled with a normal distribution (e.g., Hull, 1928; Tiffin, 1947). Inshort, we readily acknowledge that our results are circumscribed to thetypes of industries and performance operationalizations included in ourfive studies because these factors may serve as boundary conditions forour findings.
Our results point to the influential role of elite performers (i.e., super-stars), which opens new research avenues for the future. First, althoughwe know there are more superstars than a normal curve would suggest,exactly what percentage of workers can be considered superstars has notbeen established. The classification of superstars is a subjective judg-ment, and there are no norms to indicate what proportion of workersshould be considered elite. Second, research is needed on the deleteriouseffects of superstars. For example, does the presence of a superstar de-motivate other workers to such an extent that total organizational outputdecreases?
Finally, our research provides information on the performance distri-bution, but it does not examine what individual characteristics top per-formers possess nor did it investigate the stability of the top performinggroup. When and how do these individuals reach the elite group? What isthe precise composition of this elite group—do individuals rotate in andout of this group, or once in the top group, they remain in the top formost of their career? What individual, group, and cultural factors predictan individual’s membership in the top-performing group over time? Ulti-mately, certain individuals likely possess abilities and skills that increasethe probability of extraordinary performance, but the interactive nature ofperformance and context suggests that environmental factors and other ac-tors in the network also play a role in determining individual performance(Aguinis, 2009). That is, superstars likely cannot emerge in a vacuum.Top researchers can devote the necessary time to their work because thereare others who take on some of their teaching and administrative duties.
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Hollywood stars emerge in part because of supporting casts on screen aswell as off screen (e.g., agents, managers, publicists).
Concluding Remarks
Much like the general population, we, OBHRM researchers and prac-titioners, are not immune to “received doctrines” and “things we just knowto be true” (Lance, 2011). These issues are “taught in undergraduate andgraduate classes, enforced by gatekeepers (e.g., grant panels, reviewers,editors, dissertation committee members), discussed among colleagues,and otherwise passed along among pliers of the trade far and wide andfrom generation to generation” (Lance, 2011: 281). We conclude that thenorm of normality regarding individual performance qualifies to be sucha received doctrine because, even when not explicitly stated, it permeatesthe theory, design, and analysis of OBHRM research as well as OBHRMpractices. In contrast, based on five separate studies involving 198 sam-ples including 633,263 researchers, entertainers, politicians, and amateurand professional athletes, our results indicate that individual job perfor-mance follows a Paretian distribution. Assuming normality of individualperformance can lead to misspecified theories and misleading practices.Thus, our results have implications for all theories and applications inOBHRM and related fields (e.g., I-O psychology, strategic management,entrepreneurship) that directly or indirectly rely upon the performance ofindividual workers.
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