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Abstract

  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES

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 researchers, entertainers, politicians, and amateur and professional athletes. Results are remarkably consistent across industries, types of jobs, types of performance measures, and time frames and indicate that individual 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 including performance measurement and management, utility analysis in preemployment testing and training and development, personnel selection, 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 ultimately 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; Tiffin, 1947). When performance data do not conform to the normal distribution, then the conclusion is that the error “must” lie within the sample not the population. Subsequent adjustments are made (e.g., dropping outliers) in order to make the sample “better reflect” the “true” underlying normal curve. Gaussian distributions are in stark contrast to Paretian or power law distributions, which are typified by unstable means, infinite variance, and a greater proportion of extreme events. Figure 1 shows a Paretian distribution overlaid with a normal curve.

image

Figure 1. A Normal Distribution (Black) Overlaying a Paretian Distribution (Grey).

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The goal of our research is to revisit the norm of normality of individual performance and discuss implications for OBHRM theory and research; methodology; and practice, policy making, and society. Our manuscript is organized as follows. First, we describe the origins and document the presence of the norm of normality regarding individual performance. Second, we discuss the Gaussian (i.e., normal) and Paretian (i.e., power law) distributions and key differences between them. Third, we describe five separate studies involving 198 samples including 633,263 researchers, entertainers, politicians, and amateur and professional athletes. Results of each of these five studies are remarkably consistent and indicate that individual performance does not follow a normal distribution and, instead, it follows a power law distribution. Finally, we discuss implications of our results, including directions for future research.

The Norm of Normality of Individual Performance

  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES

The normal distribution has been used to model a variety of phenomena including human traits such as height (Yule, 1912) and intelligence (Galton, 1889), as well as probability distributions (Hull, 1928), economic trends such as stock pricing (Bronzin, 1908), and the laws of thermodynamics (Reif, 1965). Based on the normal distribution's prevalence across scientific disciplines and phenomena, it has seemed reasonable to assume that normality would also be the distribution of individual performance.

Although the assumption of individual performance normality is common across most research domains in OBHRM, it seems to have originated in the performance appraisal literature. More than half a century ago, Ferguson (1947) noted that “ratings for a large and representative group of assistant managers should be distributed in accordance with the percentages predicted for a normal distribution” (p. 308). The normality assumption persisted through the years, and researchers began to not only assume job performance normality but forced it upon the observed distributions regardless of the actual observed distributional properties. For example, in developing a performance appraisal system, Canter (1953) used “a forced normal distribution of judgments” (p. 456) for evaluating open-ended responses. Likewise, Schultz and Siegel (1961)“forced the [performance] rater to respond on a seven-point scale and to normalize approximately the distribution of his responses” (p. 138). Thus, if a supervisor rated the performance of her subordinates and placed most of them into a single category while placing only a small minority in the top ranking, it was assumed that there was a severity bias in need of a correction to normality (Motowidlo & Borman, 1977; Schneier, 1977). Moreover, the advice is that if an employee contributes a disproportionate amount of sales in a firm, he should be dropped from the data set or have his sales statistically adjusted to a more “reasonable” value (e.g., three standard deviations within the mean) before moving forward with a traditional analysis that assumes an underlying normal distribution. Both design practices (i.e., forced-response formats) and statistical analyses (i.e., deletion or “correction” of outliers) in performance evaluation create a normal distribution in samples regardless of the shape of the underlying population distributions.

We readily acknowledge that some researchers and practitioners may not believe that individual performance is normally distributed (e.g., Bernardin & Beatty, 1984; Micceri, 1989; Murphy & Cleveland, 1995; Saal, Downey, & Lahey, 1980; Schmidt & Johnson, 1973). However, the normality assumption is a convenient way of studying individual performance—just like economists also make assumptions so that their theoretical models can be simplified. As noted by an anonymous reviewer, some may not put too much thought into the shape of the performance distribution whereas others may believe that, with a sufficiently large number of cases, individual performance is normally distributed. Regardless of the actual beliefs, researchers and practitioners assume performance is normally distributed and alter the distribution of scores through the design, training, and analysis of raters’ judgments. Specifically, when performance scores deviate from normality, the cause is attributed to leniency bias, severity bias, and/or a halo error (Aguinis, 2009; Schneier, 1977). Rating systems where most employees occupy the same category with only a few at the highest category are assumed to be indicative of range restriction and other “statistical artifacts” (Motowidlo & Borman, 1977). In fact, Reilly and Smither (1985) provided an extensive critique of individual performance research that violates the normality assumption and provided guidance on how to reestablish the normal and presumably correct distribution of performance.

The norm of normality of individual performance is also evident in many other research domains in OBHRM. Consider the case of personnel selection that, similar to the prediction of performance and performance measurement/work outcomes category, is among the top five most popular research domains based on articles published in Journal of Applied Psychology and Personnel Psychology over the past 45 years (Cascio & Aguinis, 2008a). Utility analysis has allowed researchers and practitioners to establish the financial value added of implementing valid personnel selection procedures, and all utility analysis approaches operate under the normality assumption. For example, Schmidt, Hunter, McKenzie, and Muldrow's (1979) linear homoscedastic model of work productivity “includes the following three assumptions: (a) linearity, (b) equality of variances of conditional distributions, and (c) normality of conditional distributions” (p. 615). In the same manner, Cascio and Ramos (1986) stated that “[a]ssuming a normal distribution of performance, 55% equates to a Fisher z-value of .13, which translates back to a validity coefficient of .13 for the old selection procedure” (p. 25). More recently, Sackett and Yang (2000 concluded that “[o]n the basis of the ordinate of the normal curve at the point of selection, it is possible to infer the mean and variance of the unrestricted distribution. Clearly, the use of such approaches relies heavily on the normality assumption” (p. 115). The validity and accuracy of all utility analyses that rely on the assumed normality of individual performance would be put into question if this assumption is actually not tenable.

Summary

Although some have argued that performance may not be normally distributed (Bernardin & Beatty, 1984; Murphy & Cleveland, 1995; Saal et al., 1980; Schmidt & Johnson, 1973), theory and application regarding individual performance are built around the assumption of normality. For example, theories on performance targeting the average worker, the implementation of performance appraisal systems that include dropping outliers, and the choice of analytic techniques point to an underlying assumption of normality. Moreover, we are not aware of influential theoretical developments or applications that explicitly assume that performance follows a nonnormal distribution (Aguinis, 2009; Smither & London, 2009). So, although some may not believe in the normal distribution of individual performance, there is little evidence that this belief has affected theoretical developments or application in an influential way. Possible reasons for why skepticism about normality has not affected theory and practice may be the lack of empirical evidence negating the normal distribution and the lack of proposed alternative distributions. But, what if performance does not conform to the Gaussian distribution? What if the means are unstable and the variance of these distributions infinite? Quite simply, if performance is not normally distributed, theories that directly or indirectly build upon individual job performance and its prediction may need to be revisited. In addition, popular practices (e.g., utility analysis of preemployment tests and training and development interventions), which also rely on the assumption of individual performance normality, would also need to be revisited.

Next, we provide an alternative perspective, which draws mainly from the economics, mathematics, and statistics literatures, that challenges the norm of normality and posits that individual performance conforms to a power 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

  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES

The possibility of a nonnormal performance distribution of individual performance has been proposed in the past but the normality assumption has remained the dominant approach. Jacobs (1974) argued that in sales industries (automotive, insurance, stock) performance is not normal because a small group of incumbents who possess the expertise and salesmanship dominate activity. If performance output does not conform to a bell-shaped, normal distribution, then power law distributions may apply (West & Deering, 1995). Power laws such as Pareto's (1897) Law produce fatter tails than those seen in a normal curve. Stated differently, Paretian probability distributions allow more extreme values to be present (see Figure 1). Whereas a value exceeding three standard deviations from the mean is often thought to be an outlier in the context of a normal curve (e.g., Orr, Sackett, & Dubois, 1991), a Paretian distribution would predict that these values are far more common and 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 domains outside of OBHRM. For example, marketing researchers have reported that about 80% of a brand's volume is purchased by about 20% of its buyers (Anschuetz, 1997) and sociology researchers have reported that about 80% of land is owned by about 20% of the population (Pareto, 1897).

There are important differences between Gaussian and Paretian distributions. First, Gaussian distributions underpredict the likelihood of extreme events. For instance, when stock market performance is predicted using the normal curve, a single-day 10% drop in the financial markets 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 standard deviation, so central to tests of statistical significance and computation of effect sizes, are stable. However, if the underlying distribution is Paretian instead of normal, means and standard deviations are not stable and Gaussian-based point estimates as well as confidence intervals are biased (Andriani & McKelvey, 2009). Third, a key difference between normal and Paretian distributions is scale invariance. In OBHRM, scale invariance usually refers to the extent to which a measurement instrument generalizes across different cultures or populations. A less common operationalization of the concept of scale invariance refers to isomorphism in the shape of score distributions regardless of whether one is examining an individual, a small work group, a department, an organization, or all organizations (Fiol, O’Connor, & Aguinis, 2001). Scale invariance also refers to the distribution remaining constant whether one is looking at the whole distribution or only the top performers. For example, the shape of the wealth distribution is the same whether examining the entire population or just the top 10% of wealthy individuals (Gabaix, 1999). Related to the issue of scale invariance, Gabaix, Gopikrishnan, Plerou, and Stanley (2003) investigated financial market fluctuations across multiple time points and markets and found that data conformed to a power law distribution. The same distribution shape was found in both United States (U.S.) and French markets, and the power law correctly predicted both the crashes of 1929 and 1987.

Germane to OBHRM in particular is that if performance operates under power laws, then the distribution should be the same regardless of the level of analysis. That is, the distribution of individual performance should closely mimic the distribution of firm performance. Researchers who study performance at the firm level of analysis do not necessarily assume that the underlying distribution is normal (e.g., Stanley et al., 1995). However, as noted earlier, researchers who study performance at the individual level of analysis do follow the norm of normality in their theoretical development, research design, and choices regarding data analysis. 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 to also follow a power law distribution, as it is the case for firm performance (Bonardi, 2004; Powell, 2003; Stanley et al., 1995).

The Present Studies

  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES

We conducted five separate studies to determine whether the distribution of individual performance more closely follows a Paretian curve than a Gaussian curve. In all studies, the primary hypothesis was that the distribution of performance is better modeled with a Paretian curve than a normal curve. For each of the five studies, we used the chi-square (χ2) statistic to determine whether individual performance more closely follows a Paretian versus a Gaussian distribution. The chi-square is a “badness of fit” statistic because higher values indicate worse fit (Aguinis & Harden, 2009). That is, the greater the degree of divergence of an empirically derived performance distribution from a Gaussian or Paretian distribution, the higher the chi-square. Accordingly, for each of the samples we studied we first forced the data to conform to a normal distribution and then forced the same data to conform to a Paretian distribution. For each comparison, a smaller chi-square value indicates which of the two theoretical distributions describes the data better. To calculate the chi-square for each distribution, we used Decision Tools Suite add-on @Risk 5.5 (Palisades Corporation, 2009). This program operates within Microsoft Excel and provides estimates of fit for a variety of distributions, including normal and Paretian distributions.

The deficiency and contamination problems associated with performance measurement (collectively known as the criterion problem) are still unresolved (Cascio & Aguinis, 2011; Murphy, 2008). Accordingly, given our ambitious goal to challenge a long-held assumption in the field, we deliberately conducted five separate studies including heterogeneous industries and used a large number of performance operationalizations including qualitative evaluations (e.g., award nominations in which raters propose the names of nominees), quantitative outcomes (e.g., number of publications by researchers), and observed behavior based on specific events (e.g., career homeruns of baseball players) or overall reputation (e.g., votes for politicians). Taken together, our five studies involve 198 samples and include 633,263 researchers, entertainers, politicians, and amateur and professional athletes.

Although we deliberately chose an eclectic and heterogeneous set of performance measures, they did share several features. First and most important, each operationalization contained behaviors that directly affected important outcomes such as compensation, bonuses, and promotions. In other words, the performance measures included in our study are particularly meaningful for the individual workers because they have important consequences. Second, the outcomes we chose primarily reflect individual behavior that is largely under an individual's control (Aguinis, 2009). The determinants of an individual's performance are individual characteristics, the context of work, and the interaction between the two. Thus, even in individual sports such as golf, other players influence each golfer's behavior. However, we made efforts to minimize the effects of contextual factors on individual performance. For example, the examination of baseball errors in Study 5 was based on grouping players into their respective positions. This prevented right fielders that typically have fewer fielding opportunities to be grouped with shortstops that have more fielding opportunities. In addition, when possible, we scaled the performance of each individual to a measurement period that was time bound. For example, in Study 4, we included career performance measures as well as single-season measures and examined both single-season performance and career performance.

Our research deliberately excludes samples of individuals whose performance has been exclusively rated by a supervisor because such performance operationalizations include biases that would render addressing our research question impossible. Specifically, instructing raters to follow a bell curve, implementing rater error training programs, normalizing performance ratings, and correcting for leniency or severity bias all help to create a normal curve in a sample regardless of the true underlying distribution.

Study 1

  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES

Method

Overview.  In Study 1, we tested whether a Paretian or Gaussian distribution better fit the distribution of performance of 490,185 researchers who have produced 943,224 publications across 54 academic disciplines between January 2000 and June 2009.

Procedure

We categorized academic disciplines using Journal Citation Reports (JCR), which provide impact factors in specific subject categories across the physical and social sciences. In some cases, there were multiple subfields included within one JCR category. For instance, there are eight entries for material sciences (e.g., ceramics, paper and wood, composites), but we identified authors across all material sciences so that authors publishing in more than one area would have all their publications included. Our analyses included 54 academic fields (see Table 1). We used impact factors (also reported in JCR) from 2007 to identify the top five journals within each of the 54 fields. We chose field-specific journals to avoid having the search contaminated by authors from other sciences. For instance, Accounts of Chemical Research most likely only includes articles related to chemistry, but this assumption cannot be made with an interdisciplinary journal such as Nature, which publishes chemistry research alongside other scientific research. We next used the Publish or Perish program (Harzing, 2008), which relies on Google Scholar, to identify all authors who had published at least one article in one of these journals between January 2000 and June 2009. These procedures resulted in a total of 490,185 researchers who have produced 943,224 scholarly journal publications.

Table 1.  Distribution of Individual Performance of Researchers: Fit With Gaussian vs. Paretian Distributions
SampleNMeanSDGaussian (χ2)Paretian (χ2)
Agriculture25,0061.912.543.15E+142.02E+04
Agronomy8,9231.421.162.56E+135.07E+04
Anthropology5,7551.871.957.37E+126,460
Astronomy13,1013.103.993.17E+122,200
Biological psychology8,3321.401.111.96E+126.56E+04
Clinical psychology10,4181.892.388.24E+122,321
Computer science3,5971.451.111.53E+119,523
Criminology6781.29.773.09E+111.10E+04
Demography7371.582.916.16E+113.65E+05
Dentistry12,3452.262.981.64E+132,329
Dermatology30,5312.253.384.22E+137,801
Developmental psychology7,3031.751.901.39E+123,588
Ecology5,7301.711.686.89E+122,605
Economics3,0481.621.676.71E+114,693
Education1,2011.26.843.75E+101.11E+06
Educational psychology3,0321.701.555.97E+121,668
Environmental science2,4471.421.173.44E+113.25E+04
Ergonomics3,3091.34.902.81E+123.20E+04
Ethics1,0731.651.782.41E+121,571
Ethnic studies20031.471.382.04E+122.01E+04
Finance3,0192.142.526.05E+121,663
Forestry12,2111.821.804.47E+066,098
Genetics16,5741.712.181.83E+131.45E+04
History6,7081.54.979.04E+091.78E+04
Hospitality1,6841.381.001.85E+112.23E+04
Industrial relations1,5041.34.836.00E+127,136
Intl. relations1,4831.653.092.21E+112.19E+05
Law1,3501.551.246.09E+112,570
Linguistics3,6001.731.783.35E+103,058
Material sciences24,7231.762.423.71E+132.24E+04
Mathematics3,9721.451.023.64E+131.06E+04
Medical ethics2,9281.923.212.10E+124,982
Parasitology11,6671.782.121.27E+137,650
Pharmacology11,6541.541.683.44E+136.76E+04
Physics1,3731.18.737.25E+094.74E+05
Public administration3,4731.731.732.12E+132,408
Radiology27,1462.252.881.59E+135,184
Rehabilitation5,6611.501.525.76E+133.78E+04
Rheumatology6,6651.481.252.89E+132.86E+04
Robotics5,0211.922.177.39E+122,953
Social psychology4,4252.353.043.29E+121,171
Social work2,3571.451.161.84E+117,851
Sociology2,4171.811.495.60E+124,024
Sports medicine16,4121.792.081.25E+147,819
Statistics10,6792.082.524.32E+133,012
Substance abuse9,5131.781.952.45E+137,274
Thermodynamics9,8562.453.311.14E+131,882
Urban studies3,5481.33.835.39E+112.73E+04
Urology37,7612.252.999.90E+133.34E+04
Vet. science31,2241.902.133.34E+123.34E+04
Virology17,4802.252.884.94E+129,851
Water resources25,7572.433.797.28E+135,043
Women studies2,9821.261.005.39E+121.63E+05
Zoology14,7891.461.135.17E+126.17E+04
Weighted average   44,199,201,241,68123,888

Operationalization of individual performance.  Publication in top-tier journals is the most important antecedent of meaningful outcomes for faculty 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 the top five journals over the 9.5-year observation period. All authors of each article were recorded, and no differentiation was made based on authorship order.

Results

Results reported in Table 1 show that the Paretian distribution yielded a superior fit than the Gaussian distribution in every one of the 54 scientific 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 the misfit 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 in the order of 1:1.9 billion. Figure 2a displays a histogram of the empirically observed performance distribution of researchers. To interpret these results further, consider the field of Agriculture (see Table 1). A normal distribution and a sample size of 25,006 would lead to approximately 35 scholars with more than 9.5 publications (three standard deviations above the mean). In contrast, our data include 460 scholars with 10 or more publications. In other words, the normal distribution underestimates the number of extreme events and does not describe the actual distribution well.

image

Figure 2. Distribution of Individual Performance for Researchers (N= 490,185), Emmy Nominees (N= 5,826), United States Representatives (N= 8,976), NBA Career Scorers (N= 3,932), and Major League Baseball (MLB) Career Errors (N= 45,885).

Note. For all Y axes, “Frequency” refers to number of individuals. For clarity, individuals with more than 20 publications (Panel a) and more than 15 Emmy nominations (Panel b) were included in the last bins. For panels c–e, participants were divided into 15 equally spaced bins.

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Discussion

We tested whether the distribution of research performance best fits a Gaussian distribution or a Paretian distribution. Results based on chi-square statistics and a comparison of Figure 2a with Figure 1 provide evidence that the performance of researchers follows a Paretian distribution.

Study 2

  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES

Method

Overview.  A potential limitation of Study 1 is that performance (i.e., successful publication) was assessed by a single individual: a journal editor. Even if editors rely heavily on the opinion of associate editors and reviewers, the decision to publish each article has been made by a very small number of individuals in each case (i.e., typically an action editor and two or three reviewers). Moreover, there is evidence regarding the low reliability (i.e., consistency across reviewers) in the peer review process (Gilliland & Cortina, 1997). Therefore, it is possible that the job performance distribution of researchers is idiosyncratic enough to challenge the notion that it generalizes to other types of workers. Accordingly, we conducted Study 2 to expand the generalizability of these findings and test whether a different industry with different performance metrics and larger number of raters involved would confirm results from Study 1. In Study 2, we examined the performance of 17,750 individuals in the entertainment industry, with performance rated by a large voting body or more objective performance measures such as the number of times an entertainer 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 entertainers, we completed the following steps. First, we generated a list of the different forms of entertainment and determined that motion pictures, music, literature, and theater would serve as the population of interest given the availability of data. Second, we consulted several individuals within the film and music industries to help identify well-known (e.g., Oscars, Grammys) as well as lesser-known and more industry-specific awards (e.g., Edgar Allen Poe Award for mystery writing). Third, we proceeded with data collection by searching Web sites for relevant data. When data were not available online, we contacted the organization that distributes the awards for more detailed information. We identified more than 100 potential entertainment awards, but incomplete records and award limits (i.e., certain awards limit the number of times a recipient can win) reduced the number of qualified groups. Because a small group of awardees could diverge from normality due to either sampling error or true divergence from normality, we stipulated that a group must consist of at least 100 individuals in order to qualify for inclusion. Forty-two (42) awards and honors met our inclusion criteria (see Table 2).

Table 2.  Distribution of Individual Performance of Entertainers: Fit With Gaussian vs. Paretian Distributions
SampleNMeanSDData collection time frameGaussian (χ2)Paretian (χ2)Performance operationalization and comments
  1. Note. ACE = Award for Cable Excellence, AVN = Adult Video News, MTV = Music Television, PEN = poets, playwrights, essayists, editors, and novelists, NYT=New York Times, TV = television, nom = nominations.

AVN nom. actor1321.831.362008480  160AVN nominations across a wide variety of
AVN nom. actress2451.771.3820081.03E+04  251 categories counted towards the
AVN nom. actor1351.821.6620094.29E+04   78 performance total
AVN nom. actress3021.821.5020093.61E+07  153 
AVN nom. director1081.521.2020091.42E+08  187 
Cable ACE nom. actor1151.23.551978–19974,212  945Nominees for best director or acting role
Cable ACE nom. actress1041.21.591978–19976,3924,685 
Country Music Awards nom.1061.841.491967–20097.89E+05   52Ratings for Best Male or Female Vocalist
Edgar Allen Poe Awards nom.12115.0710.401954–2009147   53Expert rankings in Best Novel category
Emmy nom. Actor6852.862.741949–20095.49E+07  173Nomination to any category and an artist
Emmy nom. Actress4422.492.331949–20091.41E+06  110 can obtain multiple nominations in the
Emmy nom. Art direction8661.822.371949–20094.26E+101,097 same year. The nomination process
Emmy nom. Casting1932.162.011949–20092.46E+05   51 combines a popular vote with volunteer
Emmy nom. Choreography1271.711.541949–20094.93E+05  140 judging panels
Emmy nom. Cinematography5881.681.431949–20091.57E+07  387 
Emmy nom. Direction3951.952.071949–20091.01E+08   92 
Emmy nom. Editing9421.891.771949–20093.83E+13  614 
Emmy nom. Lighting1313.023.551949–20092.51E+05   29 
Emmy nom. Writing1,4572.462.721949–20093.10E+09  356 
Golden Globe nom. actor3922.072.021944–20092.38E+09  111Nomination to any category and an artist
Golden Globe nom. actress4152.052.061944–20092.14E+08  123 can obtain multiple nominations in the
Golden Globe nom. direction156 1.94 1.531944–20091.19E+0495 same year. The Hollywood Foreign
Golden Globe nom. TV actor375 2.12 1.781944–20097.25E+04203 Press Association rates and votes on the
Golden Globe nom. TV actress354 2.19 1.791944–20093.27E+04234 nominees
Grammy nom.3313 2.02 2.781959–20093.82E+121,307Nomination to any category
Man Booker Prize Fiction nom.283 1.35  .841969–20093.62E+052,018Expert rankings in Best Novel category
MTV VMA nom.561 3.98 5.581984–20091.37E+0778Fan voting and industry ratings
NYT Best Seller fiction222 2.42 3.851950–20094.54E+08219Each appearance on the New York Times
NYT Best Seller nonfiction419 1.19  .651950–20092.71E+066.20E+04 Bestseller list
Oscar nom. actor421 1.84 1.621927–20093.34E+11177Nominations as determined by Academy
Oscar nom. art direction531 2.64 3.751927–20098.10E+0894 members using a preferential-voting
Oscar nom. direction199 1.97 1.601927–20091.57E+0676 system for best director and nominees
Oscar nom. Actress432 1.80 1.501927–20094.07E+07289 in a primary or supporting acting role
Oscar nom. cinematography159 1.91 1.561927–20095.67E+0684 
PEN award voting12514.5511.451976–2009229521Nomination in any category (e.g., drama)
Pulitzer Prize nom. drama121 1.26  .751917–20092.00E+063711Selection to finalist for the drama category
Rolling Stone Top 500 albums261 1.90 1.521940–20091.78E+06137Number of appearances on the Top 500
Rolling Stone Top 500 songs247 2.02 2.191940–20091.27E+0875 list as rated by contributors and writers
Tony nom. actress583 1.59 1.181947–20093.91E+08817Nominations determined by a panel of
Tony nom. choreography108 2.10 2.101947–200944593 judges from entertainment industry
Tony nom. actor642 1.43  .941947–20091.77E+082,056 
Tony nom. director237 1.86 1.701947–20091.00E+12133 
Weighted average    2,769,315,505,4762,092 

Operationalization of Individual Performance.  Award nominations (Oscars, Emmys), expert rankings (Rolling Stone), and appearances on a best seller list such as the New York Times Best Seller List all served as measures of individual performance. These types of performance measures either are based on expert opinions (e.g., music critics) or peer voting (e.g., Oscars). Although the number of nominations a performer receives is a count variable, these counts encapsulate ratings and may better conform to traditional subjective ratings such as those most typically found in traditional OBHRM research (Landy & Farr, 1980).

Results

Table 2 shows results that are very similar to those in Table 1: The distribution of individual performance is substantially closer to a Paretian distribution than to a Gaussian distribution for each of the 42 samples. The average misfit of the Gaussian distribution was more than 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 these results better, consider the Grammy nominations under an assumption of normality. Of the 3,313 individuals nominated for a Grammy, only 5 should be three standard deviations above the mean with more than 10 nominations. In contrast, our data include 64 entertainers with more than 10 nominations. As in Study 1, the normal curve does not describe the actual distribution well.

Discussion

Results of Study 2 closely matched those of Study 1. Entertainers’ performance better fits a Paretian distribution than a Gaussian distribution. These findings across a variety of entertainment industries and with multiple performance operationalizations provides further evidence regarding the robustness of the Paretian distribution as the better model of individual performance compared to a normal distribution. As an illustration, Figure 2b displays the overall distribution of the largest sample of entertainers, Emmy nominees. This histogram illustrates that the empirically derived distribution aligns with a Paretian distribution (cf. Figure 1).

Study 3

  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES

Method

Overview.  In Study 3, we examined the distribution of performance of politicians. Study 3 includes a set of performance raters that is even more inclusive compared to those in Study 2: All citizens eligible to vote in a given political jurisdiction. In Study 3 we examined the performance of candidates (i.e., being elected or reelected) running for elective offices at the state (e.g., legislature of the state of Oregon in the U.S.) and national levels (e.g., Dutch Parliament). We included the performance of 42,745 candidates running for office in 42 types of elections in Australia, Canada, Denmark, Estonia, Finland, Holland, Ireland, New Zealand, the United Kingdom, and the U.S.

Procedure.  We identified elected officials through national and state Web sites. We first constructed a list of 195 nations, 50 U.S. states, 10 Canadian provinces, and 6 Australian territories to serve as potential sources of data. The search began at the national level, and we eliminated nations without a democratic form of government such as absolute monarchies (e.g., Saudi Arabia), theocracies (e.g., Vatican City), and one-party nations (e.g., Cuba). Next, offices with term limits or lifetime appointments were excluded as the results would be artificially truncated at the maximum number of terms an individual could serve. For this reason, we eliminated most executive and judicial branches of government, thus leaving legislatures as the primary source of data. For the remaining potential data sources, we searched for a complete list of current and past members in each country, state, and province. Lists of current members were available for nearly all governments, but relatively few governments made past members or the dates that current members were first elected available. For example, the reporting of past members for the Australian legislature was intermittent, therefore a complete list of members was not available. However, a complete list of present members and their original election to office, as well as a complete list of the most recent legislature that contained no current members (1969), were also available. Because these two groups had no overlap, we included them separately in the database. As in Study 2, we limited our search to groups that contained at least 100 individuals. We identified 42 samples from state and national governing bodies. Table 3 includes descriptive information about each of these samples.

Table 3.  Distribution of Individual Performance of Politicians: Fit With Gaussian vs. Paretian Distributions
SampleNMeanSDData collection time frameGaussian (χ2)Paretian (χ2)
  1. Note. UK = United Kingdom, US = United States, Bruns = Brunswick, Leg = Legislature, Mass = Massachusetts, Par = Parliament, S = South, N = North.

Alabama Leg.10411.438.47200979  157
Australia House1288.578.10196922  164
Australia House15310.466.842009122  119
Canadian Leg.4,0592.651.871867–20091.06E+071.05E+04
Connecticut Leg.1519.896.31200928  249
Denmark Par.17710.417.392009167  354
Dutch Par.1505.323.9020091.01E+05  184
Estonia Par.1002.001.112009225  167
Finland Par.2009.397.742009293  229
Georgia House1794.803.892009333   96
Illinois Leg.1209.966.48200960  220
Iowa Leg.1006.744.89200942   11
Ireland Par.1,1473.993.151919–200929701,443
Ireland Senate7162.401.951919–20092.06E+04  809
Kansas House5,6752.722.9420096.53E+125,636
Kansas Senate1,2094.013.341812–20093.76E+071,171
Kentucky Leg.1005.064.04200982   57
Louisiana House3,4681.931.971812–20092.09E+126,128
Maine Leg.1532.582.0620092.44E+09   24
Maryland Leg.1419.427.632009212  165
Mass. House1609.826.882009113  205
Minnesota House1344.313.662009387   47
Missouri Leg.1634.702.192009921  571
New Bruns. Par.1,1362.241.521882–20097,9332,855
New York Association14811.618.94200976193
New Zealand Leg.1228.057.492009120126
N. Carolina Association1244.633.38200968141
Nova Scotia Leg.4143.011.261867–20092,096539
Oklahoma Leg.1014.702.67200998254
Ontario Leg.1,8794.563.301867–20091.62E+055,539
Oregon Leg.3774.473.811858–20092654108
Oregon Senate1615.454.441858–2009159794
Pennsylvania House20010.769.182009269141
Quebec Leg.3993.522.401867–2009697583
S. Carolina House1258.236.44200987118
Tasmania Association5423.112.351856–20094742442
Tennessee House1005.224.10200913463
UK Par.7,2143.412.591801–20094.32E+091.70E+04
US House8,9763.423.231789–20096.39E+081.43E+04
US Senate1,8409.147.791789–20092.42E+043,264
Virginia Association10011.098.26200949796
Wisconsin Leg.1008.116.99200930989
Weighted average    1,037,389,925,0138,692

Operationalization of individual performance.  As stated earlier, elected official performance was operationalized by an individual's election to office. In most cases, this was established as the number of times a person's name appeared on each new session of the legislature. In cases where only the current legislature was available, the length of service was recorded (either days or years in office) and used as a measure of performance. Thus, this type of performance measure is essentially based on ratings—those provided by eligible voters in any given political district.

Results

Results included in Table 3 indicate that the data fit a Paretian distribution better than a Gaussian distribution for 31 of the 42 samples. The average fit strongly favored the Paretian (misfit of 8,692) versus the Gaussian distribution (misfit of over one trillion). Using the U.S. House of Representatives as an example, the normal distribution suggests that of the 8,976 individuals to have served in the House, no more than 13 representatives should be three standard deviations above the mean (i.e., serve more than 13 terms). Contrary to the expectation based on the normality assumption, 173 U.S. Representatives have served more than 13 terms.

Discussion

Results suggest that the individual performance of politicians follows a Paretian distribution more closely than a normal distribution. Specifically, the data fit a Paretian distribution more closely than a normal distribution in 74% of the samples we studied. Figure 2c illustrates the shape of the observed performance distribution for the largest sample in Study 3, the U.S. House of Representatives. One reason why the superior fit for a Paretian distribution was not seen in all samples may be that the established frequency of elections prevents superstar performers to emerge in the same way as they do in other industries like those we examined in Studies 1 and 2. We speculate that this may be a result of the measure of performance not being as sensitive and discriminating regarding various levels of performance compared to the measures of performance we used in Studies 1 and 2. Performance in Study 3 was binary with the legislator either returning to office with a simple majority vote or being ousted by another also by a simple majority vote. Therefore, an incumbent who does just enough to be reelected (e.g., victory margin of 1%) receives the same performance “score” as an extraordinary incumbent (e.g., victory margin of 25%). Nevertheless, on average, the difference in fit favored the Paretian distribution in the order of 1:119 million.

Study 4

  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES

Method

Overview.  In Study 4 we investigated the performance of athletes in collegiate and professional sports. Study 4 presents additional evidence to supplement Studies 1–3 because many of the measures of performance are more objective, they rely more heavily on measures of physical performance, and depend more strongly on the individual (see Table 4).

Table 4.  Distribution of Positive Individual Performance of Athletes: Fit With Gaussian vs. Paretian Distributions
SportNMeanSDData collection time frameGaussian (χ2)Paretian (χ2)Performance operationalization and comments
  1. Note. EPL = English Premier League, ERA = Earned run average, HR = Homeruns, MLB = Major League Baseball, NASCAR = National Association for Stock Car Auto Racing, NBA = National Basketball Association, NCAA = National Collegiate Athletic Association. NFL = National Football League, NHL = National Hockey League, PBA = Professional Bowling League, PGA = Professional Golf Association, TD = touchdowns, yd = yards.

MLB career strike outs1,0011103.67563.261900–20066.00E+11  91A variety of metrics of positive
MLB career HR1,004174.00109.441900–20064850  89 behaviors for players and managers
MLB career mgr wins647301.02450.901900–20063630 480 
NCAA Div 1-1/ERA516.25.0720095.26E+09  59A variety of metrics of positive
NCAA Div 1-HR54811.573.762009959 211 behaviors for baseball players only
NCAA Div 2-1/ERA300.31.1120092770  17 
NCAA Div 2-HR38310.263.6620095.08E+03  92 
NCAA Div 3-1/ERA500.31.1220099.69E+07  25 
NCAA Div 3-HR4247.272.9120095.08E+06  87 
NCAA pass. TDs19311.6510.412009279 171A variety of metrics of positive
NCAA rushing529407.56444.682009788 958 behaviors for football players only
NCAA WR yd.798299.09294.0320091100 649 
NCAA TE yd.297146.84190.7320091.20E+06 301 
NCAA sacks9922.552.2320095.85E+041081 
Cricket runs2524279.482205.771909–2009239  52Top 200 cricketers in runs/wickets
Cricket wickets150201.55117.841909–20091830  15 
EPL goals1,52110.9019.721992–20091.17E+12  96Number of goals scored
NBA coaches wins258183.15263.731946–20099.57E+05 147A variety of metrics of positive
NBA career points3,9322670.914308.441946–20092.62E+123517 behaviors for players and managers
PGA career wins20014.0512.621916–20092.08E+04  34All time tournament wins
Men's swimming6541.781.381896–20098.08E+07 681Gold, silver, or bronze medal across an
Women's swimming5381.751.391896–20091.19E+06 773 entire career
Men's track9811.34.761896–20094.42E+095058 
Women's track4371.45.941896–20091.41E+08943 
Men's alpine1671.46.941896–20091.10E+08265 
Women's alpine1481.64.981896–2009791198 
PBA titles2004.956.701959–20091.43E+0647All time tournament wins
NASCAR points1251138.411410.472009262119Points earned in the Sprint Cup series
NFL coaches wins41331.2546.641999–20091.19E+07104A variety of metrics of positive
NFL kick return yd.2503238.431698.951999–20092.67E+0629 behaviors for players and managers
NFL TD receptions25350.9220.591999–20092.29E+0841 
NFL field goals252110.61108.691999–2009683118 
NFL sacks25159.3828.431999–2009924037 
NFL rushing yd.2505611.012708.461999–200912720 
NFL passing yd.25016897.2011431.101999–2009312112 
NHL defense assists1,533107.12165.481917–20094.96E+09909Points scored for all NHL players
NHL centers points1,213191.55300.871917–20093.64E+05708 across their careers
NHL right wing points1,073162.36246.821917–20095.11E+07537 
NHL left wing points1,102141.81210.361917–20092.32E+06640 
NHL goalies saves3923497.994848.021917–20091650526 
Men's tennis1462.942.801877–2009108041Grand Slam tournament wins across an entire career
Women's tennis1103.684.371877–2009114029 
NCAA basketball100615.2175.0220091428Points scored for a single season
Weighted average    502,193,974,1891,076 

Procedure.  We compiled a list of individual and team sports at the collegiate and professional levels. We accessed each Web site that hosted the sport (e.g., MLB.com) and downloaded the necessary statistics from each database. In all cases, we were able to find the necessary data for the chosen sports for at least one complete season. In most cases, we collected data from multiple years, and we were able to record all players, but in some cases, only the top players were available (e.g., only the top 1,000 MLB pitchers were available).

Operationalization of individual performance.  We attempted to identify the most individual-based measures of performance. For instance, runs batted (RBI) in baseball are both a function of a hitter's prowess and the ability of those batting before him. Therefore, a less contaminated measure for baseball is home runs. For individual sports such as golf and tennis, we chose the total numbers of wins, but team sports required a different operationalization. For sports such as soccer and hockey, we used goals or points as the performance metric, and for position-oriented sports like U.S. football we used receptions, rushing yards, and touchdowns.

Results

Results summarized in Table 4 indicate that the distribution of individual performance follows a Paretian distribution more closely than a Gaussian distribution. In addition, we examined the distribution of performance within teams and for a more limited time period rather than across organizations and careers. This helps rule out the possibility that our results are due to analyses across organizations and careers that may accentuate the preponderance of outliers. We examined the most recent season (2009–2010) for teams in the English Premier League (goals), Major League Baseball (homeruns and strikeouts), and National Hockey League (points). The 94 samples (N= 1,797) for these analyses are considerably smaller, ranging from 9 to 30 athletes, thus making sampling error a limitation. However, in 84 of these 94 comparisons, chi-square statistics provided evidence regarding the superior fit of the Paretian distribution.

Discussion

Across a variety of sports, nationalities, and levels of play, the Paretian distribution yielded a significantly better fit than the Gaussian distribution. In all but one sample, the performance distribution favored a power law more strongly than a normal distribution. Moreover, the sports and types of athletic performance included in Study 4 vary regarding the extent to which an individual performer participated in a team or individual sport, and we also conducted within-team and within-season analyses. The overall weighted mean chi-square statistic for the Paretian distribution is about 466 million times smaller (i.e., indicating better fit) compared to a Gaussian distribution. Figure 2d illustrates these results in a histogram of Study 4's largest sample: National Basketball Association (NBA) career points.

Study 5

  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES

Method

Overview.  Studies 1–4 focused on positive performance (e.g., publications, awards). However, the Paretian distribution possesses a greater frequency of extreme values at both ends of the distribution. If individual performance is truly Paretian, then both sides of the performance distribution should contain a disproportionate number of individuals. Our decision to conduct Study 5 focusing on negative performance was also motivated by an increased interest in counterproductive work behaviors (CWBs), such as abusive supervision (Tepper, Henle, Lambert, Giacalone, & Duffy, 2008), employee theft (Greenberg, 2002), and workplace bullying (Salin, 2003).

The challenge to investigating the negative performance distribution is that, unlike positive performance, negative performance is often covert. Even in industries where performers are under constant scrutiny, a considerable number of negative behaviors occur without the knowledge of others. A researcher that forges his data, an actor hiding a drug addiction, and a politician accepting bribes are all behaviors that certainly qualify as negative, but quantifying their frequency is difficult. Complicating matters further, negative performance can be done intentionally (e.g., consuming alcohol while working) or unintentionally (e.g., accidentally breaking the office printer).

Procedure.  To identify the distribution of negative performance, we used samples from collegiate and professional sports. We examined the distribution of negative performance such as English Premier League yellow cards, NBA career turnovers, and Major League Baseball first-base errors. The negative performance behaviors vary in their intent, severity, and frequency, but they are similar in that they are all detrimental to the organization. Using samples from sports allows for an objective examination of negative performance that would be virtually impossible to capture in industries in which performance is not measured so systematically and with more ambiguous definitions of what constitutes positive and negative performance. Study 5 included 17 types of negative performance of 57,300 individual athletes in six sporting disciplines (see Table 5).

Table 5.  Distribution of Negative Individual Performance of Athletes: Fit With Gaussian vs. Paretian Distributions
SampleNMeanSDData collection time frameGaussian (χ2)Paretian (χ2)Performance operationalization and comments
  1. Note. 1B = first basemen, 2B = second basemen, 3B = third basemen, C = catchers, EPL = English Premier League, OF = outfielders, MLB = Major League Baseball, NBA = National Basketball Association, NFL = National Football League, NCAA = National Collegiate Athletic Association, tech/flag = technical or flagrant foul, NHL = National Hockey League, PGA = Professional Golf Association, SS = shortstops.

MLB hit batters in a single season1,00751.5426.461900–20061.02E+0565Errors assigned for MLB players
MLB 1B errors in a single season5,9335.665.751900–20062.41E+064,097 
MLB 2B errors in a single season6,4008.058.741900–20062.32E+061,534 
MLB 3B errors in a single season7,0998.018.551900–20061.53E+073345 
MLB C errors in a single season6,2765.464.731900–20064.59E+096973 
MLB OF errors in a single season13,7214.273.811900–20066.57E+112.36E+04 
MLB SS errors in a single season6,45611.9813.551900–20065.19E+063043 
EPL yellow cards1,8769.7812.261992–20094.73E+06442Yellow cards administered
NBA career turnover2,691427.94604.021946–20093.15E+072487A variety of metrics of negative
NBA career tech, flag, and ejections4328.8410.3320091.96E+09109 behaviors for players
NFL fumbles25155.2823.191999–2009203026A variety of metrics of negative
NFL interceptions253102.7460.761999–200914172 behaviors for players
NHL defense penalty minutes1,505368.67460.311917–20097.49E+061580Penalty minutes received for all
NHL centers penalty minutes1,129216.84329.991917–20098.38E+06546NHL players across their careers
NHL right wing penalty minutes1,015288.89466.391917–20099.02E+07567 
NHL left wing penalty minutes1,053286.61449.411917–20097.13E+11605 
NCAA thrown interceptions2027.024.6120099745Quarterbacks only
Weighted average    170,951,462,7857,975 

Operationalization of individual performance.  We attempted to identify negative behaviors that were primarily attributable to an individual performer. For instance, an incomplete pass in U.S. football can be either a failure of the quarterback or a failure of the receiver, but an interception is primarily viewed as a quarterback error. We identified four sports for which negative performance can largely be attributed to one individual. We contacted several individuals that currently or formerly participated in these sports at an elite level (received an NCAA scholarship or played professionally) to serve as subject matter experts and ensure that our classifications were acceptable. When possible, we divided the sport into individual positions. This was done because some negative performance behaviors 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 keeping with our focus on performance measures that lead to important outcomes, we chose negative performance that is most likely to result in meaningful consequences for the athlete (e.g., fines, suspensions, losing sponsorships, being cut from a team).

Results

Results regarding the distribution of negative performance of athletes are included in Table 5. Each of the samples fitted a Paretian distribution better than a Gaussian distribution. The average misfit of the Paretian distribution was only 7,975 whereas the average misfit of the normal distribution exceeded 170 billion. Similar to Study 4, we conducted within-team, within-season analyses to rule out a potential longevity confounding effect. We used EPL yellow cards, MLB hit batters, and NHL penalty minutes 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 performance distributions investigated in Studies 1–4. The distribution of negative performance more closely resembles a power law compared to a normal distribution. We found this same result regarding every one of the 17 samples including a variety of negative performance behaviors and across several types of sports including baseball, hockey, basketball, and non-U.S. football. As an illustration, Figure 2e includes a histogram for Study 5's largest sample: MLB errors. The within-team, within-season analyses further supported the Paretian distribution of performance output.

General Discussion

  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES

Theories and practices about performance, personnel selection, training, leadership, and many other domains in OBHRM are firmly rooted in the “norm of normality” where individual performance follows a normal distribution and deviations from normality are seen as “data problems” that must be “fixed.” Although some may be skeptical regarding this norm of normality, there is little evidence that this belief has affected theoretical developments or application in an influential way. This norm has developed many decades ago and, to our knowledge, has not been tested systematically and comprehensibly. Individual performance serves as a building block not only for OBHRM and I-O psychology but for most organizational science theories and applications. Thus, understanding the distribution of individual performance is a key issue for organizational science research and practice.

Our central finding is that the distribution of individual performance does not follow a Gaussian distribution but a Paretian distribution. Our results based on five separate studies and involving 198 samples including 633,263 researchers, entertainers, politicians, and amateur and professional athletes are remarkably consistent. Of a total of 198 samples of performers, 186 (93.94%) follow a Paretian distribution more closely than a Gaussian distribution. If, as our results suggest, most performance outcomes are attributable to a small group of elite performers, then both theory and practice must adjust to the substantial role played by these individuals. Next, we discuss implications of our findings for theory and substantive research; research methodology; and practice, policy making, and society.

Implications for Theory and Substantive Research

Our results have important implications for past and future research in substantive domains in OBRHM, I-O psychology, and other fields concerned with individual performance (e.g., strategy, entrepreneurship). We limit our discussion to key areas identified as being among the most popular in OBHRM over the past 45 years (Cascio & Aguinis, 2008a): performance measurement and management, utility analysis in preemployment testing and training and development, leadership and teamwork, and the understanding and prediction of performance.

Regarding performance measurement and management, the current zeitgeist is that the median worker should be at the mean level of performance and thus should be placed in the middle of the performance appraisal 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). Performance appraisal instruments that place most employees in the lowest category are seen as psychometrically unsound. These basic tenets have spawned decades of research related to performance appraisal that might “improve” the measurement of performance because such measurement would result in normally distributed scores given that a deviation from a normal distribution is supposedly indicative of rater bias (cf. Landy & Farr, 1980; Smither & London, 2009a). Our results suggest that the distribution of individual performance is such that most performers are in the lowest category. Based on Study 1, we discovered that nearly two thirds (65.8%) of researchers fall below the mean number of publications. Based on the Emmy-nominated entertainers in Study 2, 83.3% fall below the mean in terms of number of nominations. Based on Study 3, for U.S. representatives, 67.9% fall below the mean in terms of times elected. Based on Study 4, 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 the mean in terms of career errors. Moving from a Gaussian to a Paretian perspective, future research regarding performance measurement would benefit from the development of measurement instruments that, contrary to past efforts, allow for the identification of those top performers who account for the majority of results. Moreover, such improved measurement instruments should not focus on distinguishing between slight performance differences of non-elite workers. Instead, more effort should be placed on creating performance measurement instruments that are able to identify the small cohort of top performers.

As a second illustration of the implications of our results, consider the research domain of utility analysis in preemployment testing and training and development. Utility analysis is built upon the assumption of normality, most notably with regard to the standard deviation of individual performance (SDy), which is a key component of all utility analysis equations. 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 products and services produced by the average employee and those produced by 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 a Paretian distribution of job performance make in the calculation of SDy? Consider the distribution found across all 54 samples in Study 1 and the productivity levels in this group at (a) the median, (b) 84.13th percentile, (c) 97.73rd percentile, and (d) 99.86th percentile. Under a normal distribution, these values correspond to standardized scores (z) of 0, 1, 2, and 3. The difference in productivity between the 84.13th percentile and the median was two, thus a utility analysis assuming normality would use SDy= 2.0. A researcher at the 84th percentile should produce $11,327 more output than the median researcher (adjusted for inflation). Extending to the second standard deviation, the difference in productivity between the 97.73rd percentile and median researcher should be four, and this additional output is valued at $22,652. However, the difference between the two points is actually seven. Thus, if SDy is two, then the additional output of these workers is $39,645 more than the median worker. Even greater disparity is found at the 99.86th percentile. Productivity difference between the 99.86th percentile and median worker should be 6.0 according to the normal distribution; instead the difference is more than quadruple that (i.e., 25.0). With a normality assumption, productivity among these elite workers is estimated at $33,981 ($11,327 × 3) above the median, but the productivity of these workers is actually $141,588 above the median. We chose Study 1 because of its large overall sample size, but these same patterns of productivity are found across all five studies. In light of our results, the value-added created by new preemployment tests and the dollar value of training programs should be reinterpreted from a Paretian point of view that acknowledges that the differences between workers at the tails and workers at the median are considerably wider than previously thought. These are large and meaningful differences suggesting important implications of shifting from a normal to a Paretian distribution. In the future, utility analysis should be conducted using a Paretian point of view that acknowledges that differences between workers at the tails and workers at the median are considerably wider than previously thought.

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), has traditionally focused on the “average worker” and how best to improve a group's mean performance. Leadership theories grounded in Gaussian thinking focus on the productivity of the majority of workers rather than the workers responsible for the majority of productivity. Given a normal distribution, 68% of output should derive from the individuals located between the 16th percentile and 84th percentile. With so much of the total output produced by workers around the median, it makes sense for leaders to focus most of their energy on this group. However, if performance follows 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 workers between the 2.5th and 97.5th percentiles in a normal distribution. However, using the distribution found in Study 1, only 81% of output comes from this group of workers. With less output from the center of the distribution, more output is found in the tails. Ten percent of productivity comes from the 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 the need to revise leadership theories to address the exchanges and influence of the extreme performers because our results demonstrate that a small set of followers produces the majority of the output. Leadership theories that avoid how best to manage elite workers will likely fail to influence the total productivity of the followers in a meaningful way. Thus, greater attention should be paid to the tremendous impact of the few vital individuals. Despite their small numbers, slight percentage increases in the output of top performers far outweigh moderate increases of the many. New theory is needed to address the identification and motivation of elite performers.

In addition to the study of leadership, our results also affect research on work teams (e.g., group empowerment, shared efficacy, team diversity). Once again, our current understanding of the team and how groups influence performance is grounded in an assumption of normality. The common belief is that teamwork improves performance through increased creativity, 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 how the presence of an elite worker influences group productivity. We may expect the group productivity to increase in the presence of an elite worker, but is the increase in group output negated by the loss of individual output of the elite worker being slowed by non-elites? It may also be that elites only develop in interactive, dynamic environments, and the isolation of elite workers or grouping multiple elites together could hamper their abnormal productivity. Once again, the finding of a Paretian distribution of performance requires new theory and research to address the elite nested within the group. Specifically, human performance research should adopt a new view regarding what human performance looks like at the tails. Researchers should address the social networks of superstars within groups in terms of identifying how the superstar emerges, communicates with others, interacts with other groups, and what role non-elites play in the facilitating of overall performance.

At a more fundamental level, our understanding of job performance itself needs revisiting. Typically, job performance is conceptualized as consisting of three dimensions: in-role or task behavior, organizational citizenship behavior (OCB), and CWB (Rotundo & Sackett, 2002). CWB (i.e., harmful behaviors targeted at the organization or its members) has always been assumed to have a strong, negative relation with the other two components, but it is unclear if this relationship remains strong, or even negative, among elite performers. For example, the superstars of Study 4 often appeared as supervillains in Study 5. Do the most productive workers also engage in the most destructive behavior? If so, future research should examine if this is due to managers’ fear of reprimanding a superstar, the superstar's sense of entitlement, non-elites covering for the superstar's misbehavior out of hero worship, or some interaction of all three.

Finally, going beyond any individual research domain, a Paretian distribution of performance may help explain why despite more than a century of research on the antecedents of job performance and the countless theoretical models proposed, explained variance estimates (R2) rarely exceed .50 (Cascio & Aguinis, 2008b). It is possible that research conducted over the past century has not made important improvements in the ability to predict individual performance because prediction techniques rely on means and variances assumed to derive from normal distributions, leading to gross errors in the prediction of performance. As a result, even models including theoretically sound predictors and administered to a large sample will most often fail to account for even half of the variability in workers’ performance. Viewing individual performance from a Paretian perspective and testing theories with techniques that do not require the normality assumptions will allow us to improve our understanding of factors that account for and predict individual performance. Thus, research addressing the prediction of performance should be conducted with techniques that do not require the normality assumption.

Implications for Research Methodology

What are the consequences of using traditional Gaussian-based techniques with individual performance data that follow a Paretian distribution? A basic example is a test of differences in means (e.g., independent group t-test) for some intervention where individuals are randomly assigned to groups. The assumption is that, given sufficient group sizes, no one individual will deviate from the mean enough to cause a significant difference when there is none or vice versa (Type I and Type II errors). However, random assignment will only balance the groups when the distribution of the outcome is normally distributed (when the prevalence of outliers is low). In the case of Paretian distributions, the prevalence of outliers is much higher. As a result, a single high performer has an important impact on the mean of the group and ultimately on the significance or nonsignificance of the test statistic. Likewise, the residual created by extreme performers’ distance from a regression line widens standard errors to create Type II errors. Interestingly, the wide standard errors and unpredictable means caused by extreme performers should result in great variability in findings in terms of both statistical significance and direction. This may explain so many “inconsistent findings” in the OBHRM literature (Schmidt, 2008). Based on the problems of applying Gaussian techniques to Paretian distribution, our first recommendation for researchers examining individual performance is to test for normality. Paretian distributions will often appear highly skewed and leptokurtic. In addition to basic tests of skew and kurtosis, additional diagnostics such as the chi-square test used in the present studies should be incorporated in the data screening stage of individual performance.

Along with testing for normality, our results also suggest that the methodological practice of forcing normality through outlier manipulation or deletion may be misguided. Dropping influential cases excludes the top performers responsible for the majority of the output, and doing so creates a sample distribution that does not mirror the underlying population distribution. As such, sample statistics will bear little resemblance to population parameters. Samples that exclude outliers generalize only to those individuals around the median of the distribution. Therefore, our second recommendation for research methodology is to shift the burden of proof from outlier retention to outlier deletion/transformation. That is, influential cases should be retained in the data set unless there is clear evidence that their value is incorrect (e.g., typographical error) or belong to 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 squares regression, ANOVA, structural equation modeling, meta-analysis, and all techniques that provide accurate estimates only under a normal distribution assumption should not be used when the research question involves individual performance output. If researchers find that their data are not normally distributed, and they do not artificially truncate the distribution through outlier deletion, then this leaves the question of how to proceed with analysis. Paretian distributions require analytic techniques that are not common in OBHRM but nonetheless are readily available. Techniques exist that properly and accurately estimate models where the outcome is Paretian. Poisson processes are one such solution, and although not well established in OBHRM research, they do have a history in the natural sciences (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 theoretical assumptions that our results debunk (see Macy & Willer, 2002 for a review of ABM). ABM can be used to develop and test theories of superstars in the more fundamental context of autonomous agents independently and in conjunction with others, making decisions based on very simple rules (Bonabeau, 2002). The result is an understanding of performance based on dynamism instead of equilibrium, interdependent agents instead of independent automatons, and nonlinear change instead static linearity.

In addition, Bayesian techniques are likely to provide the greatest applicability to the study of superstars. Beyond moving away from null hypothesis significance testing, Bayesian techniques provide the additional benefit of dealing with the nonlinearity introduced by influential cases because they allow the underlying distribution to be specified a priori (Beyth-Marom & Fischhoff, 1983). Thus, a researcher can test hypotheses without having to assume normality or force it upon the data (Kruschke, Aguinis, & Joo, unpublished data). For example, one can specify that performance follows a Paretian distribution. Bayesian techniques are slowly being 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 methodological recommendation is the use of techniques that do not rely on the normality assumption.

Implications for Practice, Policy Making, and Society

Our results lead to some difficult questions and challenges in terms of practice, policy making, and societal issues because they have implications for discussions around equality and merit (Ceci & Papierno, 2005). There are several areas within OBHRM such as employee training and development and compensation that rely on the assumption that individual performance is normally distributed, and any intervention or program that changes this distribution is seen as unnatural, unfair, or biased (Schleicher, & Day, 1998). In evaluation, interventions are deemed successful to the extent that all those who go through them experience improved performance. But, if training makes the already good better and leaves the mediocre and poor performers behind, then this is usually seen as an indication of program faultiness. The Matthew effect (Ceci & Papierno, 2005; Merton, 1968) states that those already in an advantageous position are able to leverage their position to gain disproportionate rewards. It is disproportionate because the perception is that their inputs into a system do not equal the outputs they receive. Training programs that especially benefit elite performers are seen as unfair because they artificially alter the normal curve that is the “natural” distribution of performance. 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 performance and CEO compensation are an especially divisive issue, with many claiming that disproportionate pay is an indicator of unfair practices (Walsh, 2008). Such differences are seen as unfair because if performance is normally distributed then pay should be normally distributed as well.

Our results put the usual conceptions and definitions of fairness and bias, which are based on the norm of normality, into question and lead to some thorny and complicated questions from an ethical standpoint. How can organizations balance their dual goals of improving firm performance and also employee performance and well-being (Aguinis, 2011)? Is it ethical for organizations to allocate most of their resources to an elite group of top performers in order to maximize firm performance? Should separate policies be created for top performers given that they add greater value to the organization than the rest? Our results suggest that practitioners must revisit how to balance the dual goals of improving firm performance and employee performance and well-being as well as determine the proper allocation of resources for both elites and nonelites.

Beyond concepts of ethics and fairness, a Paretian distribution of performance has many practical implications for how business is done. As we described earlier, a Pareto curve demonstrates scale invariance, and thus whether looking at the entire population or just the top percentile, the same distribution shape emerges. For selection, this means that there are real and important differences between the best candidate and the second best candidate. Superstars make or break an organization, and the ability to identify these elite performers will become even more of a necessity as the nature of work changes in the 21st century (Cascio & Aguinis, 2008b). Our results suggest that practitioners should focus on identification and differentiation at the tails of the distribution so as to best identify elites.

Organizations must also rethink employment arrangements with superstars, as they will likely be very different from traditional norms in terms of starting compensation, perquisites, and idiosyncratic employment arrangements. Superstars perform at such a high level that makes them attractive to outside firms, and thus even in a recession these individuals have a high degree of job mobility. In an age of hypercompetitiveness, organizations that cannot retain their top performers will struggle to survive. At present, we know very little about the motivations, traits, and behaviors of elite performers. Our work indicates that superstars exist but does not address the motivations, behaviors, and individual differences of 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 retaining superstars and encourage practitioners to incorporate these literature streams into their work.

Potential Limitations and Suggestions for Future Research

We attempted to establish the shape of the individual performance distribution across a variety of settings and industries. Although we analyzed multiple industries and a variety of performance operationalizations, it is still possible that these samples do not generalize to other occupations. In addition, for the reasons described earlier, most of the data we used do not include performance measures as typically operationalized in I-O psychology research. We expand on these issues next.

Our results clearly support the superiority of the Paretian distribution compared 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 Gaussian distribution than a Paretian distribution. However, in Study 3 we found 11 samples favoring a Gaussian model. Note that given a total of 42 samples in Study 3, results still heavily favor a Paretian distribution (i.e., 74% of samples favored a Paretian distribution). However, a closer examination of results from Study 3 may provide some insights regarding conditions under which Gaussian distributions are likely to be found. We acknowledge the speculative nature of the material that follows, and we emphasize that, rather than conclusions, these should be seen as hypotheses and research questions that need to be addressed by future research.

Consider two measurement-related reasons for the potential better fit of a Gaussian distribution. First, a measure of performance may be too coarse to capture differences between superstars and the “simply adequate” (Aguinis, Pierce, & Culpepper, 2009). Specifically, in Study 3, performance was measured as whether an official was elected or not, and the measure did not capture differences among performers such as by how many votes an individual won or lost an election. So, industries and types of jobs for which performance is measured with coarse scales may lead to observed distributions that are Gaussian rather than Paretian. Second, consider situations in which there are constraints imposed on the ratings of performance. As described earlier, ratings of performance, particularly supervisory ratings, are one of the most popular ways to operationalize performance in I-O psychology research. These constraints can distort the shape of the underlying performance distribution when normality is introduced by the scale or rater evaluation training. In these cases, normality is likely to emerge in the observed data regardless of the true shape of the performance distribution.

Now, consider three situations and reasons why the underlying performance distribution, not just observed performance scores, may actually fit a Gaussian as opposed to a Paretian model. First, it may be the case that, in certain industries and certain job types, superstars simply do not emerge. For example, the manufacturing economy of the 20th century strove not only for uniformity of product but also uniformity of worker. Quotas, union maximums, assembly lines, and situational and technological constraints all constrained performance to values close to the mean. Even in jobs without these formal constraints, informal barriers (i.e., norms) existed in ways that limited the emergence of superstars. Productivity norms such as those found in the Hawthorne studies (Roethlisberger & Dickson, 1939) support a normal distribution of performance dependent on informal corrective actions of coworkers. Workers violating the established productivity norms were chastised, bullied, and ostracized into conforming to prescribed output levels. Hence, even organizations outside of the manufacturing sector where there are limited formal constraints to productivity may still fail to see the emergence of superstars and Paretian distributions.

In government, as is the case for the Study 3 samples, similar norms may lead to the curtailment of outliers, resulting in an observed distribution that is Gaussian rather than Paretian. Second, we also speculate that compared to the participants in the other studies, government officials as we had in Study 3 have fewer direct ties between performance and compensation. Pay raises in legislatures are generally voted on and applied equally across all members. Therefore, if a representative in the Alabama legislature wished to receive higher rewards (e.g., money, fame, power), she would either need to increase the compensation of all her fellow representatives or run for a more prestigious office. For samples in Study 3, all but one of those favoring a Gaussian distribution (the Danish Folketing) were lower houses of the legislative branch. Thus, superstar representatives may have quickly moved on to occupy higher-level and more prestigious positions such as becoming senators or governors. Finally, given the nature of work and organizations in the 21st century (Cascio & Aguinis, 2008b), we believe that the Paretian distribution will apply to an increasingly high number of industries, occupations, and jobs. However, industries and organizations that rely on manual labor, have limited technology, and place strict standards for both minimum and maximum production are likely to lead to normal distributions of individual performance. As we move into the 21st century, software engineers, consultants, healthcare workers, and educators make up an increasingly large part of the economy; but, for the foreseeable future, farmers, factory workers, and construction crews will continue to play an important role, and these types of jobs may best be modeled with a normal distribution (e.g., Hull, 1928; Tiffin, 1947). In short, we readily acknowledge that our results are circumscribed to the types of industries and performance operationalizations included in our five studies because these factors may serve as boundary conditions for our findings.

Our results point to the influential role of elite performers (i.e., superstars), which opens new research avenues for the future. First, although we know there are more superstars than a normal curve would suggest, exactly what percentage of workers can be considered superstars has not been established. The classification of superstars is a subjective judgment, and there are no norms to indicate what proportion of workers should be considered elite. Second, research is needed on the deleterious effects of superstars. For example, does the presence of a superstar demotivate other workers to such an extent that total organizational output decreases?

Finally, our research provides information on the performance distribution, but it does not examine what individual characteristics top performers possess nor did it investigate the stability of the top performing group. When and how do these individuals reach the elite group? What is the precise composition of this elite group—do individuals rotate in and out of this group, or once in the top group, they remain in the top for most of their career? What individual, group, and cultural factors predict an individual's membership in the top-performing group over time? Ultimately, certain individuals likely possess abilities and skills that increase the probability of extraordinary performance, but the interactive nature of performance and context suggests that environmental factors and other actors 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 there are others who take on some of their teaching and administrative duties. Hollywood stars emerge in part because of supporting casts on screen as well as off screen (e.g., agents, managers, publicists).

Concluding Remarks

Much like the general population, we, OBHRM researchers and practitioners, are not immune to “received doctrines” and “things we just know to be true” (Lance, 2011). These issues are “taught in undergraduate and graduate 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 and from generation to generation” (Lance, 2011: 281). We conclude that the norm of normality regarding individual performance qualifies to be such a received doctrine because, even when not explicitly stated, it permeates the theory, design, and analysis of OBHRM research as well as OBHRM practices. In contrast, based on five separate studies involving 198 samples including 633,263 researchers, entertainers, politicians, and amateur and professional athletes, our results indicate that individual job performance follows a Paretian distribution. Assuming normality of individual performance can lead to misspecified theories and misleading practices. Thus, our results have implications for all theories and applications in OBHRM and related fields (e.g., I-O psychology, strategic management, entrepreneurship) that directly or indirectly rely upon the performance of individual workers.

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  1. Top of page
  2. Abstract
  3. The Norm of Normality of Individual Performance
  4. The Paretian Distribution and Individual Performance
  5. The Present Studies
  6. Study 1
  7. Study 2
  8. Study 3
  9. Study 4
  10. Study 5
  11. General Discussion
  12. REFERENCES
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