Christopher X J. Jensen
Associate Professor, Pratt Institute

NPR drops dumb Bell Curve segment

Posted 03 May 2012 / 5

This morning, National Public Radio’s Morning Edition featured a segment entitled “Put Away The Bell Curve: Most Of Us Aren’t ‘Average’“. I am generally vigilant about stories which make broad claims about human traits and their genetic and environmental underpinnings, and this particular segment triggered my alarms to scream. Analyzing a new study on “academics writing papers, athletes at the professional and collegiate levels, politicians and entertainers”, the NPR segment more-than-just suggested that the bell curve representation of our abilities may be wrong. Given the history of the bell curve as a political tool, perhaps the editors at NPR thought this might be a nice counter to conventional wisdom. But how they interpret this study is so off base that it had me retreating to the safety of the bell curve.

The main thrust of the story is that we ought to reconsider whether the bell curve’s representation of human attributes accurately represents the distribution of these traits in real societies. If our “performance” is best represented by the bell curve, that suggests that most of us are average: in statistical terms, the mode and the mean are the same value. What this new study suggests — based on the metrics of performance it chose and the arenas in which it chose to look at this performance — is that most of us are below average, because statistics show that that our “performance” is not well-represented by the bell curve. The figure below, featured in the paper, gives a sense of this difference:

Image source: Personnel Psychology Volume 65, Issue 1, pages 79-119, 27 FEB 2012

In such a figure the horizontal axis represents the value of a particular measured trait and the vertical axis represents the frequency of that trait in the measured population. The bell curve is shown by the black line, and the defining feature of the bell curve is that the average trait value (the “mean”) is also the most frequent trait value (the “mode”), thus the symmetrical “peaked” shape of the line representing the distribution of trait values. Other distributions of traits are not symmetrical, and we call this asymmetry “skew”. The dark gray curve on the diagram above is left-skewed, meaning that the most common (modal) trait value is much lower than the average (mean) trait value.

The authors of this study present the following data in support of the idea that “performance” is not distributed as a bell curve:

Image source: Personnel Psychology Volume 65, Issue 1, pages 79-119, 27 FEB 2012

Based on their samples, there is pretty convincing evidence that populations of Researchers, Emmy-nominated actors, U.S. Representatives, NBA players, and MLB players do not show performance scores that are well-represented by a bell curve.

But does this mean that we as a society are not well-represented by the bell curve?

To answer this question, let us first consider the population of people whose “performance” was considered. All five of these populations are in some sense elite. A tiny fraction of the population gets to become a researcher, or an actor nominated for an Emmy, or a member of any of these populations. In fact, the percentage of the total population who are represented in this sample is infinitesimal, but this is not the only problem: each of these are also highly selected populations. The NBA draft is not a population-wide lottery (imagine what it would be like if it were!), it is a highly-selective process that culls the very best basketball players from the general population. So immediately we need to recognize that the results of this study cannot be applied to the population as a whole, because the trends discovered only apply to the select subpopulations considered.

So what does this have to say about whether or not our “performance” is well-represented by the bell curve? Well, perhaps we should consider what relation the chosen subsamples of these five populations have to the rest of society. Is it possible that our various talents are in fact well represented by the bell curve? As the graphic below suggests, the answer is clearly “yes”:

Image modified based on an original image by Petter Strandmark

If you only consider the top performers in any given arena, of course their distribution will be skewed to the left. The most elite performers on the right-hand side of the bell curve inevitably show a skewed distribution. This is an expected and unremarkable result of the very stringent selective processes that determine who can play Major League Baseball and who can get elected to Congress. These results have nothing to say about the distribution of “performance” across the whole society. Imagine if the NBA did draft people randomly from the population as a whole: you can bet that any performance statistic that you pulled would be distributed more closely to the bell curve than the current NBA. Obvious stuff, really.

The other big objection that I have to this study’s portrayal in the NPR piece has to do with the implicit connection the segment makes between our traits as a population and our performance. The bell or normal curve frequently provides a good representation of the distribution of traitsnot performance, in a population. While sometimes differences in traits can lead to differences in performance, the link between the two can be pretty indirect, and this is a reality that the NPR piece totally glosses over. The article has some pretty big genetic determinist overtones, as “we” as people are treated as one and the same as our “performance”. But does a study of performance by a particular criteria really tell us much about the distribution of talent in our society?

“Performance” comes as much from training as from inborn talent; in fact, it is the combination of the two — not one or the other — that determines performance. What makes someone good at something always has to do with the experience and training they are privileged to have, and what is really skewed in our society is this privilege: a few people have a lot of privilege and most have very little. I am not just referring here to the massive economic and educational inequities that permeate our society, I am also referring to much more specific factors relating to the populations included in this study:

  1. Researchers who publish good papers early in their career garner far more support for their work than those who publish less, and more support leads to further publication. This positive feedback loop can amplify rather small differences in the initial performance of these researchers, providing us with a distorted idea of what determines “performance” in this area.
  2. Emmy nominations undoubtedly are impacted by past performances: if you have been nominated before, you are certainly more likely to be nominated for the same quality of performance than a person who has never been nominated. Again, it is easy to see how slight differences in initial talent might be amplified by our reward system.
  3. This one seems almost too obvious to explain, but I will do it anyway. Members of Congress who manage to hold onto several terms (perhaps by very marginal differences in their job performance, or even by luck) climb in seniority on critical committees and then suddenly become much better supported by donors who wish to win influence. Few will get this level of support, but once they get it their re-election becomes far more likely than “average” representatives.

Perhaps the objections for the three populations above do not apply as well to the two populations of elite athletes sampled in the study, as in these occupations performance metrics are a direct rather than indirect measure of ability/talent. But still we should acknowledge that athletes who show marginal differences in initial ability or performance are going to be provided with the best training opportunities: if nothing else, the better players play against each other. We live in a society that is often “winner takes all”, and I think that all this study does is show that the elite among us contain subsets of the even more elite. Most of us may, in fact, be pretty average after all — we just live in a society that does not produce average outcomes. This failure to recognize the difference between potential ability and performance outcomes is in my eyes the most frustrating distortion provided by this NPR segment.

The researchers who produced this work seem to have their own reasons for conducting the study. In the paper they express the need to re-assess whether models of institutional performance should assume a bell-curved distribution of worker ability. This is reasonable given that most of the institutions they are imagining have some of the same selective processes as their sample: just as not everyone can be a player in the NBA, not everyone can get a job in a corporate office. But even when applied in this manner I worry that their sample data includes populations that are way too extreme in their performance to be the norm. Sure, we do not have every person in the population represented in the corporate office, but this is also not as selective a group as the U.S. Congress or even academic researchers. If I were in the business of managing a big corporation, I would be wary of applying these results based on extreme populations to my more average population of workers.

To summarize my worries about the effect of this piece, consider that listeners to the NPR story might walk away with the following wrong ideas:

  1. We can draw conclusions about “we” as a broader population by looking at the performance of elite, select populations;
  2. Looking at the outcomes produced by highly-trained and greatly-experienced individuals can tell us something about our own potential for performance; and
  3. Particular talents can be generalized to understand the aptitude of whole individuals.

The bell curve has a really bad political history: bell curves based on very particular metrics for particular traits have been used to draw broad generalizations about the talents of our population. Beyond the biases that often are inherent in the chosen metrics, these statistical assessments are problematic because they can only capture one metric at a time, and I assure you that high “performance” on one metric is no guarantee of superior performance on all metrics. Our society is in part successful because some people are really good at some tasks and other are really good at others. One of the things we do as a society to take full advantage of this diversity is to aim additional opportunity and training at those who show a particular talent, thereby amplifying differences in initial talent. Are we all below average in performance? Sure, on the 99% of things we did not train to do. But we all have strong talents as well, talents developed by our life experiences. Our various talents and aptitudes probably do map out on thousands of different bell curves, but who cares?: to succeed one need only excel at a few things. NPR would have you look at the best among us in a particular area and hang our heads in shame at being so generally below average.

I really wonder whether the researchers who conducted this study endorse the conclusions made by this incredibly misleading and just-plain-wrong story. I am flabbergasted that this story got past NPR‘s editors; whoever was on duty clearly has little understanding of what the bell curve represents for biologists. Shame on NPR for this profoundly ignorant piece.

Adaptation, Genetics, Radio & Podcasts

5 Comments to "NPR drops dumb Bell Curve segment"

Emma Thompson 5th May 2012 at 11:54 am

I had the same thoughts you have so succinctly stated in your commentary as I listened to the NPR piece. NPR may have to consider putting a real researcher or statistician on their panel to properly educate their listeners on such scientific matters. Thank you for pointing out the flaws in this article they erroneously chose to feature on Morning Edition.


Chris Jensen 5th May 2012 at 12:06 pm

Thanks Emma for this comment!

I think that many people who are not formally trained in scientific research or statistical analysis could quickly identify the many flaws in this piece: just check out the comments on the piece, which include many great reflections from laypeople.

But I agree: the way the piece interpreted this research suggests that NPR itself needs to do a better job of consulting with experts before just falling for the most flashy press release from an academic journal. It particularly bothers me when any news outlet misinterprets science with serious social and political implications: these sorts of misinterpretations do damage well beyond the realm of science.

Elizabeth 15th May 2012 at 12:01 am

Thanks so much for your comments. A friend and I were chatting last night about outliers and the bell curve, a couple seniors sitting on a deck in California drinking wine. I recalled this NPR story and told her about it. I wanted to shake her faith in the bell curve, to convince her that human ability isn’t linear but multi-dimensional. I re-read the item today and was aghast, both at my memory of the story and the ideas it contained. After I found your blog, I was relieved. Ain’t nothing as easy as it seems in a 60-second radio piece heard while vacuuming.

Dave 15th May 2012 at 9:10 pm


I found your thoughts above just what I needed to clear up a few ideas that were rolling around in my head after hearing the npr story. I agree that the subpopulations they were referencing seem to be an elite view of our society and it is understandable that the top tier of a performance based activity where a serious amount of training is involved would yield a distribution similar to the top 2.5% of a normal curve.

This had me questioning whether a performance based activity from not such an elite group would have a normal distribution. For instance, if we were to have everyone in our society take 100 free throws on a basketball court would the resulting distribution follow a normal distribution or a power distribution? Do the results of any performance based activity where training, motivation and experience are factors not yield a normal distribution if data is collected from our society as a whole?

It would be great to get some insight on this.


Chris Jensen 16th May 2012 at 7:56 am

Hi Dave:

Great question. Let me acknowledge before speculating that we are in fact in the land of speculation, so do not take what I am saying as supported by any implied direct evidence (I have none).

Your question has two underlying parts, each about performance on free throws. The first is about genetics: what are the traits that might be required to be a good free-throw shooter? These would probably include the potential for development of requisite strength, aim, and of course mental stability in the face of pressure to perform. Notice that I have to qualify my list with the phrase “potential for development” because if we are strictly talking about who was born with what traits, we are really talking about the potential to develop outcomes like strength, aim, and mental composure. Can everyone with the proper practice shoot free throws like Jamal Crawford? Probably not, as he is likely endowed with some advantages in his genetic potential for strength, aim, and composure. But that does not mean that everyone with the potential to shoot free throws as well as Jamal Crawford is in the NBA, or that Jamal Crawford is some sort of extreme genetic outlier: there are probably plenty of out-of-shape, under-practiced people who could be as good as Jamal Crawford, they just have not had the same combination of training opportunity and discipline (maybe they ended up playing too many NBA video games instead).

The second thing to notice about the genetics behind your free-throw thought experiment is that many, many genes need to be involved in coding for the potential characteristics needed to shoot well. Who knows how many genes influence each of the three skills I listed (strength, aim, composure), but notice that there are at least three distinct traits that we have identified as being important to being a good free-throw shooter. This means that the distribution of potential performance is going to be spread out, because most of us will have some mediocre potential in all three categories, but a few will possess exceptionally low or high potential combinations of all these requisite skills. When performance on a particular metric requires a combination of skills, the potential in the population could still be represented by a bell curve, but that bell curve will be more stretched out due to the fact that many genes are responsible for the trait (in the statistician’s parlance, there is greater “variance” in the population). Think about human height, which has been shown to be influenced by many genes: if there was only one gene for height there is no way that we would show so much variation across the human population, and extremes in genetic potential for height are caused by unlikely combinations of genes ending up in particularly short or tall people.

The second underlying part of your question has to do with training. Even if the potential for shooting free-throws in the population could be represented by a big, wide-ranging bell curve, does this mean that a random sample of the population will shoot free-throws such that the performance of that population could be well-represented by a bell curve? Probably not, and for two reasons related to training. The first training issue is what I would call the “barrier to entry problem”. Whatever potential a given person might have to shoot free-throws, that potential is not going to be met by anyone who has never touched a basketball before. Even through basketball is pretty ubiquitous in American society, I imagine that a substantial proportion of our society has never touched a basketball, and an even larger proportion has not spent sufficient time playing with a basketball to be able to even shoot a single free throw in one hundred tries (I would suggest that ten tries might be a better test, because even a novice might get better with one hundred chances to practice). This suggests that irrespective of genetic potential, there is a threshold level of training that each person requires in order to be able to shoot free throws. That threshold level of training might be lower for a person with greater genetic potential, and for some people that threshold might be infinite (no amount of training would help a person with a significant disability that impaired free-throwing). Because there is a training threshold for performance at this task, a large number of people are going to be incapable of shooting a single free-throw (or less extremely stated, many will shoot a very low percentage). This will lead to a departure from the bell curve, and will make the distribution more like the power distribution.

But wait, we are not done exploring the role of training! Because just as there are people who receive inadequate training at free-throwing, there are also people who are highly trained. As I suggested in the post above, these are not a random set of people: those who show early potential on the basketball court will receive a far greater quantity and quality of training than the general population. Jamal Crawford has probably thrown a basketball from the foul line thousands of times more than you or I have, which means that not only does he likely have great potential for strength/aim/composure, but he has also been given the greatest amount of opportunity to reach that potential. This is to take nothing away from his accomplishments, because let us remember that training requires hard work. This is what I like about the gene-environment interaction: nobody becomes good at anything without hard work (just don’t mistake that for meaning that anyone can do anything with enough hard work).

If there are some people who cannot shoot free throws at all because of insufficient training, some who are very exceptional, and the rest of us, we end up with a strange-looking free throw performance curve. It will be skewed to the left by people who cannot shoot at all and slightly skewed to the right by those who are well-practiced. But in the middle is likely to be the rest of us with our middling potential and moderate levels of training. The free-throw performance curve is likely to be a three-headed monster, and how big each head will be depends on how much training people need in order to throw a single free-throw through the net and how much training the average person receives in free-throwing. That’s my best guess!

So here’s one question that I cannot fully answer: why are so many great NBA players such poor free-throwers? If had to guess, I would say that there are trade-offs between different traits that make you a great NBA athlete, and mental composure in the static environment of the free throw is probably not as important as the kinetic composure most NBA superstars display. That said, sometimes free throws do win championships. Go Brooklyn Nets!!! 2013 is our year!


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