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Most people are below average! Human performance is often not distributed according to the famous 'bell curve' or 'Gaussian'. Instead, a small number of people vastly outperform the rest. A new study shows that in 186 out of 198 groups ranging from physics professors and Grammy nominees to cricketers and swimming champions, a small group of 'superstars' account for much of the success of the group as a whole. That means the majority are performing below the mathematical average - or to be precise, the 'arithmetic mean'.

This should not be depressing news, but it does mean that blindly modelling people's behavior using a bell curve is a bad idea. So is expecting that 'average' means 'typical'.

If you want details, read the original paper - it's free online:

Ernest O'Boyle and Herman Aguinis, The best and the rest: revisiting the norm of normality of individual performance, Personnel Psychology 65 (2012), 79–119. http://onlinelibrary.wiley.com/doi/10.1111/j.1744-6570.2011.01239.x/full
For decades, teachers, managers and parents have assumed that the performance of students and employees fits what's known as the bell curve — in most activities, we expect a few people to be very good...
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43 comments
 
Whether it is Gaussian or a power distribution - or log-normal distribution - doesn't really matter, other than in the narrow technical sense that taking the arithmetic mean (rather than the median) is no longer the appropriate way to characterize the distribution.

If aspects are described well by a power law or log-normal distribution, then just use that distribution instead. This feels like a revelation in the same way that stating "not all picnics happen in sunny weather!".
 
If a similar research were done before the agricultural revolution, that is before the mass stupification of farming and industrial cultures, a different conclusion might be found.
 
Have you stood in a line for any length of time recently? Have you paid attention to the people around you? If so, these results only confirm the what your empirical observations had already nudged you into suspecting. It's only bad news if you're left of the bump in the curve. If you're to the right of the bump -- well -- can you say "woohoo"?
 
Normal distributions constrained to positive values are lognormal. Has anyone suggested these distributions are bimodal instead of lognormal?
 
But why would anyone ever think these skewed populations are at all normal? Measuring academic success by counting the number of papers published, where your sample population is the tiny elite of people who are published researchers? When you throw out everything but the extreme tail of the population, of course what's left won't look normal.
 
My issue with this article is that it doesn't take into account the resources available to the performer. With the Emmy example... what percentage of performers have a choices in the role they play? In my company I am one of those "super-performers". This is due in part to the fact that I write custom software... I don't have to meet the stringent specifications that the product development teams are required to. As a result of my efforts being "subsidized" by outside resources and the lower requirements... I am simply able to push at the boundaries more often than many of my peers in the same company.
 
When measuring the abilities of a population -- whether cognitive or behavioral -- there is no reason to assume symmetry in the distribution curve to be normal. Kwon pointed out a key issue: there are unevenly distributed opportunities. Skewed distribution of opportunities will result in radically skewed societal outcomes.
 
To people who think hard about statistics, this story will not be news. But there are also people who unthinkingly assume Gaussian distributions for random variables even when they shouldn't. Of course these people are below average - but they're the majority.
 
Consider the 20-80 rule from business science : 20% of the people contribute 80% of the value, and apply this recursively ie 4% contibute 64% etc. 
 
My issue is that the article doesn't define 'average'. There are three sorts of average in statistics: mean, median, mode. By definition, exactly half the population is below median, and mean of course can be skewed badly by a few outliers. If the article is right, fewer than half the population is below the mode.
 
In a story like this, you don't have to be too far above average to expect there to be information about whether the distributions in question are lognormal or bimodal.
 
Any competent [sales] manager can tell you that the 80-20 rule is fact. But what distribution that implies ??

Matt P
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The vast majority of people have an above average number of legs.
 
This is not really news to me. This has been well known for those who did any type of demographic analysis. The problem comes though when those who are below average think they can do as well as the outliers without examining the outliers circumstances.
 
+Rahul Siddharthan it says power law, but power laws are one of the most badly fitted and over-diagnosed distributions. In particular, lognormal distributions are usually mistaken for power laws by folks who simply plot them on log-log plots or do a regression on log axes. +Cosma Shalizi has a superb paper about this particular issue, and R software for testing a power law fit versus other possibilities. This is more likely a log normal distribution, since as folks noted above, even if you posit an underlying Gaussian process, if the measurement scale is positive real, the distribution is log normal.
 
"In each of these kinds of industries, we found that a small minority of superstar performers contribute a disproportionate amount of the output."

So how are they defining "ouput"? Cashflow? Publicity? Good outcomes? Curious below average people want to know! Even those with an above average number of legs :) :)
 
+Bob Libra academia works like an echo chamber, like the corporate management. There are many good workers among them, but they are under the thumbs of their employers. They make people like Brian Cox professors.
 
There seems to be surprisingly few studies of distributions of physical instruments variability (by opposition to human procedural errors, when Gaussian and Lognormal are usually assumed for outliers elimination). Last year, I asked on +Stack Exchange "Cross Validated" a question about the error distribution of typical instruments and got only one qualified answer referring to Robert Gibbons studies. http://stats.stackexchange.com/questions/9030/is-there-a-classification-of-physical-measurements-according-to-their-statistica . I would be interested in any further reference.
 
+Rahul Siddharthan wrote: "My issue is that the article doesn't define 'average'. There are three sorts of average in statistics: mean, median, mode."

I feel sure they're talking about the mean, or more precisely the arithmetic mean. That's what people in journalism almost always mean by "average". (And obviously they don't mean the median here, since you can't have more than half the people below the median!)

Of course there are lots of other kinds of mean, like the geometric and harmonic mean. For quantities that span a vast range, the geometric mean is often more interesting than the arithmetic mean, and a log normal distribution is often a better fit than a normal one.
 
The original paper is free online, in case anyone is curious about the details:

Ernest O'Boyle and Herman Aguinis, The best and the rest: revisiting the norm of normality of individual performance, Personnel Psychology 65 (Spring 2012), 79–119. http://onlinelibrary.wiley.com/doi/10.1111/j.1744-6570.2011.01239.x/full

People who think this study "isn't news" should note the first sentence of the abstract:

"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..."

I bet it's true that lots of people in these fields assume a Gaussian distribution! The paper gives evidence for this, and explains some of the effects.
 
It just occurred to me that our perceptions are often logarithmic (physical ones at least), which inverts a power law perceptually.
 
in that case the 1 percent and 99 percent division is natural :)
 
Yes, it's very common and natural for human societies to be organized in a way where a small rich aristocracy bosses everyone around.
 
+John Baez ,only for the farming and the industrial cultures. And your stats do not include these smartest people, do they?
 
still the bell curve might be through.bell curve says that few people are very smart and the research says those few account for most of the success
 
I disagree slightly with Akira's claim that the smartest people work the least and earn the most. I think they're the ones who figure out how do what they want, whatever that may be.
 
This paradox implies that the definition intelligence changes, that it is relative. Producing the most is an industrial definition aimed at workers. A propaganda of the ruling elite.
 
That's a great paper, +Jim Stuttard. I like this line:

"In a bizarre event which one of the authors insists was planned, and the other maintains was a really stupid idea that just happened to work, the test was first administered to about 30 students on a further-education programming course at Barnet College before they had received any programming teaching whatsoever – that is, in week 0 of the course."
 
Yes, it is great ! I also like this:

"There is a vast quantity of literature describing different tools, or as they are known today Interactive Development Environments (IDEs). Programmers, who on the whole like to point and click, often expect that if you make programming point-and-click, then novices will find it easier. The entire field can be summarised as saying “no, they don’t”. It would be invidious to point the finger at any examples."
 
oh that s a relief, imagine i m not average anymore.phhhhh
 
+Jim Stuttard The last line of the abstract is also quite fun :

We point out that programming teaching is useless for those who are bound to fail and pointless for those who are certain to succeed.
 
A quick thought as to why the bell curve doesn't seem to apply to these industries. The statistical out liers at the bottom realized they should choose a different profession.

I'd love to be an artist, but I'm really, really bad at it, so I do something else to make a living. So I wouldn't be measured in their artistic samples.
 
Suppose players with skills distributed via normal (or any other, for that matter) distribution of skills repeatedly play in tournaments where the player with batter skill always wins the game. What will the distribution of prizes look like?
 
+Kevin Burger wrote: "I'd love to be an artist, but I'm really, really bad at it, so I do something else to make a living. So I wouldn't be measured in their artistic samples."

Indeed, in the radio show I laughed out loud when they said "what Aguinis is finding is that most people receive only one Grammy nomination..." Of course most people receive no Grammy nominations!
 
+Maksim Maydanskiy - if you repeatedly flip a coin and either win or lose a dollar based on the outcome, the probability distribution of your winnings or losses will be a Gaussian in the limit of many coin flips. But if you start with a dollar and either increase or decrease your money by 10% based on the outcome of each coin flip, the probability distribution will be lognormal. And the latter is closer to the actual the distribution of people's wealth.
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