What explains Jamiroquai?  How can an artist be talented enough to have a big hit but not be talented enough to stay on the map?  You can tell stories about market structure, contracts, fads, etc, but there is a statistical property that comes into play before all of that.

Suppose that only the top .0001% of all output gets our attention. These are the hits.  And suppose that artists are ordered by their talent, call it τ.  Talent measures the average quality of an artist’s output, but the quality of an individual piece is a draw from some distribution with mean τ.

Suppose that talent itself has a normal distribution within the population of artists.  Let’s consider the talent level τ which is at the top .001 percentile.  That is, only .001% of the population are more talented than τ.  A striking property of the normal distribution is the following.  Among all people who are more talented than τ, a huge percentage of them are just barely more talented than τ.  Only a very small percentage, say 1% of the top .001% are significantly more talented than τ, they are the superstars. (See the footnote below for a precise statement of this fact.)

These superstars will consistently produce output in the top .0001%.  They will have many hits.  But they make up only 1% of the top .001% and so they make up only .00001% of the population.  They can therefore contribute at most 10% of the hits.

The remaining 90% of the hits will be produced by artists who are not much more talented than τ.  The most talented of these consist of the remaining 99% of the top .001%, i.e. close to .001% of the population.  With all of these artists who are almost equal in terms of talent competing to perform in the top .0001%, each of these has at most a 1 in 10 chance of doing it once.  A 1 in 100 chance of doing it twice, etc.

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(*A more precise version of this statement is something like the following.  For any e>0 as small as you wish and y<100% as large as you wish, if you pick x big enough and you ask what is the conditional probability that someone more talented than x is not more talented than x+e, you can make that probability larger than y.  This feature of the normal distribution is referred to as a thin tail property.)

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