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The Superstar Equation, Disproved?

Levitt and Dubner have written before about the origins of star-making talent. But can the road to pop culture megastardom be calculated as a matter of statistical probability? Back in 1994, Kee Chung of SUNY-Buffalo and Raymond Cox of the University of Ontario Institute of Technology applied an equation called the Yule-Simon Distribution to this question. Their findings were that the probability distribution implied by the Yule model mirrored data gathered in the pop music industry — thereby indicating that the model could be used as a map to generate the next pop superstar.

Now, the economists Laura Spierdijk and Mark Voorneveld have tested Chung and Cox’s conclusion in their paper, “Superstars Without Talent? The Yule Distribution Controversy.” Using a “parametric bootstrap and several powerful test statistics,” they checked Chung and Cox’s data and found overwhelming evidence refuting their conclusion. Spierdijk and Voorneveld sum up their predecessors’ apparent mistake as follows:

They base their statement on an approximation of the Yule distribution, a power law. QQ-plots point out where things go wrong: although the Yule distribution seems a fairly accurate approximation of the lower quantiles of the empirical distribution, it puts too much weight in the right tail of the distribution. Consequently, the Yule distribution captures stardom, but not superstardom.

As such, it looks like using statistical equations to find the next Britney Spears may not be such a good plan after all.