Estimating iPhone App Store Sales From Rankings

Estimated average daily sales versus popularity ranking for paid apps between the Top 10% and the Top 50% in App store popularity (out of 265k paid apps).

Everybody talks about the top apps in the iOS app store. But there's still a story to be told about the other 90%+ of apps. The story is that Apple is likely paying 100's of millions of dollars per year to these developers, but with that revenue spread incredibly thinly though a very long tail.

Ajnaware’s Weblog posted an interesting hypothesis about App store unit sales. The hypothesis is that sales, plotted against popularity rankings, follows a power law curve. This curve can then be integrated to get total app sales. Phenomena with long tails often seem to follow power law curves. So, given the long tail of around a quarter million paid apps in the iOS app store, a power law seems to be a quite reasonable starting hypothesis.

I used a tiny number of data points for paid apps, ones I've randomly heard about, spread across the entire App store, instead of just the top, and tried to fit my own power law curve to those points. I ended up with a vaguely reasonable fit using this equation:

unitSales = totalPaidApps * ((1 + rank) ^ -1.0) - 1.5

with a steeper exponent of -1.0 instead of Ajnaware’s estimate of -0.75. (The carat symbol is old fashioned Basic syntax for the infix exponentiation operator.) I also ignore negative sales due to the small bias subtracted from the curve. The curve fits thousands of sales per day for a top 100 app, 100's of sales per day for a top 1000 app, but less than 10$ per day for apps below the top 15%, and less than 1 sale per day for the median or 50th-percentile popularity app. Given 265,000 total paid apps, this curve integrates to almost 3 million paid app sales per day, or over $140M in app sales per month if the average app price is $1.65. So my guess is that this equation is at least correct within an order of magnitude.

Power law curves are very different from bell curves. There is no central tendency average. So asking other developers about the average number of sales to expect is fairly useless, because the mean is so far from the median. There seem to be no average apps, only a few winners and a huge number of losers, maybe with odds and payoffs more similar to a game of roulette than a predictable business opportunity for developing new apps.

(Graph and some commentary added on 2011-July-24)

Added 2012-July-26:
Here are some results from an iOS game developers survey, which show a similar revenue distribution curve: http://www.streamingcolour.com/blog/2011/09/28/results-ios-game-revenue-survey/