Are Amazon’s rankings Zipfian?

Will Oremus at Slate writes that “Sales of George Orwell’s 1984 Are Up 5,000 Percent on Amazon”.

And that’s certainly how it looks on his screenshot of Amazon.com’s movers and shaker’s page. Here’s my screenshot (which shows a different number, because it was taken later). This particular edition of Nineteen Eighty-Four has gone from rank 3,151 to rank 89:

But the Amazon Movers and Shakers page says that it displays “Our bigger gainers in sales rank overs the past 24 hours. Updated hourly.” That is, they’re looking at sales rank, not raw sales. Can we really conclude from that 3,440% number in the screenshot that sales have gone up by a factor of 35?

Perhaps we can, if the sales follow Zipf’s law – that is, if the sales of the kth-highest-ranking item are 1/k the sales of the highest-ranking item. So if the sales of the highest-ranking item are S, then sales have gone up from S/3151 to S/89 – a percentage rise of (3151-89)/89, or 3440%. This formula agrees with the percentage results that Amazon states for all the books on the Movers and Shakers page.

Of course this doesn’t mean that Amazon’s sales are actually Zipfian – it’s much more likely that they want a convenient formula that gives reasonable-looking rankings. But if they are, then these percentages are not too far form the truth.

(Why is Nineteen Eighty-Four suddenly so popular? The PRISM scandal. I’m not rehashing that.)