Amazon Sales Rank, and What Math Geeks Do

Today, I asked my son’s if they would like to buy The Oatmeal’s Why Grizzly Bears Should Wear Underpants. They laughed uproariously at the title, and then Eli asked, “Is that the #1 book on Amazon?” In fact, it’s not. At the time of this writing, its ranking was #624. “That’s not #1,” Alex affirmed, then added, “but it’s a lot better than your book.”

Ha-rumph.

“A lot better” is highly subjective. Sure enough, the #3,517 ranking of Math Jokes 4 Mathy Folks has an absolute difference of 2,893 compared to WGBSWU; or, if you’re into ratios, the rank of my book is five times as much as the rank of WGBSWU. But what does that really mean?

In practical terms, it means that the number of copies of WGBSWU that will sell on Amazon this week is approximately six times the number of copies of MJ4MF that will sell during the same period. If my calculations are correct, that is. No one is really sure how ranking translates to sales, but I estimate that approximately 250 copies of MJ4MF and 1,500 copies of WGBSWU will sell this week.

This is what math geeks do: We try to understand everything quantitatively.

I took weekly sales data for MJ4MF and compared that with the book’s average ranking for the week. I randomly chose 20 weeks in 2012-13 for this analysis, because while pulling weekly sales data is relatively easy — it’s provided at Amazon Author Central — determining weekly average ranking is more difficult, since data has to be pulled day by day. And it’s not as simple as just exporting the data to Excel or a CSV file… the data is provided in a graph, and if you want to manipulate that data in any way, you have to look at each point on the graph, determine its value, and then enter it manually. Ugh.

The graph below shows the relationship between average rank and weekly sales:

The regression equation S = 914.77 × R^-0.977 gives a reasonably good fit (r = 0.89). What’s interesting is that this formula is less accurate in November and December than during the rest of year. There are two reasons for that. First, sales increase dramatically during the holiday shopping season. Second, such a formula is bound to be less accurate with larger numbers.

The average rank for December 9-15 was #3,592, and using the formula above, approximately 253 copies of MJ4MF should have sold. (I suspect that estimate is a little low. For the same week last year, the average rank was #4,573 and 277 copies were sold.)

Amazon posts sales data for each week on the following Friday. Sales data for last week won’t post until December 20. I’ll update this post on Friday and let you know how well I did.

[Update, 12/20/13: A record-breaking 335 copies of MJ4MF sold December 9-15. (Thank you!) But as predicted, the estimate was indeed low. As I gather more data, perhaps I will be able to create a better model.]