June 8, 2006

Sometimes it’s amazing how deeply buried the useful nuggets of information are. Here is a power law that converts Amazon sales rank to units sold per week.

Sales/week = e to the power (10.526-(.87*sales rank)

As an Excel formula: =EXP(10.526-(0.87*LN(rank)))

This formula is buried deep inside an academic paper by MIT econometricians Brynjolfsson and Smith — equation (9), if you’re curious — referenced on Chris Anderson’s LONG TAIL web site.

The formula is backed up by four different studies conducted from 2001 to 2005 which have all found r, or measures of correlation, of .8 or higher for values of beta ranging from -.855 to .-91 (above, I used -.87) using sales data for samples containing as many as a thousand titles. In other words, although it obviously isn’t perfect, this is a pretty darned handy approximation of sales rank to units sold. Incredibly, although the formula is extremely simple and can be expressed in one line, I have never seen it reproduced anywhere else. I offer it here as a service to readers.

Tip: I did a retrospective calculation using my Ingram sales data and Amazon sales ranks for my best-selling title, which usually sells in the range between 10,000 and 40,000, and found that a beta of 0.936 accurately predicted total sales to date.

The Rank Economy: Publishing Business Books Ranked on Amazon
… The main thing I’ve learned from watching this list is how writers prioritize their work. Ignoring the style references for editors and academics, the main priority for writers is finding places to mail their manuscripts. Next comes a whole slew of books about how to get the editors and agents to actually look at the manuscript, rather than chucking it in the slush pile. A few publishing business titles are sprinkled in for writers who decide they’ll be better of publishing themselves, or simply give up on finding a traditional publisher. The lowest priority appears to be generating sales for books once they get published. I guess a lot of authors either just want to see their name on a book cover, or are too exhausted by the process when they get there to worry about sales. It could also be that most authors still believe that once a book is published, it will generate sales on its own through word of mouth or some passive means. Good luck!

Ouch. Well said.