Amazon Rankings: A Statistical Analysis?

Apologies for missing out on this week's SFFS posting...the week's been a mess with many things going on, and by the time I gathered myself together, I'd already missed the deadline for signing up. Hopefully, next week, we'll get back into my short story "Downtrodden" but for now, I wanted to post some information on a favorite topic of mine.

Those pesky Amazon sales rankings...everyone wonders how they come up with the numbers they do, and how they correspond to sales (especially for books where you haven't self-published through the KDP program, and you don't have instant access to your sales numbers, although things are a little bit better now that you can review historical data on sales rankings of all your books through Author Central).

Everyone (hopefully) knows the basics of sales rankings. The lower the number, the more copies you've sold. If a copy of your book sells, the number gets lower. As time passes without sales, your number gets higher. But how exactly do they determine the number? I've taken some sales numbers for my two Triple-Shot collections for about a month's period, and am going to run some analysis on those. The reason is simple. My books don't sell hundreds of copies a day (in fact, each of these changes takes place after a single copy of each sold), so it will hopefully give some insight into how sales impact the ranking.

Just for having all the facts, I'll mention at the time of this posting (and at the time of these sales listed below), DMF had two 5-star reviews, and Temptation had one 4-star review. Also, DMF has more total sales, but Temptation has sold 50% more copies this year than DMF.

So, let's first look at my first Triple-Shot, featuring "Dead Man's Forge." Each date range corresponds to the three-day period surrounding the date of purchase, and the rankings on each day.

18-Jun	19-Jun	20-Jun
621463	83959	158286

21-Jun	22-Jun	23-Jun
242962	116176	204661

24-Jun	25-Jun	26-Jun
270981	79911	185757

30-Jun	1-Jul	2-Jul
383636	91069	155854

5-Jul	6-Jul	7-Jul
346592	87791	166719

14-Jul	15-Jul	16-Jul
464262	82844	127117

And now the numbers for the second Triple-Shot, featuring "Temptation" (note: the first has four dates, as two copies sold, once on the 15th and another on the 16th)

14-Jun	15-Jun	16-Jun	17-Jun
1101143	100249	72888	159123

18-Jun	19-Jun	20-Jun
225398	79764	150470

21-Jun	22-Jun	23-Jun
227376	114281	200625

30-Jun	1-Jul	2-Jul
454136	91333	156508

6-Jul	7-Jul	8-Jul
389278	90126	205350

14-Jul	15-Jul	16-Jul
464331	82883	127182

And now for the analysis...

First off, notice that Temptation sold two copies on sequential days (the first line of the data), but yet the ranking on that second purchase didn't boost it much higher than the other times that a copy was purchased.

Notice also on those date ranges where copies of both books were sold, that the increase in sales rankings were not a matched amount, and that on the following days, the drop in sales rankings were not linear between the two (i.e., one book dropped faster than the other).

Also notice that on two separate sets of days, the starting ranking for Temptation was almost identical (6/18 and 6/21), but a single copy caused it to boost to different rankings after the sale.

Now I will mention at this point that Author Central gives you a daily ranking, but doesn't tell you when the book sold during the day. I've sat and studied it by anecdotal means, but there's no way to record such data that I know of. A copy sells and boosts the ranking, and immediately begins dropping, but the AC value usually matches up to a value somewhere along the path down.

So, what are we to make of all this? I have a theory I'd like to share:

I believe until you start selling multiple copies per day, that you're included in a vast range of numbers starting at some value determined by repeat daily sales-books (likely in the 70K range). When your book sells a copy, you're bumped up to the top of that list. The next single-sale book that sells out of the Kindle store moves you down the list (unless a book starts selling more than one copy per day, in which case it gets bumped to the next tier up), and each subsequent book moves you farther down the list. Author Central would then take a snapshot at the end of each day, which is the number that gets published to your ranking chart. The only thing I'm not sure about is whether reviews get added into the equation somehow...I have an additional theory that if books are sold at around the same time (perhaps in a 5-minute window), that the number and level of star-ratings boost a book higher than the other with fewer and/or lower ratings. I'm also not sure how a book that was selling multiples per day affects the rankings when it stops selling that many on a particular day, but my belief would be that it drops back down into that lower tier and pushes copies that had just sold a copy that day down.

This would explain how a book that was sitting at nearly one million in the rankings (as mine was) would immediately reach a value of about 100K, but then sell a copy the next day and only bump up to about 73K. 

This would also explain how books that sell on the same day ended up moving up to different rankings, because if they sold later in the day, their ranking would by default be higher than another book that sold earlier in the day.

This would also explain how a book drops faster than another, if a book drops down to the lower tier before another book sells a copy.

Obviously this is just conjecture on my part, so maybe one of you out there has a theory they'd like to share, or another comment to make of some sort. Suffice to say, that Amazon truly does have the market cornered on keeping around the most complex algorithm for sales rankings known to man.

Please, feel free to comment and discuss...