# Quantization of Books 4: How Many Books Is That Again?

I've toyed around in the past with ways to use the Amazon sales rank tracker to estimate the sales numbers for How to Teach Physics to Your Dog. It's geeky fun, but not especially quantitative.

Yesterday, though, I found a reason to re-visit the topic: calibration data!

OK, "calibration data" is probably too strong a description. "Calibration anecdote" is more accurate.

Yesterday when I went into work a little after 10, a comment somebody made sent me to the actual Amazon page for the book, where I saw a little note next to the price information saying "Only 5 left (more are coming)-- order soon!" That's very cool to see-- I don't know how many they ordered initially, but retailers selling out their whole stock is always good (for the author, not so much the potential reader).

When I got back from lunchtime hoops, the little message was still there, but the number left had dropped from 5 to 1. Which suggests that four copies sold between 10am ET and 1pm ET, and that provides a way to calibrate the effect of selling a copy on the sales rank.

So, the relevant rankings from the tracker data table are:

2645

2525

2871

2223

(the times in the table are Pacific time, so those are 0700-1000 on 20100127). That suggests that four sales in three hours boosts the rank from 2645 to 2223, or 422 spots. That's a change of 16% from the start, or 15% from the peak.

Of course, you might reasonably argue that such a cluster of sales ought to produce a more noticeable change in the rankings, and it wouldn't be unreasonable to expect there to be a lag between the actual sale and the change in the ranking. So, what's the biggest shift we could see from these data? If you take the next three points, you get:

2040

1753

1693

(the next point after that goes up again). The largest difference from high to low in this larger data set would be from 2871 (noon ET) to 1753 (3pm ET), a difference of 1118, or 39% of the peak. That would suggest a two-hour lag between the sale of a book and the adjustment of the sales rank, which seems a little big, but not wildly unreasonable.

Of course, this depends on a bunch of information of unknown quality-- for these analyses to make any sense, the number of books listed in the little notice has to be accurate, and not just a sales tactic (later in the afternoon, the "only 1 left" notice seemed to disappear then reappear then disappear again, which isn't a good sign). The number also needs to reflect the number that have been ordered, and not the shipping of books ordered a day or so earlier.

Assuming those assumptions aren't wildly off base, though, this suggests that three hours at a sales rank between 1500 and 3000 equals roughly four books sold. Using that gives a lower bound for Amazon sales at ranks below 3000 of 556 books (417 hours of ranks below 3000 in the dataset). That's an extreme lower bound, mind, as 191 of those hours were below a sales rank of 2000, and thus presumably account for more than 1.33 sales/hour, but it's the right order of magnitude, at least.

So, there's your fun with numbers item for this Thursday.

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