## Posts tagged ‘rank’

### Results of **Hold On… How Many Copies?** Contest

As predicted, I did not meet my self-imposed deadline of posting the winner of the *Hold On… How Many Copies?* contest on Saturday. But I think you’ll agree I have a good excuse. When I woke at my in-laws on Saturday morning, my wife and kids surprised me with the pronouncement that we’d be spending the day at the Museum of Mathematics in New York City. (A post about that coming soon. It was awesome!) But after a full day of mathematical thinking and a late dinner, I didn’t have the energy to post results last night.

So, sue me.

But without further adieu, I can now announce the winner. Not before some data analysis, though.

The ten responses were:

{21, 137, 301, 333, 392, 429, 453, 595, 1637, 3142}

With a range of **3,121** and an average of **744**, there was quite a spread to the data.

I certainly love the optimism of the respondent who predicted that 3,142 copies were sold! But with Q1 = 390 and Q3 = 559, the responses of 1,637 and 3,142 would both be considered outliers. Indeed, the actual number was lower than either of those guesses, but you won’t hear me complain about selling **634 copies** of *Math Jokes 4 Mathy Folks* from Dec 15 to Dec 21!

**The winner guessed 595 copies.** Well done! He or she will be contacted via email or can contact me directly at patrick@mathjokes4mathyfolks.com.

For what it’s worth, I would not have won my own contest. Knowing that sales vs. rank is generally exponential but also knowing that sales decline during the third week of December, I used a purely linear regression to generate a guess of 473 copies. This would have resulted in a third-place finish. Oh, well. I take solace knowing that a third-place finish is far superior to where I would have placed if I had sponsored a marathon instead.

So, thanks to everyone who bought a copy of the book last week. Wow! Who would’ve thought sales would still be that brisk five years after publication! For that matter, thanks to everyone who’s ever bought a book. This has been an incredible ride!

Thanks, also, to those of you who entered the contest. Sorry if you didn’t win, but I hope you had fun playing.

**Happy holidays!**

### 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.]

### Rank Math Trick

The Amazon sales rank for *Math Jokes 4 Mathy Folks* fluctuates between 20,000 and 300,000. The highest rank to date was 11,394, which occurred July 7, 2010, the morning after a review of the book appeared in Maria Miller’s Homeschool Math Blog and in her email newsletter.

Today, the Amazon sales rank was 113,113. Cool number, eh? Reminds me of an arithmetrick:

- Take a three‑digit number
*abc*. Then, write it twice to make a six‑digit number*abc*,*abc*. (For instance, if you chose 113, then your six‑digit number would be 113,113.) - I’m feeling lucky, so divide by 7.
- Hmm… I’m not feeling quite as lucky now, so divide by 11.
- Uh-oh. I no longer feel lucky at all. Divide by 13.
- Check your result. Should be the three‑digit number you started with,
*abc*.

The following joke is a hint to why this trick works, in case you haven’t already figured it out:

Teacher: Can you find the prime factorization of 1,001?

Student: I didn’t even know it was lost!