## Posts tagged ‘Amazon’

### Why is Today “Prime Day”?

Today is July 11, which the marketing folks at Amazon* have dubbed “Prime Day.” They’ve even created a spiffy, little banner image for it:

Ooh… pretty!

The selection of 7/11 as Prime Day was no doubt deliberate, since both 7 and 11 are prime numbers, though one has to wonder why Amazon ignored the other 52 (or 53, if it’s a leap year) dates they could have chosen:

- February
- 2/2
- 2/3
- 2/5
- 2/7
- 2/11
- 2/13
- 2/17
- 2/19
- 2/23
- 2/29 (some years)

- March
- 3/2
- 3/3
- 3/5
- 3/7
- 3/11
- 3/13
- 3/17
- 3/19
- 3/23
- 3/29
- 3/31

- May
- 5/2
- 5/3
- 5/5
- 5/7
- 5/11
- 5/13
- 5/17
- 5/19
- 5/23
- 5/29
- 5/31

- July
- 7/2
- 7/3
- 7/5
- 7/7
- 7/11
- 7/13
- 7/17
- 7/19
- 7/23
- 7/29
- 7/31

- November
- 11/2
- 11/3
- 11/5
- 11/7
- 11/11
- 11/13
- 11/17
- 11/19
- 11/23
- 11/29

One of my favorite problems is based on the numbers 7 and 11. Here’s a modified version of it, tailored to Amazon’s special day:

An online shopper placed four items in his cart. When he checked out, his credit card was charged $7.11. Shortly thereafter, a programmer realized there was an error in the code, and total price had been calculated by

multiplyingthe prices of the four items. The customer service department was about to alert the customer to the error, but the programmer informed them that the total price would have still been $7.11 if the prices had beenadded. No harm, no foul.There was no sales tax. What was the cost of each item?

Good luck! Happy shopping!

* No, Amazon did not pay me to write a blog post about Prime Day.

### Hold On… *How Many* Copies?

How many copies of *Math Jokes 4 Mathy Folks* do you think sold last week?

Make Your Prediction Here (Google Form) |

Why would you want to make a prediction? Well, lots of reasons…

- Like the author (and readers) of this blog, you’re a math geek.
- You swoon at the sight of data.
- You’ve never met a puzzle you didn’t like.
- You want to show the world how awesome you are.
**You’d like to win a signed copy of***Math Jokes 4 Mathy Folks*, some cool MJ4MF stickers, and a surprise gift, all shipped to you in exclusive MJ4MF packaging!- All of the above.

If you’re reading this blog, then you surely love being alive in the Age of Big Data. I love it, too, and I devour any data that I can get my hands on.

Amazon feeds my desire by providing two valuable pieces of data about * Math Jokes 4 Mathy Folks*. First, they provide the

**sales rank**for the book, which is updated hourly. Second, they provide

**weekly sales data**. The downside to this latter stat is the delay in its release — they provide data for Monday-Sunday, but it isn’t released until the following Friday. The upside is that big dorks like me use the time from Monday through Thursday to make predictions.

The chart below shows the average sales rank and weekly sales for Nov 24 through Dec 14. (The “average sales rank” is the average of the sales ranks for the seven days each week. Although it’s updated hourly, I don’t have the time to check it that frequently, so I rely on Author Central, which reports the sales rank at the end of each day.) It also shows the average sales rank (but not sales) for last week, Dec 15‑21.

Week |
Amazon Sales Rank(Weekly Average) |
WeeklySales |

Nov 24-30 |
4,742 | 114 |

Dec 1-7 |
3,437 | 279 |

Dec 8-14 |
2,390 | 435 |

Dec 15-21 |
2,063 | ? |

**The question: How many copies of MJ4MF were sold last week?**

Oh, sure… I could just wait until Friday to find out — but what fun would that be?

Instead, I constructed several mathematical models, and then I tweaked them to predict how many books were sold. The tweaks were based on some things I’ve learned over the past couple of years:

- Holiday sales are most vigorous in the first two weeks of December. They slow down a bit in the third week. Consequently, a sales rank of 1,655 on Dec 1 does not equal a sales rank of 1,655 on Dec 21.
- The long-term trend is not linear. In fact, this graph from Foner Books shows that it’s logarithmic.

Which brings us to the contest. Go to the Google form and **enter your prediction and email address**. (The email is only so I can contact you if you win.) **Closest guess to the actual number of sales will win the grand prize.** In the event of a tie, a winner will be randomly selected (or if I’m feeling generous, maybe there will be multiple winners… it’s hard to predict my disposition on any given day).

So, what are you waiting for? Open Excel or SPSS or your stat software of choice, muddle through a few regressions, and submit your entry!

**Winners will be announced on Saturday, December 27, 2014.** The exact time will depend on what time I roll out of bed, what activities my wife and kids propose for the day, and my particular disposition on Saturday. On second thought… safest if you check back on Sunday.

Good luck!

### Great Dates

Today is a great date, and I almost missed it!

**12/13/14**

Today’s date (in U.S. format) is the last time this century that the month, date, and year are consecutive numbers. If you choose not to celebrate this momentous occasion, you’ll have to wait almost 89 years for this to happen again.

Another great date with consecutive numbers happened 5 years ago.

**8/9/10**

That’s the date that **Math Jokes 4 Mathy Folks** was published.

And I rather like **12/11/14**. That’s just two days ago, when *Math Jokes 4 Mathy Folks* reached a rank of 2,210 on Amazon. That’s the highest sales rank it’s ever received. Woo-hoo!

Every year around this time, there is a significant spike in sales of *MJ4MF*. Ostensibly, it’s a good gift to give your engineer husband, statistician wife, or geometry teacher. And I am ecstatic that so many people are enjoying the book. But I’m wondering if we can blow the roof off of the Amazon rank; with a concerted effort, can we get the ranking of *MJ4MF* to below 1,000?

Here’s my request:

If you’re thinking of buying

Math Jokes 4 Mathy Folksfrom Amazon for someone as a gift this holiday season,please make your purchase of MJ4MF between noon and midnight ET on Tuesday, December 16.(Use this conversion chart if you’re in a different time zone.)Ordering by Tuesday, December 16 will still allow the book to arrive in time for Christmas or the last night of Chanukah, especially if you have Amazon Prime.

Since Amazon sales rank is based on a 24-hour period, any purchase on Tuesday will help with the ranking, so we don’t need to be much more specific than that.

And if you’re **not** thinking of buying *Math Jokes 4 Mathy Folks* this holiday season, well, what the hell is wrong with you? All the cool people are doing it.

### 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.]

### Annotated Amazon Review of *MJ4MF*

The paperback version of *Math Jokes 4 Mathy Folks* was released on August 9, 2010. During its first three years on Amazon, it received 17 reviews, with an average rating of 4.76. Recently, however, an unimpressed reviewer gave it just 2 stars:

This reminds me. If you’ve read *MJ4MF* and liked it, please post a review on Amazon. (If you disliked it, please post your review on MySpace.)

But I digress. Back to my point. The disparaging review that appeared on Amazon contained just 21 words:

jokes are not very funny – seems like they were stretching it to find enough jokes to fill a book to sell

To fully understand this review, I offer the following annotations.

jokes are not very funny

“I wouldn’t know humor if it bit me. I often travel to Branson, MO, to see Yakov Smirnoff perform live, and I think that Carrot Top’s performance on Star Search is the funniest moment ever.”

seems like they

“I’m unaware that the author is a single person,” or possibly, “I’m not familiar with rules of English grammar.”

were stretching it

“I don’t understand common English idioms. A friend pointed out that the correct phrase is just ‘were stretching’ without the ‘it.’ Oops.”

to find enough jokes

“I failed to realize that the book contains 400+ math jokes, yet a Google search for ‘math jokes’ returns 2,830,000 results. Simple percentages show how selective the author has been. I also hadn’t visited this blog before posting my review; I now see that a significant number of jokes not in the book have appeared on this blog, so clearly the author did not exhaust the supply.”

to fill a book to sell

“The author is a money-hungry swine who would sell his grandmother’s secret recipe for Hungarian pierogi for 50 bucks.”

Sadly, this last claim is mostly true. But my grandmother’s pierogi were divine, and the recipe is worth far more than $50. Kindly submit your bid in the Comments.

But I’m not bitter. I don’t care that this review reduces my average rating by 0.15 stars or that it single-handedly drops the book to #19 when someone searches for ‘math jokes’ on Amazon and sorts by “Avg. Customer Review.”

Instead, I prefer to remember the *MJ4MF* review written by Caregiver x 2, who said:

This morning I gave this book to my son, he didn’t put it down for a long time. He was laughing and flipping the pages as fast as he could. And he was on his summer break!

She is wise beyond her years, and I appreciate that she took the time to share her insightful comments with the world.

### Coming Up Through the Ranks

Through some special features at Amazon Author Central, I am able to know the daily sales rank of Math Jokes 4 Mathy Folks. My sales rank at the end of each of the last three days was 44,404, 96,990, and 35,355, respectively. I thought that was interesting — three days in a row when the sales rank was a five-digit number in which one digit occurred at least three times. What’s the likelihood of that? Stated more formally:

Assuming that the sales rank of MJ4MF is always a five-digit number, what is the probability that three consecutive days’ sales ranks will contain a digit that occurs in the sales rank at least three times?

The sales rank of MJ4MF has never been a five-digit number in which the same digit is repeated five times. (Bummer!) The probability of that occurrence, though, is even less likely than the situation described above — though I won’t tell you exactly how much less likely, so as not to spoil your fun!