Sales

Distribution of E-Book Sales on Amazon

For e-books on Amazon the relationship between the daily sales rate s and the rank r is approximately given by:

s = 100,000 / r

Such an inverse proportional relationship between a ranked quantity and the rank is called a Zipf distribution. So a book on rank r = 10,000 can be expected to sell s = 100,000 / 10,000 = 10 copies per day. As of November 2013, there are about 2.4 million e-books available on Amazon’s US store (talk about a tough competition). In this post we’ll answer two questions. The first one is: how many e-books are sold on Amazon each day? To answer that, we need to add the daily sales rate from r = 1 to r = 2,400,000.

s = 100,000 · ( 1/1 + 1/2 + … + 1/2,400,000 )

We can evaluate that using the approximation formula for harmonic sums:

1/1 + 1/2 + 1/3 + … + 1/r ≈ ln(r) + 0.58

Thus we get:

s ≈ 100,000 · ( ln(2,400,000) + 0.58 ) ≈ 1.5 million

That’s a lot of e-books! And a lot of saved trees for that matter. The second question: What percentage of the e-book sales come from the top 100 books? Have a guess before reading on. Let’s calculate the total daily sales for the top 100 e-books:

s ≈ 100,000 · ( ln(100) + 0.58 ) ≈ 0.5 million

So the top 100 e-books already make up one-third of all sales while the other 2,399,900 e-books have to share the remaining two-thirds. The cake is very unevenly distributed.

This was a slightly altered excerpt from More Great Formulas Explained, available on Amazon for Kindle. For more posts on the ebook market go to my E-Book Market and Sales Analysis Pool.

Five Biggest Mistakes In E-Book Publishing

Are you thinking about publishing an e-book? If yes, then know that you are entering a highly competetive market. Publishing a book has never been easier and accordingly, many new authors have joined in. To have a chance at being read, you need to make sure to avoid common mistakes.

1. Lack of Writing Experience

Almost everybody can read and write, it’s a skill we learn from an early age on. But writing is not the same as writing well. It takes a lot of practice to write articles or books that make a good read. So before you start that novel, grow a blog and gain experience. This provides a chance to see what works and what doesn’t. And the improvement will become noticeable after just a few weeks and months. As a plus, the blog you grew can serve as a marketing platform once your e-book is finished. In such a competitive market, this can be a big advantage.

2. Writing for Quick Cash

Writing for quick and easy cash is a really bad idea. This might have worked for a short while when the e-books were new and fresh, but this time is long gone. Just browse any indie author forum for proof. The market is saturated. If your first e-book brings in 30 $ a month or so, you can call yourself lucky. If it’s more, even better, but don’t expect it. Writing and selling e-book is not a get-rich-quick scheme. It’s tough work with a very low ROI. If you do it for the money, you’re in for a disappointment. Do it out of passion.

3. Lack of Editing

If you spend three weeks writing a book, expect to spend another three weeks on fine-tuning and proof-reading. To find the mistakes in the text, you have to go over it again and again until you can’t stand your book anymore. You’ll be amazed that seemingly obvious mistakes (the same words twice, for for example) can be overlooked several times. And no spell checker will find that. Tedious editing is just part of writing and if you try to skip that, you will end up with many deserved one-star reviews.

4. No or Ineffective Marketing

With 2.5 million e-books on Amazon, many of high quality, getting noticed is tough. Without any marketing, your sales will most likely just disappear in an exponential fashion over time. The common marketing means for indie authors are: growing a blog, establishing a facebook fan page, joining facebook groups and interacting, becoming active on twitter, joining goodreads and doing giveaways, free promos via KDP Select, banner and other paid ads (notably on BookBub – as expensive as it is effective), and and and … So you’re far from done with just writing, editing and publishing. You should set aside half an hour a day or so for marketing. And always make sure to market to the right people.

5. Stopping After The First Book

Publishing the first e-book can be a quite sobering experience. You just slaved for weeks or even months over your book and your stats hardly move. Was it all worth it? If you did it out of passion, then yes, certainly. But of course you want to be read and so you feel the frustration coming in. The worst thing you could do is to stop there. Usually sales will pick up after the third or fourth book. So keep publishing and results will come in.

E-Book Market & Sales – Analysis Pool

On this page you can find a collection of all my statistical analysis and research regarding the Kindle ebook market and sales. I’ll keep the page updated.

How E-Book Sales Vary at the End / Beginning of a Month

The E-Book Market in Numbers

Computing and Tracking the Amazon Sales Rank

Typical Per-Page-Prices for E-Books

Quantitative Analysis of Top 60 Kindle Romance Novels

Mathematical Model For E-Book Sales

If you have any suggestions on what to analyze next, just let me know. Share if you like the information.

How E-Book Sales Vary at the End / Beginning of a Month

After getting satisfying data and results on ebook sales over the course of a week, I was also interested in finding out what impact the end or beginning of a month has on sales. For that I looked up the sales of 20 ebooks, all taken from the current top 100 Kindle ebooks list, for November and beginning of December on novelrank. Here’s how they performed at the end of November:

  • Strong Increase: 0%
  • Slight Increase: 0 %
  • Unchanged: 20%
  • Slight Decrease: 35 %
  • Strong Decrease: 45 %

80 % showed either a slight or strong decrease, none showed any increase. So there’s a very pronounced downwards trend in ebook sales at the end of the month. It usually begins around the 20th. Onto the performance at the beginning of December:

  • Strong Increase: 50%
  • Slight Increase: 35 %
  • Unchanged: 10%
  • Slight Decrease: 5 %
  • Strong Decrease: 0 %

Here 85 % showed either a slight or strong increase, while only 5 % showed any decrease. This of course doesn’t leave much room for interpretation, there’s a clear upwards trend at the beginning of the month. It usually lasts only a few days (shorter than the decline period) and after that the elevated level is more or less maintained.

Mathematical Model For (E-) Book Sales

It seems to be a no-brainer that with more books on the market, an author will see higher revenues. I wanted to know more about how the sales rate varies with the number of books. So I did what I always do when faced with an economic problem: construct a mathematical model. Even though it took me several tries to find the right approach, I’m fairly confident that the following model is able to explain why revenues grow overproportionally with the number of books an author has published. I also stumbled across a way to correct the marketing R/C for number of books.

The basic quantities used are:

  • n = number of books
  • i = impressions per day
  • q = conversion probability (which is the probability that an impression results in a sale)
  • s = sales per buyer
  • r = daily sales rate

Obviously the basic relationship is:

r = i(n) * q(n) * s(n)

with the brackets indicating a dependence of the quantities on the number of books.

1) Let’s start with s(n) = sales per buyer. Suppose there’s a probability p that a buyer, who has purchased an author’s book, will go on to buy yet another book of said author. To visualize this, think of the books as some kind of mirrors: each ray (sale) will either go through the book (no further sales from this buyer) or be reflected on another book of the author. In the latter case, the process repeats. Using this “reflective model”, the number of sales per buyer is:

s(n) = 1 + p + p² + … + pn = (1 – pn) / (1 – p)

For example, if the probability of a reader buying another book from the same author is p = 15 % = 0.15 and the author has n = 3 books available, we get:

s(3) = (1 – 0.153) / (1 – 0.15) = 1.17 sales per buyer

So the number of sales per buyer increases with the number of books. However, it quickly reaches a limiting value. Letting n go to infinity results in:

s(∞) = 1 / (1 – p)

Hence, this effect is a source for overproportional growth only for the first few books. After that it turns into a constant factor.

2) Let’s turn to q(n) = conversion probability. Why should there be a dependence on number of books at all for this quantity? Studies show that the probability of making a sale grows with the choice offered. That’s why ridiculously large malls work. When an author offers a large number of books, he is able to provide list impression (featuring all his / her books) additionally to the common single impressions (featuring only one book). With more choice, the conversion probability on list impressions will be higher than that on single impressions.

  • qs = single impression conversion probability
  • ps = percentage of impressions that are single impressions
  • ql = list impression conversion probability
  • pl = percentage of impressions that are list impressions

with ps + pl = 1. The overall conversion probability will be:

q(n) = qs(n) * ps(n) + ql(n)* pl(n)

With ql(n) and pl(n) obviously growing with the number of books and ps(n) decreasing accordingly, we get an increase in the overall conversion probability.

3) Finally let’s look at i(n) = impressions per day. Denoting with i1, i2, … the number of daily impressions by book number 1, book number 2, … , the average number of impressions per day and book are:

ib = 1/n * ∑[k] ik

with ∑[k] meaning the sum over all k. The overall impressions per day are:

i(n) = ib(n) * n

Assuming all books generate the same number of daily impressions, this is a linear growth. However, there might be an overproportional factor at work here. As an author keeps publishing, his experience in writing, editing and marketing will grow. Especially for initially inexperienced authors the quality of the books and the marketing approach will improve with each book. Translated in numbers, this means that later books will generate more impressions per day:

ik+1 > ik

which leads to an overproportional (instead of just linear) growth in overall impressions per day with the number of books. Note that more experience should also translate into a higher single impression conversion probability:

qs(n+1) > qs(n)

4) As a final treat, let’s look at how these effects impact the marketing R/C. The marketing R/C is the ratio of revenues that result from an ad divided by the costs of the ad:

R/C = Revenues / Costs

For an ad to be of worth to an author, this value should be greater than 1. Assume an ad generates the number of iad single impressions in total. For one book we get the revenues:

R = iad * qs(1)

If more than one book is available, this number changes to:

R = iad * qs(n) * (1 – pn) / (1 – p)

So if the R/C in the case of one book is (R/C)1, the corrected R/C for a larger number of books is:

R/C = (R/C)1 * qs(n) / qs(1) * (1 – pn) / (1 – p)

In short: ads, that aren’t profitable, can become profitable as the author offers more books.

For more mathematical modeling check out: Mathematics of Blog Traffic: Model and Tips for High Traffic.

Computing and Tracking the Amazon Sales Rank

The webpage http://www.novelrank.com/ provides a very neat simple way to track the sales rank of any book on Amazon. This service is completely free.

The sales rank is computed from the sales rate. The more a book sells per day, the lower the rank will be.  Here’s an approximate formula, taken from: http://www.edwardwrobertson.com/2013/02/a-quick-way-to-calculate-amazon-sales.html.

100,000 / rank = sales per day

So if a book is on rank 50,000, it sells about twice a day. As far as I know, a borrow counts as a sale and a free download as one third of a sale.

I use novelrank to track my ebooks. This is what the output looks like (launch of “Great Formulas Explained”):

novelrankgreatformulas

Indeed a neat tool to see how a book is performing. Note that the tracking starts on the day you add it, dates before that are not shown.

As you can see, during the period when no sale is made the sales rank increases more or less linearly at about # 50,000 per day. The average rank during this time can be calculated by the formula: final minus initial rank divided by 2. When a sale is made, the rank makes a discontinuous jump to a lower value.