I recently completed a Countdown Promotion in Amazom.com on Kindle Select.

Before the promotion my book (The Black Orchestra) was priced at $3.99 and selling at a rate of 4 books per day on Amazon.com. The promotion ran as follows (times are GMT):

Noon Dec 6 to noon Dec 8 selling price 99c = 0.25 of the usual price

Noon Dec 8 to noon Dec 10 selling price $1.99 = 0.5 of the usual price

Noon Dec 10 to noon Dec 12 selling price $2.99 = 0.75 of the usual price

I expected the volume of sales to be influenced by the selling price, but I was amazed at how predictable this relationship turned out to be.

**The royalty from each stage was constant.**

In mathematical terms, this can be expressed as follows:

**N*d = M*D**

where N is the number of books sold per day, d in the discount selling price, M is a (constant) “Magnification factor” and D is the number of books sold per day before the promotion started.

We can adjust the formula to give the number of books sold at each increment:

**N = M*D/d**

Applying this formula to the three stages of the promotion, we get:

**N(1) = M*D/0.25**

**N(2) = M*D/0.5**

**N(3) = M*D/0.75**

In the case of my book, D = 4 and (based on sales at increment 1) M turned out to be 7. Predicted sales, based on the formula are:

**N(1) = 7*4/0.25 = 112**

**N(2) = 7*4/0.5 = 56**

**N(3) = 7*4/0.75 = 37**

The promotion for each increment ran for 2 days, giving predicted sales of

**224 + 112 + 74 = 410**

Actual sales were:

**225 + 109 + 86 = 420**

Sales for each increment continued beyond the cut-off. I can only suppose that the data was being collated manually. The last sale in the last increment was recorded close to midnight (GMT) on 12 December, 12 hours after the promotion had ended.

The “Magnification factor”, M obviously depends on the amount of publicity given to the promotion. In my case, I used twitter and a friend gave it some twitter exposure as well. I also put notices on a number of Facebook sites that welcome these sorts of notices (thanks to Mary Louisa Locke for these). I paid no one to help advertise the promotion.

The Amazon ranking, which stood at 26,000 before the promotion, dropped (ie rose) to 1,350 and fell away again. At the end of the promotion, the ranking was 2,500.

The total predicted royalty income from the promotion is easy to calculate:

**6*D*M*R**

The normal effective royalty rate, R is $2.3 (70% of $3.99 in US and some other countries, 35% in other countries).

**6*D*M*R = 6*4*7*$2.3 = $386**

The actual income was higher, as the sales figures exceeded the predictions.

The expected average royalty per book over the whole promotion is independent of D and M and depends only on the discount increments:

**3*$2.3/(4+2+4/3) = $0.94**

The actual average royalty per book was slightly above $1.09

The expected income in the absence of the promotion would have been 6*D*$2.3 = $55, so the predicted gain from the promotion was $386 – $55 = $331. The real gain, of course, is 400 new readers and maybe some new reviews.

The promotion also generated about 20 borrows on KDP Select at $2.40 each.

It would be interesting to compare these results with the experiences of others to see if my formula holds up for other books and to examine the effect on the “Magnification” factor of increased publicity.

Any volunteers?