## Ebooks, predictions, math that lies.

Yesterday, the American Association of Publishers posted the lastest report on publishers’ sales revenue, for the month of April 2011

I’ve been tracking these numbers for a while. Obviously, the big headline is about the growth of the ebook format; here’s what the chart looks like with the latest

[image: ebook baseline]

I think we can all see a trend. It’s not *quite* exponential growth; that would be even more dramatic of an upward trend. In fact, I tried to graph it — messing around with numbers, seeing if there was a formula I could use to predict ebook sales. [a fool’s errand, but once I started playing with the math I was having too much fun to quite let the idea go.]

Eventually, it occurred to me to try looking for other mathematic models, beside 2^{x} or some other exponent in the formula. Eventually I remembered sigmoid functions and after playing around with a few of *these* I hit the operator that produced a best-fit curve. Thankfully, it was not only blessedly simple — tanh(x) — but also something that is supported by OpenOffice Calc.

[image: bestfitcurve]

The original data is messy, and this is an *awfully* small sample, but hey – I’m just playing with numbers. I ended up with

ebook(t)=k * (1 + tanh(t))

Where k is a constant one selects out of one’s ass (a surprising number of scientific constants work that way) and t is the time variable. t, in my graph above, is counted off in units of [roughly] π/60, and t=-π at some arbitrary point in the past —in this case, November of 2006: one year before the kindle came out.

After all the trial and error to squeeze the math into the data I had, it turns out these have some meaning: constant k is equal to sales at the inflection point of the curve, and as such is roughly 1/2 of ‘equilibrium’ sales, and by counting in units of π/60, we’re looking at the dynamic part of the graph [tanh(-π) to tanh(π)] over the course of 10 years [120 months]

So those were my assumptions – and the function used – and I like this graph.

Even using the same math — the exact same function — one can mess with the constant and time variable though, to make a very similar graph

[image: projection2]

that at first blush seems to be the same. In this case, instead of t=-π at Nov 2006, I pushed it forward to t=-π at Nov 2007 — in effect saying the growth in ebooks didn’t really start until a year later. To make the new graph fit the same numbers, I had to change my constant k.

That’s hard to see above, but let me project both graphs out to 2015.

[image: to 2015]

The red line, my first projection, shows ebook sales perhaps hitting $200 Million *a month* as early as January of 2013. At this point, ebook sales would constitute about half of all book sales (currently at an average of about $575 Million a month for trade books, at least over the past 5 years — a number that includes ebooks) and that soon after, the growth of ebooks would level off.

Using the same function but with different assumptions (the yellow line) you can see that ebook sales will continue to grow almost out of control, increasing by about $100 Million every sixth months through 2012 and 2013, and not really levelling off until 2016. At that point, ebook sales would be $750-$800 Million *each month* – about 50% bigger than the entire current trade book market, all by itself.

**Please note** I only included the second projection to show how the math can be manipulated, and that even the models that *seem* to fit the available data can also be made to fit someone’s assumptions and conclusions.

**That said**, I think the available data does in fact support a modelled sigmoid growth curve, which means ebook sales *will* eventually level off. When, and at what level, is the hard part to figure out.

To me this only makes sense, as there will be a natural saturation point — everyone who wants an ebook reader (or who already owns a smartphone or computer) will have one, and everyone who wants to read ebooks will be doing so. The market for ebooks *can’t* grow past a certain level, except of course as all markets naturally grow given inflation and growth of population.

At any rate, I think we’ll have enough data in one year’s time to be able to better model the ebook market. I’ll save this spreadsheet and break it out again when we have another six to eight months of sales data.

Sigmoid growth curves in the adoption/sales of new technology is probably

verycommon – something to remember when considering dotcom booms, and dotcom bubbles.Anyone care to do this for, say, Facebook?

Comment by Matt Blind — 24 June 2011, 13:42 #

Yes, a sigmoid is the normal curve for expansion into a new niche. At first, expansion is primarily limited by the base already in place, which is the close to exponential growth phase, but as it grows into its niche, expansion comes to be more and more limited by the unexploited potential still remaining.

I’d be skeptical of starting with the Kindle ~ the Sony Reader would be the first eInk reader to get the ball rolling in this market, even if a early follower captured a larger market share. Its not uncommon that an early introduction reveals not only promise but also reveals rough edges that if smoothed away can yield a competitive advantage.

Also note that the saturation of this niche is not necessarily the end of the story ~ the point of market saturation starting to come into sight is likely to shift focus from growing this niche to finding neighboring niches to expand into, which can give additional growth curves in those niches on top of this one.

Comment by BruceMcF — 25 June 2011, 20:50 #

@BruceMcF

when I revisit this dataset in the fall, I’ll take that into consideration, and pull the ‘inception’ point for ebooks even further back.

obviously, I hope a few more data points will make the trend obvious, even without the fancy maths.

Comment by Matt Blind — 25 June 2011, 21:54 #