Math is Hard: A Surface Story (Updated)

UPDATE: As expected, readers quickly found issues with the numbers I provided yesterday. Rather than change the story---which would be both a nightmare and an unacceptable re-writing of history---please see the end of this article for a major correction. Thanks for all the feedback. --Paul

While Microsoft refuses to release hard numbers for Surface sales, I'm wondering if there isn't a way to calculate rough unit sales figures for Surface Pro 4 and Surface Book.

Buckle in, folks. This one is going to involve a lot of math, and several important assumptions that could easily unravel this whole thing. So let's look at this as an intellectual exercise, and see if anyone can poke some enormous holes in my theory, and my assumptions. I suspect it will be all too easy.

OK, here we go.

Earlier today in Windows Device Stats for December Looks at Windows 10 Mobile and Surface, I used the latest AdDuplex data to report on the relative strength of various Surface devices. This data is based on usage, or what we might call usage share, and not market share, which represents sales. These are different things.

That said, because Surface Pro 4 and Surface Book are new, it's fair in this case to say that usage share does equal market share (sales). And that's assumption number one: That the newness of these devices means that their relative usage numbers is, in fact, the same thing as sales. Each device sold is being used.

If you believe this, and I think you should, that means that we can then calculate the rough unit sales---e.g. market share---for both, using those AdDuplex numbers.

Let's start with Surface Pro 4.

We know that there are 1.5 billion active Windows PCs (or, as we now say in 2016, devices) in the world. We know this because Microsoft tells us this is so, and based on my ongoing examination of Windows 10 sales, I've come to believe that this number is accurate. But yes. That is assumption number two.

Based on AdDuplex data, we know that Surface overall represents 2.5 percent of all PCs out in the world. This is assumption number three: That AdDuplex's data is representative of the real world. And if you buy that, then overall Surface usage is 37.5 million units out in the world. Because 1,500,000,000 times 0.025 is 37,500,000.

Based again on AdDuplex data---assumption number four if you want to be completely pedantic, and you do---we know that Surface Pro 4 accounts for 37.4 percent of all Surface devices in use. So we can calculate the actual number of Surface Pro 4 devices in use around the world. Which is the same as the number sold, because, again, these are the same thing in this one case.

And that number is 14 million Surface Pro 4 units sold. Because 37,500,000 times 37.4 percent is 14,025,000.

Doing the same math for Surface Book---which AdDuplex says represents 6 percent of all Surfaces in use---we can arrive at the approximate number of Surface Book units sold: 1,500,000,000 times 0.025 times...