I post numbers like these for time to time, because I find them interesting and other people sometimes find them useful. Every time I do people ask me for the source, and my answer is generally 'my model'.
This is an accurate reply, in that I've worked out almost all of the numbers myself from first principles in a large Excel file. But it's also not very informative, so I thought it might be useful to lay out exactly how I or anyone else would go about getting to them. As you will see, the complete answer to 'what is the source' does not really fit on Twitter.
One upon a time, all of this was pretty straightforward.
Mobile operators reported their connections (both contract customers and prepay) every quarter
Most of the handset market was taken by companies who reported their unit sales every quarter, and Nokia (which had close to 40% of the market by volume and so was in a position to know) also produced an estimate of the total market size.
So, you knew how many handsets were being sold, and how many were being used, and most of that came from primary sources - these were the actual real numbers, not estimates or informed (or ill-informed) guesses. All you had to do was collate the data from all of the companies' financial reports every quarter (or pay someone else to do it). Sometimes, for the mobile operators, a national regulator or industry association would make it easy by collecting all the numbers in one place.
Not any more.
First, mobile penetration has now risen above 100% in most developed markets, because many people have more than one live connection: they have several prepaid SIMs to get the best coverage and to take advantage of on-network pricing deals, or just have one they don't use much. This started happening well before things like dongles and tablets, which boost the total further but which are at least easy for mobile operators to split out. Hence, the number of connections globally is now well over 7bn but the number of people who actually have a mobile phone is rather lower.
The problem is that no-one has access to a 'correct' number of how many. Any given mobile operator has no way to know that you have a SIM from it and also from a competitor, so mobile operators cannot strip out the duplication. Theoretically, if all SIM cards were registered with your identity, it would be possible to strip this out nationally, but I'm not aware of any such analysis actually being attempted. Instead, we have surveys and estimates, of which one of the more comprehensive is shown in these two charts from the GSMA's analysis unit, showing first total reported connections (containing a few estimates for operators who don't report, plus their own estimate for future growth) and then estimated actual unique humans with a phone.
These numbers are derived using a reasonable methodology, but they're only estimates and the correct number might be higher or lower. If I could clone myself, or had a different job, I might go about trying to generate my own version of these numbers from the bottom up, but that's not on my to-do list this year. This is as good as it gets.
For phones, meanwhile, the problem is simply that almost no-one reports unit sales anymore. Apple does report unit sales of iPhones and iPads (in fact it reports both 'sell-in' to distributors and 'sell-through' to actual people: in this as in most things except future plans it is actually a model of transparency). Samsung used to and stopped, Nokia's phone unit stopped after Microsoft bought it, and the other big OEMs stop, start and stop again seemingly at random. Meanwhile the 'other' category, which encompasses several hundred companies and at least a dozen that are significant, collectively makes up a third of the market, and mostly says nothing.
This leaves us three ways to estimate phone sales.
The first is to assume a replacement cycle for the number of unique mobile users - if 3.5bn people buy a phone every two years, then you get, say, 1.7-1.8bn units. This is really only valuable as a sanity check, though - there are rather too many assumptions being multiplied together for comfort.
The second is to look at the component players, most obviously ARM and Qualcomm but also newcomers like Mediatek and Spreadtrum, who sell to the vast majority of phone makers in one way or another (to simplify hugely) and therefore ought to know how many phones are being sold, and more importantly they also make consistent, regular public statements about how big they think the market is. Hence Qualcomm produces this estimate of 3G/4G device sales (of course, this includes tablets, dongles and M2M units as well as phones).
The catch here (besides the non-phone stuff included) is the note 'estimated to be reported' - that is, how many Qualcomm expects to be told about and have a license fee paid on, as opposed to how many will actually be sold. Some portion of Chinese manufacturers, for a range of complex reasons, are selling phones that they do not report to Qualcomm and pay royalties on. So even Qualcomm does not know what it is supposed to know.
The final avenue is that followed by some of the industry data firms, such as Gartner and IDC, which is to spend a lot of time in China talking to anyone and everyone - not just Qualcomm and ARM, but lots and lots of other component companies and handset manufacturers who don't want to give public numbers for competitive reasons. Theoretically, if this is done properly, it should give a pretty solid number. In practice, these firms sometimes disagree by a significant amount and sometimes adjust their figures retrospectively - in other words, they're still estimates. But they do give a sense of the general market size and direction.
However, there's another complicating factor. We now care rather less about precisely how many mobile subscribers there are, or how many handsets per se are being sold, than about smartphones. And we care about how many smartphones are in use and from which ecosystem rather than how many units any given OEM is selling. If you're an Apple shareholder or an LG shareholder than their respective unit sales matter, but to anyone else it's the ecosystem that matters.
For the ecosystem, the relevant number is not actually how many units are being sold, but rather the install base of live devices - not how many sold last quarter but how many there are in total and how that's changing. For this, Apple's iOS and Google's Android pose different challenges.
As I described in some detail here, Google used to give cumulative activations of Android devices, at irregular intervals and in round numbers, and occasionally daily activation rates (which generally were not consistent with the cumulative number). So as long as the amount of time between numbers was not too large, you could calculate the cumulative activations by extrapolating a growth rate from the last public numbers, and then make an assumption about how long a device remained in use once it had been activated. (Early in the history of Android the OEMS themselves gave unit sales numbers that you could add up, but as mentioned above that hasn't been the case for years.)
However, at IO in the summer of 2014 Google stopped giving activations (in fact it hadn't given any since announcing '1bn' cumulative activations in September 2013). Instead it switched to giving MAUs for the first time, including historic data - but only on an annual basis, and we've had no more numbers since then (the chart below gives '1bn' for June 2014, without the precision of previous years).
Moreover, it turned out by comparing the old and new data sets (cumulative activations over time versus MAUs over time) you could see that the life-span of an Android device had been changing - for one horrible period it looks like Android phones were averaging an active life of less than a year. By the summer of 2014 it looks like the problems had eased and the Android replacement cycle had lengthened to perhaps 18 months (though this is very approximate). Compare that with Qualcomm's estimate (and note that this is only an estimate, though a well-informed one) for the overall market.
Meanwhile, trying to extrapolate an annual MAU number given in round numbers into a formal estimate for December 2014 is not much more precise than the previous method.
So today, we have no primary data for Android activations or device sales, nor for MAUs more recently than last summer, nor for the growth rate (yes, we know the growth from summer 2013 to summer 2014, but that's on a curve and we don't know if the curve has changed shape). Happy days.
Google does at least give monthly percentages for screen sizes (profile and a resolution bracket) within the active base, which theoretically gives you a split for tablets versus phones versus phablets. This has to be taken with some caution. Handset OEMs have been known to change the profile reported by a given device between firmware versions, and as the resolution of phones increases it's hard in practice to say whether a particular reported resolution represents a 4-5" phone or a 7-8" tablet anyway.
Next, Google itself only knows about devices that ship with its services. It doesn't know about Kindle Fire tablets nor Kindle Fire phones, and Amazon isn't saying (though the big write-off of Fire Phone inventory is pretty informative). The Fire platform is unlikely to be significant on a global scale, though. China is, and the vast majority of Android phones sold in China come with no Google services on them and so aren't in Google's statistics at all. This amounts to something like a third of all Android devices. Here, again, we have to fall back on occasional disclosure from OEMs (Xiaomi gave a figure for 2014 sales, for example, which were almost all in China) and beyond that again the analyst firms for national unit sales estimates. However, there is a ray of sunshine here: Baidu regularly says how many Android and iOS devices it sees hitting its networks. This of course is biased towards active users, and may be incomplete, but it does help us claw our way slightly closer to a primary source.
Now for iOS.
Apple reports exactly how many iPhones and iPads are sold each quarter, and we have a pretty good sense of how many iPod Touches it sells (Apple includes the unit sales within the iPod number and gives regular pointers towards the sales mix, though the number is shrinking fast). However, we do not have a number from the company as to how many are in use. The products have been in the market long enough that not all can be, but how many?
Without a number from Apple, the most straightforward approach is to look, again, at the replacement cycle (📢🚨📢). In this case we are helped by the fact that there are a bunch of sites that can give us a pretty good sense of the mix of different iPhone and iPad models in the active base by analyzing their traffic. So we can look at the proportion of older and of no-longer-on-sale models in the base, make an assumption (informed by the average selling price) about the current sales mix of new and older models, and arrive at an average lifespan. (Incidentally, this is theoretically possible for Android, but the sheer number of models makes it much harder).
So, Apple has reported selling a cumulative total of 827.7m iPhones and iPads by September 2014, and given indications that lead me to estimate the iPod Touch number as a bit over 100m. If we assume a 24m life this would give 480m live devices. For a bunch of reasons, this seems too low. It is very clear that iPads are not replaced every two years, while the size of the second-hand market for iPhones (especially in China) and the number of iPhone 4 and 4S units still apparent in the base from traffic data also indicate a longer lifespan. So, I've estimated 3 years for the iPod Touch and the iPad and 2.75 years for the iPhone, which gives an active number of 640m devices. Add in a rise in iPhone sales for December and a fall in iPad sales, and the number rises to 650-675m. As Groucho Marx almost said, these are my guesses - if you don't like them I've got others.
I have not even attempted to estimate how many people have both an iPhone and an iPad. I could, I suppose, but I have no basis for doing so other than a pure guess (50% overlap? In which direction? Who knows?). Apple has this data, of course.
If you're still paying attention, you'll have noticed that I'm estimating a rather longer life for an iPhone than an Android phone - and that I used Google's own numbers to work out that at one point Android phones were lasting less than a year. At that time, Google had to sell at least twice as many Android phones as Apple had to sell iPhones to get the same number of active users. This is why looking at the install base and replacement rate is so important. If you only look at unit sales, you miss what's happening to the ecosystem. (And, of course, you have to look at how these devices are actually used, which is a whole other conversation.)
Finally, for any given country you can often return full circle to the mobile operators. They know exactly which devices are connecting to their networks and often give indications of the smartphone penetration rate, data plan take rate and even occasionally a platform split. Until a year or two ago the U.S. operators disclosed iPhone unit sales, for example.
Then, briefly, there are the PCs, Macs and Linux. For PCs I take the industry analyst consensus, which aligns to a roughly 4.5 year replacement cycle. Apple gave a figure of 80m active Macs in the summer. Desktop Linux (I wasn't including embedded or servers) is fuzzy. I outlined some estimates here - 75m is an upper limit, I think, but I'm open to better estimates.
If you think all of this sounds flakey, vague and deeply problematic - you're not the only one. But this is how the sausage is made.