Windows may still be winning the desktop operating system war, but according to a Goldman Sachs report, Clash of the Titans, that doesn't matter because Microsoft has been badly losing the far more important computing device war to Apple iOS and Google Android.

Why? Because, "The compute landscape has undergone a dramatic transformation over the last decade with consumers responsible for the massive market realignment. While PCs were the primary Internet connected device in 2000 (139mn shipped that year), today they represent just 29% of all Internet connected devices (1.2bn devices to ship in 2012), while smartphones and tablets comprise 66% of the total. Further, although Microsoft was the leading OS provider for compute devices in 2000 at 97% share, today the consumer compute market (1.07bn devices) is led by Android at 42% share, followed by Apple at 24%, Microsoft at 20% and other vendors at 14%."

Goldman Sachs' analysis isn't in a vacuum. Mary Meeker, once a superstar Wall Street analyst, and now a well-respected venture capitalist, recently presented a Kleiner Perkins Caufield & Byers report titled Internet Trends Year-End Update. The report found that tablets and smartphones were out-selling PCs in 2010's 4th quarter and have since left them in the dust. By 2013's 2nd quarter, Meeker predicts, the Apple- and Android-dominated smartphone and tablets installed base will be greater than the Windows PC installed base. Today, by Meeker's numbers, Apple iOS and Google Android have 45% of the market to Windows' 35% .

Goldman Sachs, like Meeker, sees this trend away from Microsoft-dominated PCs to Apple and Android mobile devices only growing stronger. "Platform stickiness is set to drive convergence of OS share in tablets and smartphones as tablets increasingly become an anchor device, given users more for content on these devices. If left without a meaningful competitor in tablets, Apple's dominant share is likely to pull its smartphone share steadily upward over time. Thus, a credible tablet becomes a strategic imperative for Google, or they run the risk of a steady decline of Android smartphone share starting in CY13."

While Google and Android, thanks to Android-powered tablets such as the Nexus 7 and the Amazon Kindle Fire HD , is challenging the iPad, Microsoft, with little presence in either smartphones or tablets , even after the arrival of Windows Phone 8, Windows RT, and its Surface tablet/notebook hybrids, has a far harder row to hoe.

"Microsoft faces an uphill battle (though not insurmountable) given it lacks meaningful share in either tablets or smartphones and as such will need to rely on its appeal to knowledge workers to help drive adoption as its complement ecosystem will remain behind the iOS and Android platforms at least over the next 6-12 months." observed Goldman Sachs.

2013 will, according to Goldman Sachs, determine if Microsoft can reverse its sharp decline or become a company relying upon the shrinking PC legacy business . "After watching its market share of total consumer compute fall from 93% in 2000 to 20% expected in 2012, we expect the recent launches of Windows Phone 8 and Windows 8 tablets to help the company reclaim some share in coming years. This transition is particularly meaningful given the Goldman Sachs view of the health of the consumer PC market, which we forecast will be flat in 2013."

This will not be easy since [my emphasis] "Microsoft would have to sell roughly 5 Windows Phones or roughly two Windows 8 RT tablets to offset the loss of one traditional Windows PC sale, which we estimate has an overall blended selling price of $60 for business and consumer."

The bottom line is that "It took a compute revolution to unseat Microsoft from its dominant market position." It was not that Linux-based Android or Apple ever managed to knock Windows off its desktop throne. They haven't. It was that the smartphone and tablet rebellion has unseated the desktop. "Fundamentally, Microsoft’s business was disrupted by other vendors who successfully introduced compelling new device categories" But, "thus far, Microsoft has failed to establish a meaningful foothold in [these new] key growth categories."

So, "With Microsoft on the sidelines up until recently, the consumer compute OS market had come down to two key vendors: Apple with iOS and Google with Android. Apple’s strong market presence (we estimate 24% share of total consumer compute in 2012) is the result of its role as a successful pioneer of key new compute devices, including the smartphone and tablet."

Apple hasn't managed to keep its first-mover advantage.

"The company’s software and application ecosystem is tied to its hardware devices, there was a need for an alternative cross-platform operating system to enable competitive form factors. Google met this need with the introduction of the Android operating system (open source) in November 2007, which has proliferated across smartphones in particular, but tablets as well. In fact, May 2012 data from OpenSignalMaps suggests there are more than 4K distinct devices running Android with Samsung, HTC, Sony and Motorola as key device vendors. "

Thus, "with an estimated 42% of the total consumer compute market in 2012, Google/ Android has captured the dominant position, largely driven by Android’s success in the smartphone category, where attractive device form factors have been introduced by Samsung and others." Still Goldman Sach expects " Android share to tick down slightly to 41% share of total consumer compute in 2013/14 partly as Microsoft captures incremental share with Windows 8 and Windows Phone 8."

Can Microsoft catch up? Goldman Sachs views "the success of Microsoft’s Surface tablet as critical to its ability to compete in this new compute paradigm... Microsoft’s tablet offerings will likely be the key anchor in determining pull through of Windows-based smartphones. Further, we would not be surprised to see the company release a Microsoft-branded smartphone at some point, following in its lead of developing its own tablet offering, Surface. As such, we would expect Microsoft to increase its share in both the tablet and smartphone markets, but at what level remains to be seen."

If Microsoft really needs Surface to be a smashing success, Microsoft is real trouble.

Leaving aside Windows Surface RT's poor quality , until recently Microsoft made it difficult for users to buy Surface devices . It's hard to gain market share with a new kind of device, a hybrid tablet/laptop, unless users can see and handle it.

True, the far more powerful Windows 8 Pro-powered Surface will start shipping in January. But I foresee a good deal of customer confusion between it and the Windows RT models since they look alike but come with very different capabilities and price-tags. This, in turn, will lead to slow adoption at the exact time that Android and iOS-powered devices will be passing Windows PC in the total number of legacy devices.

Very quietly, and without many of us even realizing it, open-source Android and Apple iOS have become the world's top personal operating system leaving Windows in the dust of computing history. Short of a smartphones and tablet Microsoft miracle, Windows' day of the dominant end-user operating system is almost over.

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