PALO ALTO, Calif. — By some measures, Tony Bates has accomplished a lot at Skype since Microsoft paid $8.5 billion for the Internet calling service.

The statistics tell the story. In seven months, the number of people using the service each month has jumped 26 percent to nearly a quarter of a billion, affirming Skype’s status as one of the crown jewels of consumer Internet services.

But the deal, the biggest acquisition in Microsoft’s history, will ultimately be judged by whether Microsoft can weave the product deeply into its vast product portfolio, providing a superior Skype experience on products as various as Windows PCs and Xboxes. In that regard, Bates, who was previously the chief executive of Skype and became president after the deal, and his Microsoft colleagues have not yet delivered.

“It’s still promising and intriguing, but we really haven’t seen it rolled out across the products,” said Bill Whyman, an analyst at ISI, an investment research firm.

One important milestone will come this year, when Skype is expected to release a preliminary version of its calling software that runs on Windows 8, a coming overhaul of Microsoft’s flagship operating system intended to work well with touch-screen computers. The idea that Skype can give Windows and other Microsoft products an edge is the only way the company can justify the high price it paid, analysts say.

Bates is performing a tricky balancing act in Microsoft. As part of the deal, Microsoft gave Skype a longer leash than it grants most of its divisions, even allowing Bates to work in Silicon Valley — important not least for its symbolism. With offices scattered across time zones in Sweden, Estonia, Luxembourg, Prague and London, Skype is the only Microsoft division located almost entirely outside the parent company’s Seattle-area home base.

In an interview in his spacious office here in Palo Alto, Bates, an affable Briton, said he insisted that his employees receive new security badges stamped with the Skype logo, not the standard Microsoft badges.

Another sign of his independence is the Apple MacBook Air on his desk. While using Apple products publicly is not unheard-of among Microsoft executives, it is nevertheless considered a mild form of sacrilege at a company where everyone is expected to fly the Windows flag.

“We’ve kept our identity and our autonomy,” Bates, 45, said.

The distance has helped Skype stay true to its mission of allowing people to make calls from practically any device connected to the Internet, not just the ones powered by Microsoft software. In the past several months, Skype has cranked out versions of its calling software for Google Android smartphones, a Sony portable game console, Comcast set-top boxes and Apple mobile devices. Skype is the fourth-most-downloaded free app of all time for both the iPhone and iPad.

The level of attention to building software for other companies’ devices is remarkable at Microsoft, a company for which Windows and related software products account for a vast majority of profits. While most Skype calls still happen on Windows PCs, much of Skype’s growth is likely to come from new mobile devices, a category in which Microsoft is struggling to play a major role.

Beloved for its cheap and free Internet calls, Skype’s use has continued to grow briskly, jumping 40 percent to 100 billion minutes of calls in the first three months of this year from the same period last year.

Still, Bates and other Microsoft executives cannot afford for Skype to be too independent. They want to avoid repeating what happened after Skype was acquired by the auction site eBay for $2.6 billion in 2005.

The audience for Skype soared after that deal too. But when expected synergies with eBay did not materialize, eBay spun off Skype into a separate company with new investors.