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, Mr. 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.