Facebook’s figures also imply that over the past year, it has caught and taken down roughly 90 percent of fake accounts that are created on its site — most, it said, “within minutes of registration.” Facebook said it also stopped millions of fake accounts from registering each day.

Mr. Schultz said such a success rate was possible because “the vast majority of accounts we take down are from extremely naïve adversaries,” who typically create automated accounts that are easy to spot. The smaller number of fake accounts that elude detection are generally manually created accounts.

Mr. Schultz added that Facebook was cautious in removing manually created accounts because it didn’t want to erase authentic profiles. “We don’t want to over-enforce,” he said. “So what we actually focus on is the harmful behavior.”

Yet obvious fake accounts that are engaging in harmful behavior slip through. Last year, I found dozens of fake accounts masquerading as the company’s founder, Mark Zuckerberg, to scam Facebook users out of cash. Some had been up for years.

Facebook also said the vast majority of fake accounts it removed were ones that it had spotted, rather than ones that users had reported. Of the 2.8 billion fake accounts it took down in the year that ended Sept. 30, Facebook said, it found 99.3 percent on its own.

Those numbers also contradict my experience. Last year, I easily created 11 Facebook accounts that used the same name, occupation and profile photo as my verified account. They remained live for five days, until I reported them to Facebook. Instagram, which Facebook owns, also left up 10 impostor accounts I had created until I reported them; it took down only five, until I alerted a Facebook spokesman.

If an account appears to be impersonating another user but isn’t “engaged in harmful behavior,” Facebook often leaves it up, Mr. Schultz said. He said such duplicate accounts could be from people who had lost their password or were confused.