How much did the Winter Olympics in Sochi, Russia, cost? There’s no easy answer to that question, even though the Western news media have tried to simplify it. Or perhaps oversimplify it.

The consensus figure is $50 billion, which, give or take a few billion, would easily qualify Sochi as the most expensive Olympics ever, about 25 percent more than the $40 billion spent on the much-larger 2008 Summer Olympics in Beijing .

That eye-popping number has appeared in nearly 2,000 news articles about the Games since last year, according to the Nexis database; more than 1,000 articles have tweaked the figure to a more-precise-sounding $51 billion.

But how did we land on this amount?

Both numbers more or less hardened into the “official” estimate when the Games opened last week. Although few stories mention it, the source of that estimate was Dmitry Kozak, a deputy prime minister who headed Russia’s Olympic preparatory commission, which was charged with supervising the work in Sochi. Last February, Kozak told reporters in Moscow that Russia was prepared to invest 1.5 trillion rubles in Sochi, which was the equivalent of $50 billion.

But like most large round numbers, this one needs a few caveats and asterisks.

For starters, currency fluctuations over the past year have altered the original value of Kozak’s estimate. Based on current exchange rates, his 1.5 trillion rubles had shrunk to $43.1 billion when Sochi staged its Opening Ceremonies on Friday.

The second problem is that Kozak’s figure is a year old. Given that the cost estimates for Sochi quadrupled between 2007 — the year Russia was chosen to host the Games — and 2013, there’s reason to be skeptical about a year-old number. Wouldn’t an additional year add to, or at least change, a figure that had been wildly inflating over the preceding six years?

Also, estimating the cost of the Games depends on how, and what, is counted.

Kozak said that the Russian government would spend $6.7 billion on Olympic facilities. He said Russia would invest another $16.7 billion in upgrading rails, roads and other infrastructure surrounding Sochi. That comes to $23.4 billion in 2013 money — massive, but not even halfway to $50 billion.

The rest of his projection included private, speculative investment by Olympic sponsors, including billionaire friends of Russian President Vladi­mir Putin. Russia hopes the Olympic stimulus will turn the Sochi area into a year-round tourist magnet long after the Olympics are over, and it encouraged investment in hotels and other facilities in the region.

But not all of this spending was directly related to the Olympics, such as the construction of a Formula One racetrack in Sochi that reportedly cost $350 million. And as Kozak noted, some of this money would have been spent by public and private sources without the Olympics.

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Then there are the allegations of corruption to consider. Dissident Russian politicians, such as Boris Nemtsov and Alexei Navalny, have said Putin’s oligarchs padded their Olympic construction bills by the billions in order to skim government-backed loans. It’s difficult to be certain of this — government officials dispute claims of widespread fraud — but the numbers floated are as fantastic as the official figures; Nemtsov says as much as $30 billion has been stolen.

All of these nuances have been compressed, or perhaps overlooked, in the widely reported $50 (or $51) billion price tag. Attention-grabbing by itself, the big number seems to support a larger media theme: The Sochi Olympics are designed to showcase Putin’s autocratic rule and to make a grand statement about a newly assertive Russia. “For President Putin [staging the Games] is a chance to show off Russia as a resurgent superpower,” wrote the Times of London.

The questionable cost figure may also have gained currency in media accounts because it “resides on the cusp of plausibility,” a key factor in the spread of media-driven myths throughout the ages, said W. Joseph Campbell, a professor at American University and the author of “Getting It Wrong: Ten of the Greatest Misreported Stories in American Journalism.” Plus, he said, it’s easier for journalists to go with a figure repeated by other news outlets than to do “the very hard work required to develop an independent estimate.”

Indeed, there’s a lot of monkey-see, monkey-do behind the reporting of the Olympic budget, said Craig Silverman, author of the Regret the Error blog and a book about media mistakes.

“Journalists love numbers,” he said. “Give us stats, dollars, polls, percentages and we eat them up and spit them out to push forward an assertion, trend or angle. So when a nice, big number about an important event makes its way into stories by seemingly credible outlets, that figure basically becomes true and usable in the view of other media outlets.

“It’s kind of scary when you think about it,” Silverman added. “If you can manage to get a fake or exaggerated figure into one or two reports, chances are it will take on a life, and credibility, of its own. This phenomenon repeats itself ad nauseam.”

Perhaps no one outside the innermost recesses of the Kremlin will ever know for sure what the Sochi Olympics cost. But you could pretty safely wager $50 billion that the price tag wasn’t $50 billion.