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I’ve been getting an Olympic-size headache trying to figure out the actual cost of hosting the Summer Games.

Sure, Boston 2024 lays out its budget in a slick 19-page bid document telling us the price tag, not including security and infrastructure, will be $8.1 billion. All of the funds, in theory, will be put up by the private sector and institutions like the University of Massachusetts Boston that will use the facilities afterward.

The $8.1 billion is money that will go toward the operating budget and sports-related costs, everything from temporary stadiums to technology necessary to put on the Summer Olympics. Security is a separate line item because the federal government almost certainly will pick up the tab for that, and infrastructure improvements are also separate because they would happen regardless of the Games.

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That seems simple enough. But if you believe that $8.1 billion will be the final price, then I’d like to introduce you to an investment adviser named Bernie Madoff.

It’s not that Olympics boosters are trying to pull a fast one on us, but history has not been on their side — bid budgets have rarely come even remotely close to the final numbers.

A 2012 study from Oxford University’s Said Business School analyzed available Olympic data on expenses and found the Games, on average, end up with a cost overrun of 179 percent. That would mean a Boston bid could wind up at about $22.6 billion.

Now, this study looked only at expenses and did not factor in whether additional revenues offset the overruns. Some people might tell you it doesn’t matter what expenditures are as long as the Games bring in enough money to cover them. Atlanta in 1996 broke even, and Los Angeles in 1984 turned a profit.

Doug Arnot, who was the director of Games operations at the 2012 Summer Olympics in London, said operating budgets that grow more than originally forecast do so only when organizers know revenue will be bigger, too. Revenue for the host city comes in the form of sponsorships, ticket sales, and a contribution from the International Olympic Committee that comes from selling broadcast rights.

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“We run very much like a private business,” said Arnot, an adviser to the United States Olympic Committee on bids and game operations. “We don’t spend money we don’t have.”

All true, but I think we should all go into this with our eyes wide open. Even if local taxpayer money isn’t being used, it’s somebody’s money, and we should know what happens when the Olympics come to town.

Now let’s say we give the hometown the benefit of the doubt under the belief we can get our act together by 2024. Olympic planners have become better at estimating costs, so let’s just look at the Games since 2000. Since then, the average cost overrun has been 55 percent. That would put a Boston Olympics at $12.5 billion.

So why does a bid budget balloon by the time the Olympic flame is lit? For starters, blame optimism, said the study’s coauthor, Bent Flyvbjerg, a professor of management who specializes in megaprojects. Organizers need to persuade politicians and others that hosting the Games isn’t a money pit, so they come up with a number everyone can live with.

Second, the IOC, the group that awards the Games, isn’t stuck with the tab of putting on the sports extravaganza — the host city is, and up until recently there has been little incentive to rein in fancy stuff like showy stadiums and shiny new parks.

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Lastly, the host city has seven years from the time the IOC makes its selection to get ready — and a lot of things can change, but one thing that cannot is the delivery date. If you’re behind schedule, there’s often only one solution. “You have to spend more money,” Flyvbjerg said.

When I presented my concern about the bid budget to the IOC brass in Switzerland, I got such a fast response that I thought Usain Bolt might have been at the keyboard. “We are not sure what you mean by ‘cost overruns at the Olympic Games’ and would like to share the following information with you,” wrote Emmanuelle Moreau, the IOC’s head of media relations, in an e-mail.

Moreau explained the operating budget typically “results in a surplus, which is often reinvested back into sport in the host nation. Indeed, all recent editions of the Games, summer and winter have either broken even or made a profit on this budget.”

If you’re confused, it’s because Moreau is referring only to the operating budget. (In Boston, that amounts to $4.7 billion, or a little more than half of the bid budget.) It is the nonoperating outlay that can get out of whack when organizers start to build stadiums and other venues.

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Boston, which is billing its Olympics as sustainable, plans three projects outside of the operating budget: the athletes’ village, media center, and land development around the stadium. Other venues will be temporary or rely on existing structures such as Harvard Stadium or TD Garden. It’s the kind of Games the IOC is promoting since fewer cities want to host because they don’t want go into debt.

“The more infrastructure that is already in place, the less a city will have to spend to build new stadiums and other facilities,” wrote Moreau.

But after the Big Dig, Bostonians feel vulnerable to cost overruns. And with good reason: The original estimate to depress the Central Artery was $2 billion; the final bill was $22 billion.

Given our history, does Boston 2024 fear we could have another Big Dig on our hands?

“I don’t fear it, but at the same time I’m not going to sit here with some bravado and say ‘No problem,’ ” said Richard Davey, the newly installed Boston 2024 chief executive and former state transportation secretary. “If we win this thing, we’re going to have to have rigorous project management control to make sure that no costs go up, period.”

To keep expenses in line, Davey said, organizers are looking at using modular building techniques. They also will write contracts that penalize vendors for being late and over budget, and reward them if they get done early and under budget. Davey has successfully done this with state contracts: Callahan tunnel repairs were finished ahead of schedule.

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As much as we harp about the Big Dig, Davey said, we’re capable of pulling off megaprojects. Case in point: the $4 billion Deer Island project to clean up the Boston Harbor. That was delivered under budget and pretty much on time.

If anything, Davey thinks we’ve learned from Big Dig mistakes.

“At the end of the day, it was a pretty good project,” he said, sitting in the Boston 2024 offices on the Fan Pier, an area that benefited from the Big Dig, “and it transformed the city.”

So what’s the final accounting? If we win the Olympics, we won’t know for years — if not decades — whether it was worth it all.


Shirley Leung is a Globe columnist. She can be reached at shirley.leung@globe.com. Follow her on Twitter @leung.