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Listen to Bostonians debate the city’s Olympic bid and you are sure to hear two seemingly irreconcilable points at the heart of their arguments.

It is accepted as gospel by opponents that every Olympics since 1960 has had cost overruns.

Supporters will take it to their graves that the last three Games in the United States — in 1984, 1996, and 2002 — turned profits.

Who is right?

Well, neither statement is unconditionally true, according to a Globe review of Olympic budget documents, though both contain elements of truth — if you don’t mind some caveats.

Olympic Games do commonly end up costing more than original predictions, though there does not appear to be enough data to claim this always happens.

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It also appears to be the case that organizers of the Olympics in Los Angeles, Atlanta, and Salt Lake City closed their books with profits or broke even, due to higher-than-expected revenues, leaving no overrun bills for city taxpayers. In the case of Atlanta and Salt Lake, however, the Games enjoyed generous federal support, which supplemented the organizers’ privately funded budgets.

The reality is Olympic financing is much too complicated to be boiled down to political slogans. Data on past Games are hard to come by and often incomplete, and the definition of an Olympic-related expense can be subjective.

But that hasn’t stopped partisans on both sides of Boston’s Olympic-sized political debate from making their claims.

“Every single Olympics since 1960 has overrun its initial budget,” opponent Chris Dempsey said in testimony to the Boston City Council in March. He repeated the claim at a Brookline Town Meeting and in a radio debate last month with Rich Davey, chief executive of Boston 2024, the group working to bring the Games to Massachusetts.

Opponents base the statement on a 2012 University of Oxford study, Dempsey, cochairman of the group No Boston Olympics, said in a Globe interview. The Oxford study compares the original Games budgets filed with the International Olympic Committee with the final costs of staging the events, from 1960 to 2012.

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But — and here’s the caveat — though the study says, “every Games, without exception, has experienced cost overruns,” it just as plainly states that it refers only to the Games the researchers could analyze. Many Olympics lacked crucial data, and in the end, they were able to review only 17 of 28 Summer and Winter Olympics from 1960 to 2012.

Those 11 Olympics not covered include a key one: The 1984 Los Angeles Games.

The ’84 Games were famously frugal, organized under a voter-approved restriction on the use of public money. Los Angeles held most of its events in existing venues, building only an aquatic center, velodrome, and tennis facility, according to a 2004 study by Holger Preuss, a sports economist in Germany.

After the Games, one report of the Los Angeles organizing committee said expenditures were $546 million. Other sources, including the US Government Accountability Office, reported a lower figure of about $413 million.

Original budget numbers for those Games are not readily available; even the International Olympic Committee says it does not have them.

But a retrospective published in 1985 by the Los Angeles Olympic Organizing Committee reported that its financial plan, developed in 1979, called for approximately $347 million in spending and enough revenue to leave a $21 million surplus.

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Those Games were organized at a time of high inflation. A quick computation using US Department of Labor statistics to deflate the final costs of the Los Angeles Olympics into 1979 dollars would suggest the Games cost roughly 9 or 10 percent more than original estimates when using the higher account of the costs. Using the lower GAO cost suggests the Games were well under budget, corrected for inflation.

On the revenue side, Los Angeles raised far more than anticipated, leaving a surplus of more than $200 million.

Opponents wave away these results as an anomaly, due to the fact that the city, as the only viable bidder for the 1984 Olympics, was able to negotiate favorable terms with the IOC.

Atlanta Olympic organizers, around 1990, submitted a $1.005 billion plan to host the 1996 Games. They predicted raising $1.162 billion in private revenue from TV rights, corporate sponsorships, ticket sales, merchandising, and other sources, leaving a $156 million surplus, according to the original budget provided by the IOC.

After the Games, organizers reported that expenses and revenue had penciled out even, at $1.7 billion each, according to the committee’s official report. Some sources reported a $10 million profit.

Atlanta’s operating expenses ended up about 42 percent higher than the original budget, after a rough adjustment for inflation. The original budget lacks the detail for a close comparison, but cost estimates for transportation and construction appear to have been too rosy.

But the committee also raised about 23 percent more private money than it had planned, with corporate sponsorships and ticket revenue outpacing expectations.

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The extra revenue, along with the planned surplus, balanced the budget, according to the documents.

Those results, supporters say, show that higher costs are not an issue when offset by higher revenues.

“Costs may have exceeded the budget because [organizers] said, ‘We have this extra revenue and we can add in some extras that would be nice to have,’ ” said Davey, speaking generally about past Olympics.

Opponents say public contributions make the numbers look better than they really are.

Federal and local governments contributed about $377 million to the Atlanta Olympics for direct costs, in 1996 dollars, the GAO reported.

“If you can find a way to get the public to pick up the tab, then you’re going to be able to claim profitability,” Dempsey said. “Were you truly and honestly profitable?”

Boston 2024 has long maintained it needs the federal government to provide $1 billion or more for security or Boston would be unable to host. The group plans a $4.6 billion Olympic operating budget, and depends on $4 billion in private-sector investment. The committee has called for $775 million in taxpayer-financed transportation projects, which it insists are needed with or without the Olympics.

For the 1996 Games, the Oxford researchers reported far higher numbers than those from the Atlanta committee for the total cost and for the increase from the original budget.

In response to questions from the Globe, Allison Stewart, coauthor of the study, said “it’s possible” the researchers double-counted hundreds of millions of dollars in spending. “Thanks for drawing our attention to this possibility for Atlanta,” she said by e-mail. “We’ll look at it again when we publish our updated study next year.”

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Organizers of the 2002 Salt Lake Winter Games originally proposed an operating budget and sports-related capital budget that totaled about $1.37 billion, according to IOC records and to Stewart.

Like Atlanta, the 2002 Games benefited from government largesse. Three layers of government paid roughly $570 million, or about 30 percent, of the $1.9 billion total cost, according to GAO numbers. Much of the government help was for security for the first Olympics held after the Sept. 11 terrorist attacks.

When Salt Lake organizers closed the books on their $1.3 billion budget for staging the Games, they celebrated a $100 million profit.


Mark Arsenault can be reached at mark.arsenault@globe.com. Follow him on Twitter @bostonglobemark