When Rio de Janeiro won its bid to host the 2016 Summer Olympics back in 2009, the Brazilian government estimated that costs directly related to hosting the games would run just shy of $3 billion. But by the time Vanderlei de Lima lit the Olympic torch at last week’s opening ceremonies, the country had already spent some $4.6 billion on venues, administration, transportation and the like, putting the games roughly 50 percent over budget. By the time the games close on Aug. 21, the tally for the games will likely be higher still.

But it could be much worse. The 2014 Winter Games in Sochi blew their budget by 289 percent. The 1980 Winter Games in Lake Placid overtopped projections by 324 percent. And the 1976 Games in Montreal ran a staggering 720 percent over projections; the city spent three decades paying down the bill. While outliers such as these distort the average cost overruns somewhat (176 percent for Summer Games, 142 percent for Winter Games), the median cost overrun for all games for which we have data is 90 percent, making Rio’s cost overrun somewhat lower than the historical norm, at least so far.

The modern Olympic Games, in other words, are wildly expensive — and wildly more so than host cities expect when they make their bids. The Olympics have a well-deserved reputation for accelerated construction schedules and poor oversight, as well as for the cost overruns associated with them. Since the 1960 games in Rome, every single edition of the Olympics for which data is available has been more expensive than originally projected. But until recently it was unclear exactly how those cost overruns stack up next to each other, as well as next to other major civic megaprojects.

The numbers above come from a new study led by Bent Flyvbjerg at the University of Oxford’s Saïd Business School, who looked at six decades of Olympic budgets. It wasn’t easy — detailed cost overrun data is only available for 19 of the 30 games taking place since 1960, a paucity which Flyvbjerg and his colleagues found galling. “It means — incredible as it may sound — that for more than a third of the games between 1960 and 2016 no one seems to know what the cost overrun was,” they wrote. (Flyvbjerg said he suspects the 11 other games also ran over budget, but the lack of available data makes it impossible to know for sure. The Oxford researchers excluded those games from their analysis.)

To tabulate the costs, Flyvbjerg and his colleagues looked only at the costs of staging the games themselves — direct capital costs such as the building of the Olympic village and competition venues, transportation, administration and workforce and so on. Indirect capital costs such as upgrades to local public transit (which can add significantly to a host city’s total investment in the games) are not included in the totals. The researchers also accounted for inflation and currency valuation according to international standards to provide cost comparisons in real terms.

To put those cost overruns into perspective, Flyvbjerg and his colleagues compared the Olympics to other megaprojects such as bridges, dams, highways, railway lines and major IT projects. The Olympic Games average 156 percent cost overruns, outdistancing all other types of megaprojects. For comparison, road projects average overruns of 20 percent; bridges and tunnels 34 percent; energy projects 36 percent; rail projects 45 percent; dams 90 percent and IT projects 107 percent. Even road, bridge and rail projects come in under budget 10 percent of the time. Of all the types of projects compared, only the Olympics has a flawless record for going over budget, making the games a particularly risky undertaking for governments unprepared to absorb those additional costs.

“For a city and nation to decide to stage the Olympics Games is to decide to take on one of the most costly and financially most risky type of megaproject[s] that exists,” Flyvbjerg and company wrote, “something that many cities and nations have learned to their peril.”

Given that one city or another hosts the Olympics every couple of years, why do governments and organizing committees continue to have such a hard time projecting and containing costs? Part of the problem is baked right into the International Olympic Committee bidding process, said David Goldblatt, author of “The Games: A Global History of the Olympics.” Writing for Time magazine in July, Goldblatt estimated that the price tag of the Rio Games (including both direct games-related costs and other infrastructure and ancillary expenditures) could reach $20 billion, meaning the cost of hosting the games has multiplied as much as 2,000 times since the first modern games were held in Athens in 1896. While much of that growing cost has to do with the expansion of the games to include more of everything — more events, more athletes, more venues, more staff, more spectators — it also has to do with the proliferation of prestige projects and engineering one-upmanship. Grandiose architecture combined with a can’t-miss deadline leads to costly accelerated construction schedules, the costs of which are not reflected in the original bids.

“There’s this kind of relentless underestimation of costs, because if anyone knew the real bill at the beginning they would never sign up,” Goldblatt said in an interview. In other words, in an effort to win their bids, organizing committees are under intense pressure to present a low-cost budget — even if it doesn’t necessarily reflect reality. “If a realistic estimate was made in the first place, then the scale of overruns wouldn’t be quite as vast as they are.”

For instance, when London first began preparing its bid for the 2012 Summer Games in the early 2000s, organizers floated a total cost of around £2.3 billion (about $3.37 billion USD at the time). “It turned out to be nearer 11 [billion pounds], and 2.3 was just farcical,” Goldblatt said. “But who’s looking?” The sports media has become more skeptical over time, Goldblatt said, due to repeated cost overruns, but even so, “people have been getting away with a sort of statistical and accounting murder.”

In the 1990s, the IOC instituted Olympic Games Knowledge Management Program, an initiative meant to help organizing committees from future host cities learn from the experiences of previous Olympic hosts, with an eye toward curbing costs. Flyvbjerg and company suggest it seems to be working to some degree. For games before 1999, the median cost overrun was 166 percent. Post-1999, it fell to 51 percent.

Potential host cities increasingly view the Olympics with skepticism. In 2014, Stockholm, Lviv, Krakow and Oslo all bowed out of their bids for the 2022 Winter Games, citing ballooning costs as a primary concern. The IOC eventually loosened the rules for the bidding process and the games went to Beijing (again), despite the fact that it doesn’t typically snow on the mountain that will host downhill skiing events.

For its part, Rio is on track to come away from the 2016 Games more or less in line with what’s become the normal amount of additional expense on its books. But the implication of Flyvbjerg’s research is that Rio still may have been better off building $3 billion in roads and bridges (which likely would have ended up costing $3.6 billion to $4 billion because of their own overruns) than hosting the Olympics (which will end up costing at least $4.6 billion, and likely quite a bit more).

At the very least, the return on investment would have likely been greater. While most major infrastructure projects go over budget, megaprojects such as bridges, dams and railway lines tend to yield economic benefits for longer than the few weeks that many Olympic facilities are used. Host cities almost invariably fail to cover Olympics costs with associated revenues (for instance, in 2012 London took in $3.5 billion in revenues and shelled out something like $18 billion to host the games), leaving them with piles of debt and various useless venues. Research has repeatedly shown that in most cases the Olympics are a money loser for cities, particularly those in developing nations where the cost-benefit proposition tends to skew even worse.

For its part, Rio is on track to reverse the trend toward more expensive games established by the Beijing, London and Sochi Games. But even these comparatively frugal games don’t look like much of a bargain. That’s because the dollar value of cost overruns is often less important than a given country’s ability to absorb them, a lesson Brazil is learning the hard way. When countries bid for the games seven years out, it’s impossible to account for shifting political and economic circumstances, said Kevin Wamsley, academic vice president and provost at St. Francis Xavier University in Antigonish, Nova Scotia, and an expert on Olympic politics. Brazil is hosting the Summer Games while dealing with presidential impeachment proceedings and its worst economic crisis since the 1930s. While the Olympics didn’t cause Brazil’s current problems, they are a multibillion-dollar burden on a country already struggling to cover basic expenses.

“Look where Brazil finds itself,” Wamsley said. “They’re not paying their police officers and other public service workers, they’re not paying their professors, they’re in all kinds of trouble. That’s just an unbelievably horrible context in which to host an Olympic Games.”