The water in one swimming pool turned green. Apart from that, the 2016 Summer Olympics in Rio de Janeiro went off without a hitch. Preliminary figures also indicate that the Rio Olympics 'only' cost 51% more than originally budgeted – which by Olympic standards is a great success.

But that this could be considered good news hides the bigger, uglier truth: all Olympic Games go over budget. In fact, they are the only type of mega-project in the world to do so. These graphs show the total cost of 18 Summer and Winter Olympics held between 1968 and 2016, and the cost overruns for each of those Games. That should give cities hoping to host the Olympics some pause for thought.

At first glance, the message of these two graphs seems positive: a few outliers notwithstanding – most notably London 2012 and Sochi 2014 – the cost of Olympic Games seems relatively stable; and again discounting Sochi, the worst of the cost overruns occurred before the year 2000.

But let's take a closer look at those figures. They were taken from a research paper produced for Said Business School at Oxford University, the first study ever into cost and cost overrun at the Games. It focuses on sports-related costs (i.e. operational costs such as admin and catering, and direct capital costs such as the construction of the venues and Olympic village). The study excludes indirect capital costs (i.e. upgrading transport and hotel infrastructure), because data on these costs is rare and unreliable – even though they are often higher than sports-related costs.

Even excluding indirect capital costs, reliable data for the amounts of the original bid and the eventual cost was available for only 19 out of the 30 Summer and Winter Olympics held since 1960. “Incredible as it may sound for more than a third of the Games (discussed here), no one seems to know what the cost overrun was”, the researchers note. “For some Games, hiding costs and cost overruns seems to have been more important, for whatever reason”.

So the available figures probably paint a conservative picture of Olympic cost and cost overruns. Keeping that in mind , the average outturn cost (i.e. budgeted cost plus cost overrun) for Summer Games is $5.2 billion, and $3.1 billion for Winter Games. The costliest Summer Games ever were those in London 2012 at $15 billion, followed by Barcelona 1992 at $9.7 billion and Montreal 1976 at $6.1 billion. Only the Winter Games at Sochi 2014 were more expensive than London 2012, at $21.9 billion. The second-most expensive Winter Olympics was Turin 2006, at $4.4 billion; followed by Salt Lake City 2002, at $2.5 billion.

After London and Sochi, and fortunately for the troubled finances of Brazil, the Rio Games herald a return to the average, at an overall turnout cost of $4.6 billion. This includes the 51% extra alluded to earlier – again, in line with median cost overrun since 1999.

The gold medalist in cost overrun is Montreal, which went over budget by 720%. This despite the city's then-mayor boasting, in 1973, that “the Montreal Olympics can no more have a deficit, than a man can have a baby”. Fewer predictions have been more wrong: no other host city has overrun its initial cost estimate for the Olympic Games by as much as Montreal. The Summer Olympics of 1976 saddled the city with a mountain debt that took it 30 years to pay off.

But Montreal is just the worst example of a remarkable phenomenon: all Olympics go over budget. Percentage-wise, Sochi – the most expensive Games overall – doesn't even take the silver. That goes to the 1980 Winter Olympics in Lake Placid, which went over budget by 324%. On the lower end of the scale are the 2002 Winter Olympics in Salt Lake City (24%), the 2010 Winter Olympics in Vancouver (13%) and the 2008 Summer Olympics in Beijing; although researchers take the allegation that those only cost 2% more than budgeted with the grain of salt required when ingesting any Chinese government information.

But also the relatively good score for London 2012 – 'only' 76% over budget is deemed a bit suspect: “In 2005 London secured the bid with a cost estimate that two years later was revised upwards with around 100%. When the final outturn costs were slightly below the revised budget, the organizers falsely, but very publicly, claimed that the London Games had come in under budget. Such deliberate misinformation of the public about cost and cost overrun treads a fine line between spin and outright lying”.

In fact, the average cost overrun for the Olympics is 156% (176% for Summer Games, 142% for Winter Games). Almost four out of five Games studied in the paper overrun the initial cost estimate by at least half, while almost one in two end up costing at least double. Compare that to other megaprojects: road building typically overruns by 20%, bridge and tunnel construction by 34%, megadams by 90% and large IT projects by 107% - but none of them all the time.

So why is it so singularly difficult to deliver the Olympics within budget? As the report somewhat sarcastically summarizes: “If, perversely, one would want to make it as difficult as possible to deliver a megaproject to budget, then one would (1) make sure that those responsible for delivering the project had never delivered this type of project before, (2) place the project in a location that had never seen such a project and (3) enforce a non-transparent and corrupt bidding process that would encourage overbidding and place zero responsibility for costs with the entity that would decide who wins the bid. This, unfortunately, is a fairly accurate description of the playbook for the Olympic Games”.

To be fair, the International Olympic Committee has created an Olympic Games Knowledge Management Program (OGKMP), specifically to transfer skills from former host cities to new ones. It came into effect for the first time in the run-up to the Sydney Summer Games in 2000. And indeed, median cost overrun before that date was 166%, while it dropped to 51% for all the games after that year. It would take only one or two cost overrun outliers like Sochi to erase the benefits of the OGKMP.

So, all eyes turn to PyeongChang, South Korea for the 2018 Winter Olympics and to Tokyo, Japan for the 2020 Summer Olympics. Which budgetary records will they break?

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