With the Winter Olympics under way in Sochi, attention has finally turned to the athletes following months and years of discussion about terrorism, human rights and all sorts of other things that are not directly sport-related.

The event itself will fly by compared with the prolonged build-up. It always happens: the last Olympics – the summer event held in London in 2012 – passed in the blink of an eye following years of anticipation.

But although the Games will be over soon, these things always leave a legacy – whether good or bad – and it will be interesting to see the aftermath of Sochi.

The success of Olympic Games is often measured in financial terms. Every event seems to surpass its predecessors, and the cost being bandied about in relation to the Sochi Games is $50bn, or about £30bn.

That is more than all other Winter Olympics combined have cost to date, and 25% more than the spectacular Chinese summer Olympics in 2008.

Moody’s, the ratings agency, says the money poured into the Games will benefit Sochi and the surrounding area in the short term, but the investment could backfire in the future.

In a report entitled Uncertainty Over Long-term Legacy Overshadows Benefits, the agency also said that the economic boost for Russia as a whole would be negligible, if anything at all.

Governments always chuck a lot of money at these things, but centralised countries such as Russia do so even more than others. President Vladimir Putin sees the Olympics as a chance to show off what he considers his strength and dominant leadership.

No country wants to be embarrassed by a failure to deliver a spectacular show, but a country obsessed with its own internal PR is even more determined than others to show off its brilliance. Centralised governments throughout history have poured huge resources into trying to persuade their own people how fantastic their leaders are.

An example of how obsessed Russia is with portraying a positive image to its own people came during the opening ceremony when one of the displays failed.

Broadcasters around the world showed what was happening in real time, but the state Russian broadcaster quickly switched to footage of the dress rehearsal, when things had gone off without a hitch. The domestic Russian audience remained blissfully unaware of the error.

So with the state fully supporting the project, there was always going to be enough financial clout behind the Games. But it is what’s going to happen afterwards that is less certain.

Moody’s said the Games would probably prove to be “credit neutral”, due to the high cost of maintaining the new facilities once the Olympics have ended and “the uncertainty as to whether these regeneration efforts will sufficiently boost revenues from tourism and other areas”.

In terms of individual sectors, the legacy is likely to be mixed.

Telecoms operators are likely to see a quick return on their investment because the infrastructure they have installed has been needed in the region for some time.

But the money spent on hotels is less likely to be of long-term benefit. There’s no doubt that Sochi is receiving fantastic global publicity so it is likely the resort will see an increase in visitors over the coming years, but there are fears that the scale of the new developments is just too much for future demand.

The Olympics in London also saw massive investment in hotels across the capital, but there had been shortage of capacity in the city beforehand.

“The long-term gain depends on the hotel sector because the majority of the private investors invested in the hotel segment,” Sergei Grushinin, of Moody’s, told Reuters.

“It depends on the Russian government’s efforts to attract new tourists to Sochi, which we estimate need to increase by two-and-a-half or three times after the Olympics to ensure that the majority of the hotels are full.”

Meanwhile, as well as staking his personal prestige on hosting a successful Games, Putin also hoped that the massive investment would give the wider Russian economy a boost.

So far that seems not to have happened. The rouble has fallen by more than 5% against the US dollar since the start of 2014 and economic growth this year is expected to be much slower than during Putin’s first spell as president.

So are there any economic winners? Yes – the global corporate giants.

The story is very different for the sponsors who have invested heavily. Companies such as Procter & Gamble and General Electric will enjoy a worldwide boost to their profiles and brands, according to Moody’s.

That is nothing new. Whether it’s the Olympics or the football World Cup, or the Premier League or the Superbowl, we are well used to seeing mind-boggling sums of money spent by global brands. These companies are not stupid, and that sort of investment clearly works.

But it is interesting to compare the outcome of the billions spent by the Russian government and its state-backed banks, and the billions spent by private companies.

Go back to Sochi in a year’s time and you might find it busier than before, but you won’t witness the evidence of the huge sponsorship that you would if you went today.

It will be long gone and will instead be somewhere else – probably thousands of miles away, en route to Brazil for this year’s World Cup and the 2016 summer Olympics. Corporate budgets have no loyalty and are constantly searching for their next destinations.

The physical legacy of the infrastructure investment, meanwhile, is left behind.

One minute Sochi is taking the plaudits on the winner’s podium with the eyes of the world focused on it. The next the attention and the big money moves to the next event.

The corporates will pick up their next batch of shiny gongs, leaving Sochi with a tarnishing medal and fading memories.