We are almost there. Less than three weeks until the starting pistol is fired on the world's greatest sporting spectacular. Flags are being unfurled, bunting hung and bus passengers terrorised by police. Soon there will be snipers in the skies, streets shut off for foreign dignitaries and the capital handed over to the sleazy potentates who govern the Olympic Games.

Given his political and economic woes, David Cameron must relish the chance to tap into the excitement over the Games. The Coalition has long seen the festival as a rock to build recovery on. So it was little surprise to hear the Prime Minister proclaim that London 2012 would boost the British economy by £13bn over the next four years, aiding tourism, sales and foreign investment.

All hosts say the same. It is the political choreography, and almost as much a part of the Games as the opening ceremony, the use of performance-enhancing drugs and a sudden interest in minor sports. Unfortunately, it's not true. Perhaps the greatest mythology in sport is over the claimed benefits of these huge events.

Take the cost. The final bill at this time of austerity will be £11bn, an astonishing fourfold increase in the promised costs since London first put in its bid. It is another prime example of incompetent state procurement. For all the fine talk and opaque nature of Olympic financing, the Games are unlikely to show a real profit – it is almost three decades since they last did, since when they have expanded. No wonder barely a third of Britons think them worth the cost.

It is impossible to disprove the figures bandied around. We will never be able to look back at our economy and determine its size if beach volleyball had not been held on Horse Guards Parade. But a series of academic studies have found that big sporting events do not boost economic growth, help employment or even increase tourism. They can do precisely the opposite – and not just because so many workers are being told to stay at home, and many of those working are demanding bonuses to do their job.

For a start, the infrastructure is highly specialised, built fast and to the requirements of organisers rather than the needs of the host city. So we have the obscene spectacle of spending £40m on a basketball arena and £19m on a water polo venue, only to be pulling them down once the crowds disappear. Even Sydney, among the best organised recent Games, tore down several venues – hardly surprising, since it must hold one event a week to cover running costs of its surviving Superdome.

As job creation schemes, these mega-events are flawed. Much of the work making expensive venues is highly specialised, so of limited help for unemployed locals. In the longer term, jobs in sporting centres are often part-time, low skilled and low paid. Any help to the job market is highly inefficient: one American study found the cost of each job generated was four times the cost of the next best alternative. Other studies speculate that the Olympics actually cost a country jobs when so much taxpayers' money is frittered away.

Stratford was going to be regenerated regardless of winning the Olympics. But few people setting out on an urban regeneration scheme would seek to spend vast sums on flamboyant sports stadiums. The usual style is to use limited state revenues on facilities for daily living such as homes, offices, schools and hospitals. For Britain, this has been compounded by spurning the opportunity offered by the Wellcome Trust, which wanted to spend £1bn buying the Olympic Park to create a global scientific research hub with 7,000 jobs; instead, organisers sought a fast buck by selling the athletes' village to the Qatari royal family and a firm of private developers.

Amid all the hype, there is much talk of tourism. So Londoners hoping to rent out homes at inflated prices were surprised when the promised goldrush never materialised. Meanwhile, music festivals have been cancelled and West End theatre bookings are down by 20 per cent.

The truth is that some visitors would have been coming to London anyway, while many more avoid the circus and business travel is deferred. When we last held a global sports event – the Euro 96 football finals – only 100,000 of the expected 250,000 foreign visitors turned up, and they spent peanuts by comparison with overall tourist spending. When Greece held the centenary Olympics in 2004, it took tourism two years to recover to pre-Games levels.

Then there is the promised sporting legacy, the idea we will be so inspired by Usain Bolt's exploits that we will pull on tracksuits and start sprinting round the local park. The suggestion is clearly ridiculous. If this was really the aim, it would make more sense to spend those billions building swimming pools and sports centres across the country, restoring the damage done by successive governments selling off school playing fields. And if organisers want us to be healthier, why are Cadbury, Coca-Cola and McDonald's among their "partners"?

Don't despair entirely. Holding a major sporting event can make a country happier. It can engender a genuine feel-good factor – especially when the host nation outperforms expectations. Unfortunately, this is far more pronounced with football contests. The impact of the Olympics appears less perceptible and more transitory. But enjoy it while it lasts. The money has mostly been spent – and our nation's need for a little lift has rarely been greater.

Twitter: @ianbirrell