Both Scottish nationalists and unionists have been attempting to make political capital out of the achievements of Scottish athletes at the Olympic Games.

SNP ministers, who are hoping Scots will vote for independence from the UK in a referendum due to be held in 2014, refused to use the name “Team GB” in their video message to athletes from north of the border. First Minister Alex Salmond has taken to referring to Sir Chris Hoy and his compatriots as “Scolympians”.

Unionists, for their part, have expressed delight in seeing Andy Murray drape himself in the union flag following his gold medal victory over Roger Federer.

The athletes themselves have been reluctant to drag politics into the occasion, but those who have spoken out have conspicuously failed to back independence.

Sir Chris said: “I’m Scottish and I’m British…All I can say is that I’m very proud to be part of this team, to be part of the British team.” Showjumper Scott Brash insisted he was “100 per cent Scottish” but said the experience of competing in London had made him “feel more British”.

Nevertheless, it remains the policy of the nationalist-controlled Scottish government that, in the event of a “yes” vote two years from now, Team Scotland will fly the Saltire in Rio.

Why can’t Scotland have a separate team now?

After all, the home nations compete separately in football, rugby and at the Commonwealth Games. The Olympics is a different animal, however, thanks to the iron rules of the International Olympic Committee.

Rule 30 states that a country can only form a National Olympic Committee if it is “an independent state recognised by the international community”. So it’s unlikely that a vote for “devolution max” or anything short of full independence will be enough to please Jacques Rogge and co.

The Scottish government, in any event, appears to accept this. A spokesman told us: “The First Minister has previously stated it is his desire to see a Scottish team competing in the 2016 Games on the back of a Yes vote in the referendum.”

Where would a separate Scotland be in the medal tables?

Assuming Scots do vote to end the Union in 2014, what kind of Olympic form could we expect from the country’s athletes? A fairly strong one, depending on how you look at it.

Scottish athletes won 13 of Team GB’s 65 medals, and seven of them were golds. If you think that’s a fair way to look at it, it means Scotland would be in a respectable 12th place in the world medal rankings.

And if you allow for population size, it’s even more of an achievement. With a population of just 5.2 million, Scotland would be in the top five of the per-capita medal tables.

But while some of those gongs were individual achievements (like Murray’s demolition of Federer), others were team efforts involving non-Scots (a minority of the women’s hocky team who won bronze today were Scots). Do you include the team medals in the “Scottish” total?

If not, the total is three medals, two golds courtesy of Murray and Hoy and a silver from swimmer Michael Jamieson, which puts the Scotland in 36th place globally at time of writing, and in around 25th place if we adjust for population.

Would Scottish athletes automatically join Team Scotland?

The short answer is that no one knows, but UK Sport, the body that funds Team GB’s elite athletes using a mixture of money from the National Lottery and the government, told us they think it’s unlikely that anyone will be forced to switch flags.

There’s a strong precedent here in the shape of Northern Ireland, which is technically under the jurisdiction of the Olympic Council of Ireland, despite being part of the United Kingdom.

The obvious sensitivities mean that athletes from the province can choose which team to join, thanks to an agreement between the Irish and British Olympic committees. It’s difficult to imagine such an arrangement not being put in place in the event of Scottish independence.

Would they still be allowed to train in England?

The prospect of losing access to training facilities south of the border was a worry for Sir Chris Hoy, who trains in Manchester, after Beijing 2008. He said at the time: “They have to start investing in sport before they can think about anything like a Scottish Olympics team.”

The Scottish Government told us it is addressing precisely that problem, saying: “We continue to increase the number of world-class facilities across Scotland, such as the Commonwealth Arena, the Sir Chris Hoy Velodrome, the refurbished Commonwealth Pool, the Aberdeen Sports Arena, and the Tollcross Aquatics Centre.”

In any event, national sports agency sportscotland told us that in principle, there’s no good reason why the country’s athletes would be confined to the borders of an independent Scotland.

A spokesman said: “We send our high-performing athletes to the best environment for them, and we envisage that that will continue. A lot of athletes go and train in different climates and with different coaches around the world. Andy Murray went to live in Spain as a teenager.”

As things stand, a reciprocal agreement between the governing bodies in the different home nations means that English students in Scotland get to use local facilities and vice versa.

It’s possible that an outburst of petulance from the English authorities following a “yes” vote could put an end to that kind of agreement, but then English athletes would suffer too. So there’s no reason to assume that the Hoys of the future couldn’t base themselves in England too.

But who will pay the bills?

It’s impossible to ignore the fact that Team GB’s recent successes followed a huge injection of money, mostly from the National Lottery, in the 1990s.

Holyrood’s official line about post-referendum sport in Scotland is: “Under all constitutional circumstances, sportscotland will ensure that high performance athletes continue get the best possible training that is right for the individual, their circumstances and their sport.”

But that raises more questions than it answers, since sportscotland doesn’t hold the purse strings for Scotland’s elite sport programmes. Most of the money comes from UK Sport, and if that funding stream were suddenly switched off, there would effectively be no major cash pot for Scotland’s top athletes.

The Scottish government would have to massively ramp up spending and/or come to an arrangement with the National Lottery to bag a certain percentage of the takings. Of course, the economics of independence are fiendishly complex and we don’t know how Scotland’s finances would shape up.

If an independent Scotland found itself rolling in oil money it could afford to splash the cash on sport, but that’s another FactCheck.

UK Sport told us it has no contingency plan for Scottish independence and “could not even begin” to answer the question of whether funding for Scottish athletes would be cut off.

By Patrick Worrall