The recriminations started early this time around. The Olympic flame was barely fired up before administrators, politicians and pundits alike were weighing in on Australia’s poor performance.

John Coates, Australian Olympic Committee president, thinks members of the swimming establishment in particular should “have a look at themselves” in light of lacklustre achievements in London, and an enquiry is set to get underway. The International Olympic Committee member Kevan Gosper blames inadequate government funding on elite sports. The Australian Financial Review reports that it might even have something to do with the exchange rate.

Having placed 4th on the medal tally in Sydney and Athens and 6th in Beijing, it’s feasible Australia could have its worst performance since the 1988 Games in Seoul, where we placed 15th.

Whatever the case, it’s clear one thing will have a defining place in debates and enquiries about performance: the Olympic medal tally.

But how valuable is the medal tally, really? How useful is it for measuring a nation’s Olympic performance? And, most importantly, in the emerging debate over sports funding, should it continue to play the type of prominent role that it has so far?

The logic of the medal tally goes thus: nation versus nation – may the best one win. Even to the casual observer, this must seem like a curious way to rank performance, given the vast disparities between nation-states.

For a country such as Guyana, with a population of just under 800,000 in 2010, it hardly seems right to compare it to the United States, a country with a population in excess of 300 million. Similarly, Germany’s US$3.5 trillion economy (in terms of GDP) would make it considerably easier to be competitive than Malta’s economy of just less than US$9 billion.

What if we took into consideration some of these built-in biases of the official medal tally? The UK’s Royal Statistical Society, along with The Guardian’s Datablog and researchers from Imperial College, London recently took on this task.

On Tuesday August 7 they released alternative medal tallies, weighting the number of medals won against different indicators, such as GDP and population size. The results throw fresh light on notions of Olympic success.

At the time this work was published, China the US and the UK were atop the medal tally, in that order. By weighting medals won against national economic size (GDP) it emerges that Grenada (1st), Jamaica (2nd) and Armenia (3rd) are the Olympic powerhouses. By factoring in population size it is revealed that Grenada (1st), Cyprus (2nd) and Slovenia (3rd) have prevailed.

(These rankings have changed slightly since publication and will continue to change throughout the remainder of the Games. Live data are available for download here.)

This leaves me wondering: why haven’t I picked up on the international adulation for Grenada’s stellar efforts (a gold medal in the men’s 400m competition – the nation’s first ever medal.)

For Australia, the results are mixed. From an official medal tally position of 8th, the GDP weighting sees Australia move down to 33rd place. But this should be seen in the context of the UK (equal 33rd), the US (57th) and China’s (43rd) results. New Zealand have earned bragging rights, coming in at 19th place.

Weighted for total population size, Australia’s rank goes up one place to 7th, just ahead of the UK (12th), and miles ahead of the US (40th) and China (58th). New Zealand wins out – again – in 4th place.

These alternative rankings and their statistical biases should be treated carefully when making inferences. But in a broad sense they do change the way we can think of Australia’s much-talked-about Olympic performance slump.

For one thing, in both of the alternative medal tallies I’ve just referred to, Australia outranks the nations currently at the top of the official medal tally – China, the US, and the UK – and in most cases by large amounts.

My point is that we should be wary of something as problematic as the official medal tally in guiding the debate over sports funding which will no doubt continue long after the Olympic flame is extinguished.

We need to be considered about the way we conceive of sporting success and realistic about the level of success we aspire to. Medal-chasing is likely to be a costly exercise and may serve only to further disguise our many sporting achievements.