Daily Archives: 3 October 2012

Record highs

As well as being a demonstration of nationalism and the fact that money can buy gold, the London Olympics gave us the usual advances in human performance. But is there a limit to how fast, high and strong we can get? Sounds like a question for science.

It’s a tricky one though: you’d expect there to be restrictions from physiology or mechanics, but we don’t necessarily understand those well enough to draw a line. Plus there’s always the chance of some innovation in technology or technique that pushes those limits further – for example, the Fosbury flop in the high jump.

But the other way to tackle the problem is to look at the statistics and see whether records are approaching a limit, which is just what Spanish physicist Filippo Radicchi from the Universitat Rovira i Virgili has done (Radicchi F 2012, “Universality, limits and predictability of gold-medal performances at the Olympic Games”, PLoS ONE, vol. 7, no. 7, e40335, doi:10.1371/journal.pone.0040335).

Graph of the probability of reaching particular time milestones as a function of the year, for five different athletic events - men's 100 m, men's 400 m, men's 10,000 m, men's marathon and women's 100 m. The probability of breaking these records increases over time.
The probability of reaching particular milestones – measured in seconds – in five different athletic events increases every year (image F Radicchi, PLoS ONE)

Radicchi looked at medal-winning performances from previous Olympics and showed that they followed a normal distribution relative to each other, which implies that they can be considered to be exponentially approaching a future limit or asymptote. Looking at the rate they’re approaching this limit also enables a prediction for each future Olympic Games.

As an example, we’ll look at the big one, the men’s 100 metre sprint. Radicchi’s calculations, published on 12 July 2012, predicted a time of 9.63±0.13 seconds for the London Olympics. On 5 August 2012, Usain Bolt won the gold medal in this event with a winning time of… 9.63 seconds.

Unfortunately, Radicchi says that some of the early data for these shorter events is unreliable, so calculating the ultimate limit is a bit tricky. The unadulterated calculations give an estimate of 8.28 seconds. But discarding some of the dodgier figures – blame them on less sophisticated timing techniques – a more conservative figure is 8.80 seconds.

Compare that with Usain Bolt’s own 2009 world record time of 9.58 seconds. Even with the conservative estimate, the limit is still a while off.

The table below shows a similar story in a number of other major events:

Event Predicted limit Current
world record
Gold medal
2012 London Olympics
Men’s 100 m (sec) 8.28 9.58 9.63
Men’s 110 m hurdles (sec) 11.76 12.87 12.92
Men’s 400 m (sec) 41.62 43.18 43.94
Men’s marathon (hr:min:sec) 1:36:11 2:03:38 2:08:01
Men’s pole vault (metres) 6.87 6.14 5.97
Women’s 100 m (sec) 9.72 10.49 10.75
Women’s long jump (metres) 8.12 7.52 7.12

At each successive Olympics the advances are expected to be smaller and smaller, meaning breaking records will get less and less likely. Eventually, we’ll reach the limit of not only human ability, but reasonable comparison between events, when you take into account things like weather conditions or even the accuracy of the length of the track.

But at least Radicchi’s predictions suggest we haven’t quite reached those limits. So if you’re an athlete with world record aspirations, don’t give up just yet.