Usain Bolt, sprinter from Jamaica, currently holds the world record in the 100 meter sprint with a time of 9.69 seconds.  Whenever new records are set, people ask 'what is the limit on human performance?'

So how fast can a human run?  

Two econometricians from Tilburg University in the Netherlands, Professor of Statistics John Einmahl and former student Sander Smeets, say have calculated the ultimate records for the 100-meter sprint. The good news; there is still room for improvement in both the men's and women's times in the near future.

They used extreme value theory to calculate by how much the current records for the 100 meter sprint could be improved.  

Extreme-value theory is a sub-sector of statistics, which tries to answer questions about extreme events (which by definition are uncommon), using information about less extreme events. The theory is normally applied within the financial and insurance world to estimate the risk of extreme damage resulting from storms, earthquakes or the bursting of a dyke, for example, in order to calculate premiums.

With a little modification, they say it can apply to sports as well.

Einmahl and Smeets analyzed the records of 762 male and 479 female athletes. Each athlete was listed once, and the times were recorded between January 1991 and June 2008. Times run before 1991 were discounted on account of the inadequate doping controls before this date. The men's times varied between 9.72 and 10.30 seconds, and the women's from 10.65 to 11.38.

According to Smeets and Einmahl, the fastest time that the men are capable of sprinting is 9.51 seconds, which knocks 0.18 seconds off Usain Bolt's current world record. For female 100m sprinters, another 0.16 seconds can be knocked off the 10.49 run by Florence Griffith-Joyner, which would mean a time of 10.33. In a more cautious estimate (with a 95% confidence interval), the predicted times are 9.21 for the men and 9.88 for the women.

Sander Smeets studied Finance and Actuarial Sciences at Tilburg University and now works as a junior actuary at AZL, in Heerlen. John Einmahl is Professor of Statistics at Tilburg University.

Paper: 'Ultimate 100m world records through extreme-value theory', CentER Discussion Paper nr. 57