Winning and the marathon of life

Look at the finishers in a typical marathon and a simple pattern immediately emerges.

After the race winner, there is a trickle of fast finishers that gradually turns into a steady flow as the finish time approaches 3 hours. The main pack arrives in the range of 3–6 hours, with a decreasing stream of progressively slower stragglers.

It is easy to imagine that this distribution would be pretty smooth, given the number of runners in these events. Sanjib Sabhapandit and colleagues at Universite Paris-Sud in France thought so too until they looked at data from the entire field of male runners at races in Boston, Chicago, New York between 2000 and 2007.

It turns out that the distribution of finish times has some interesting characterstics. For a start, there are spikes just before the 3 and 4 hour marks as runners attempt to beat specific milestones. In the Chicago marathon, where the course is flat and relatively easy to pace, there are secondary peaks just before the times of 3:10 and 3:20.

“The existence of such peaks suggests that the distribution of finish times in this range does not reflect a performance limit, but rather, the surmounting of a psychological barrier,” say Sabhapandit and buddies.

Another feature is crowding at the front of the pack among runners who finish with a time less than 2:15. These are the elite runners who enjoy considerably incentives to maintain their competitive edge, such as appearance money and access to the best support institutions.

But acheiving a slightly slower time of between 2:15 and 2:30 is still a significant feat that requires a considerable investment in time. This cannot be done without financial support and so there is a deficit of runners in this cagetory. This is what makes the front seem crowded.

Of course, all these features are easy to predict given agood knowledge of the way marathons work.

What’s curious is that Sabhapandit says a similar crowding effect can be seen in human age distributions where the longest-lived individuals survive longer than the distibution would imply. “There seems to be a self-selected sub-population of advantaged individuals who gain advantage both innately and perhaps because of external reinforcement,” they say.

These people are analogous to the elite runners who receive a financial incentive to perform well.

If Sabhapandit is correct, what factor performs the role of appearance money for people running the race of life?

Ref: arxiv.org/abs/0802.1702: Crowding at the Front of the Marathon Packs