Tuesday, January 09, 2007

Mathematically proved limits on marathon times

What is the fastest theoretical time that a human can run a marathon? According to Dutch mathematician John Einmahl of Germany's Tilberg University, Paul Tergat could improve his world record time of 2:04:55 by 49 seconds. Women marathoners could take as much as 8:50 off Paula Radcliffe's 2:15:25 world record. Sprinters, apparently, could do even better from a percentage perspective.

(Paul Tergat sets the world marathon record in Berlin, Germany in 2003 -
don't tell him he could have gone 49 seconds faster!)

It's all part of the mathematical study of "extreme values" that helps determine upper limits. A quote from the story:
"For a lot of athletes it is probably depressing when they are confronted with our extreme values," Einmahl told the German news agency dpa. "But this is a very serious study - the extreme theory as a part of mathematics and statistics is an accepted science."
It's all math, so there is certainly the chance of a breakout performance. I wonder what the 100-mile limit would be? Perhaps this will be one of Professor Einmahl's graduates thesis.


[Thanks to The Final Sprint for pointing me to this story]


  1. Didn't scientists used to say something similar about the 4-minute mile? Some people seriously thought Bannister's heart would explode if he ever broke the "physiological barrier".

    It's an interesting discussion, if not credible science.

  2. It does sound very similar to the 4 minute mile debate. I really enjoyed the book on this called "The Perfect Mile". I noticed on amazon that there is a 50th anniversary copy of Roger Bannister's book.

    Here is the link:



  3. I wouldn't exactly call this a mathmatical proof.

    This is statistics. There is an enourmous differance.

    If everyone made assumptions about the limits of human capability, not only in sport, based only on what had been achieved already (which is exactly what they are doing), a great deal of what is now common among elites never would have happened...

    I bet we will see multiple sub 2:04 marathons withing the lifetime of the grad students who did the work for this paper.

  4. The original paper can be found at http://greywww.uvt.nl:2080/greyfiles/center/2006/doc/83.pdf or you can google for "records in athletics through extreme value theory". I note that the authors are not trying to predict the fastest possible times that can be run. They are trying to determine the fastest possible times given the skill level, training, etc. that exists today.

    I find it very, very, very hard to believe that the women's marathon record and Michael Johnson's freakish 200m record are that soft. I'm not competent to judge the math but.... damn. That just ain't right.

  5. All records are made to be broken..at some point. Thats why they are records, for others to pursue. Roger Bannister was my idol during my youth and was the main factor in my pursuit of the 4 minute mile and HS records..of course I came up short, 4:07 in 1993. Regardless of what scientists say, they all will fall. An interesting note is this article about Unbreakable Records, no where do they mention the current running records. http://www.askmen.com/sports/fitness_top_ten/38_fitness_list.html :-(


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