Running: A race against gender

Lucy Proctor Lucy Proctor on the 13-mile run

Can men and women ever compete fairly in a sport like running? Yes, but it requires a little bit of maths know-how.

"What time did you get?" It is the first question runners ask of each other when the race is over. But is it the right question?

You see, distance running is unfair.

Men experience this unfairness as they get older. Ten miles into a half-marathon, older men can only struggle on with growing irritation as younger men - men who would not have stood a chance against them in their prime - sail past.

For women, the feeling of injustice comes as soon as we start racing.

Men have bigger hearts and can take in and move around oxygen much more efficiently than women can. So men can beat us even if we are "better" runners. So is it possible to adjust for age and sex to level the playing field?

To solve this maths problem I challenged my 52-year-old colleague David Lewis to race against me, a 28-year-old woman, in the Great North Run half-marathon.

Then I went in search of a statistician.


  • Lucy Proctor will be talking about her challenge on BBC Radio 4's More or Less
  • The programme is broadcast at 1330 BST on Friday, 24 September...

Alan Jones, a retired IBM engineer, is the ultimate number-crunching runner. For decades, he has worked on this very problem for World Masters Athletics (WMA) - the international association for veteran athletes.

Another running enthusiast and statistician, Howard Grubb, has used Alan's figures to create the excellent age-grading calculator now featured on the Runner's World website.

It is painstaking work. Alan plots the best time ever attained at each age and for both sexes over all the commonly run distances, using data from many competitions. He then plots them on a graph - one graph for each distance.

Alan then draws a curve just underneath the times. By comparing points on the curve to the world record time for the 10 kilometres and marathon races, he is able to work out an age-factor.

By multiplying any time at any distance by the correct age-factor and turning the new time into a percentage of the fastest time possible, we get the performance score - how good a given time is compared to the best.

Alan Jones's optimum half-marathon times

For example, if I get a time of one hour 40 mins, I first turn it into seconds - 6,000. Using Alan's tables, I can see the age-factor for my age of 28 is 1 - because I am too young to yet have one. So I just divide the top possible time for that distance by a woman - 3950 seconds - by 6,000 to see how I compare, and I get a performance score of 65.8%.

If David did the same time, he would look to Alan's tables and see he has an age factor of 0.8693. He multiplies his 6,000 seconds by that age factor, and gets 5215.8 seconds. By dividing the top possible time for that distance by a man - 3553 seconds - by 5215.8, he gets a performance score of 68.1%.


As women are only compared with other women, and men with other men, the performance percentage automatically adjusts for sex.

Alan's numbers give us the secret to a fair race. For example: if you compare the best possible time for men and women over a half marathon you get a factor of 0.8995. The age-factor for a 48-year-old man is also 0.8995.

So a young woman (younger than 30) can race against a 48-year-old male happy in the knowledge that it is a fair contest.

"Of course, it is fair anyway," says Alan. "If he runs faster than you, he runs faster than you. That's the nature of a race."

I chose to ignore that bit, as David and I made our way to Newcastle.

So, who won?

Alan's tables throw up an interesting Great North Run fact. Because he uses times for the marathon and 10km races to plot the half-marathon times, he has shown that the current female half-marathon world record set by Lornah Kiplagat in 2007 - one hour, six minutes and 25 seconds - is short of what should be possible.

How did they do?

Lucy Proctor and David Lewis
  • Half marathon - 13.1 miles
  • Great North Run 2010 winning time: Haile GebreSelassie 00:59:33 (37-years-old)
  • Haile's performance score: 101.26%
  • David's finishing time: 1:40:23
  • Lucy's finishing time: 1:37:19
  • David's performance score: 67.86%
  • Lucy's performance score: 67.65%

His tables show a best possible time of 1:05:39. The fastest time ever run by a woman at half marathon was by our very own Paula Radcliffe, in the Great North Run, in 2003. She achieved 1:05:40- but, sadly, the Great North Run isn't recognised as a world record course.

Using Alan's tables and working backwards, I calculated out that if David and I were both to finish between one hour 30 minutes and one hour 40 minutes, I would have to beat him by at least three-and-a-half minutes just to get an equal percentage score of 68%. By 52, it seems, age is a greater handicap than sex.

In the end I finished exactly three minutes earlier than David. So according to Alan Jones, David beat me by 30 seconds.

But forget fairness. I still crossed the line first.

Add your comments using the form below

This is fascinating stuff, not only because at last we can compare the sexes in the same race (we have to ignore the pacemaking factor!) but as I grow older, I would be able to compare how I perform against myself at a younger age - for example, if I ran 100 minutes for the half marathon when I was 30, and 105 minutes at 50, have I 'improved'.

Gavin James, Winchester

I disagree with this article. I am male, 170cm and 75 kg, and although I do various sports, long distance running is something my body is not the best at because I don't have long legs and I'm too muscled. Nevertheless, I don't try to scale up or down my performance according to some statistical graphs based on body length, BMI, age, etc. That's life, some of us are better than others at some things. Introducing factors that shift our performances for "more objective judgment" is, in my opinion, killing the very idea of competition. I think also comparing yourself to the ones in your "category" will hinder your desire to improve yourself on an absolute scale.

Chris , Cambridge

If a man and woman are the same height, weight, age and fitness would the man still have an advantage and be a faster runner?

Jaime, Gloucester

Fun idea but I hope this is never used in serious competition, unless of course they develop a handicap for not-training and having a bit of a fast pie-arm, in which case, I too would be a contender.

Dave Amos, Beckenham

Age grading is a great thing. It helps me stay motivated. You can improve your age grading just by maintaining your times over the years. Age grading is a big part of parkrun - the network of nearly 50 free weekly timed 5km runs that take place in England, Scotland and Wales every Saturday morning.

Mick Turner, Croydon

What a load of tosh! How can it be competitive, when your rival is 5 yards ahead and you burst through on the line to pip them at the tape, that is a race. It isn't a race when ten minutes aftwerwards someone says "we have calculated it and you lost by 2 seconds, when you know you could have put more burn into the last hundred yards. What about weight factors etc, bone mass etc, if you want to get scientific you will need to look at hundreds of more items to enable comparison.

Martin Hollands, Aylesbury

Excellent article. The best organised races now commonly give you this percentage with your time. It can be dispiriting to see that you only did 70%, but when you figure that this is a comparison to someone like Haile GebreSelassie or the near-superhuman Paula (no surname required), then you feel a bit better. By the way, when you look into the record books, you will find Paula's name writ large - her running record is extraordinary, even against the very best of East Africa. We don't know how luck we are to have her. Why isn't she yet a dame?

Robert McCaffrey, Epsom, Surrey

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