In light of today's news story from Mary Cain, I was wondering what it takes for a female to run sub 4 for 1500m.
My guess was that 114lbs wasn't an arbitrary weight that Alberto pulled out of thin air. I compiled the height and weight of all women who have ran sub 4 since 2009. My assumption was that you would find a pretty tight cluster around 0.304kg/cm which would correspond to Mary Cain weighing 114lbs at a height of 5'7. While the average less Caster is pretty close to the 0.305 kg/cm that Alberto was pushing, a histogram of the data is more telling. Roughly 57% of the data sits between 0.30 and 0.330 and 79% of the data sits between 0.27 and 0.330.
Generally, it looks like you can be 8% on either side of 0.30 kg/cm and still be within the data limits. In Cain's case this would mean that she should have been fine anywhere between 105lbs (0.280 kg/cm) and 123lbs (0.328 kg/cm).
I realize that this isn't terribly scientific, but I think it is a good basis for discussion about weight and running. People who follow most sports understand that extreme bodies exist at the extreme limits of performance. We'd be fooling ourselves if we pretended that a runner's weight didn't matter at the highest levels.
From David Epstein:
"For an American man aged between 20 and 40, standing between 6ft and 6ft2in the chances of playing professionally in the NBA are five in a million. If he's 6ft2in to 6ft4in there is a still-distant 20 in a million chance. But if he's 6ft10in to 7ft, the odds shorten to 32,000 in a million. And if he stands 7ft, there is a one-in-six chance he will currently be playing in the NBA."
Certainly something to consider...
Below is a list of 29 of the 31 women who have broken 4min since 2009.
Mean: 0.308
Median: 0.311
Range: 0.145
Same group less Caster
Mean: 0.305
Median: 0.310
Range: 0.066
Laura Muir 0.300 kg/cm
Sifan Hassan 0.288 kg/cm
Shannon Rowbury 0.315 kg/cm
Jenny Simpson 0.327 kg/cm
Shelby Houlihan 0.331 kg/cm
Lisa Dobriskey 0.327 kg/cm
Maryam Yusuf Jamal 0.267 kg/cm
Konstanze Klosterhalfen 0.276 kg/cm
Faith Chepngetich Kipyegon 0.267 kg/cm
Hellen Obiri 0.313 kg/cm
Genzebe Dibaba 0.309 kg/cm
Gabriela Stafford 0.325 kg/cm
Gudaf Tsegay 0.307 kg/cm
Maureen Koster 0.324 kg/cm
Christin Wurth-Thomas 0.327 kg/cm
Winnie Nanyondo 0.293 kg/cm
Anna Willard 0.331 kg/cm
Viola Jelagat Kibiwot 0.291 kg/cm
Caster Semenya 0.410 kg/cm
Gelete Burka 0.269 kg/cm
Winny Chebet 0.288 kg/cm
Rababe Arafi 0.311 kg/cm
Abeba Aregawi 0.305 kg/cm
Dawit Seyaum 0.304 kg/cm
Axumawit Embaye 0.313 kg/cm
Btissam Lakhouad 0.320 kg/cm
Besu Sado 0.326 kg/cm
Tatyana Tomashova 0.315 kg/cm
Hind Dehiba 0.265 kg/cm