I DO believe that my estimations are sound.
It's very easy to prove the OP is wrong (skip to bottom ----- if you're bored), but first i'd like to trash the OP thusly:
"Sound" estimations? Hello? What college did you go to? Let me know just as a reminder *not* send my kids there.
An argument is sound only if it is both valid, and all of its premises are actually true. You've done nothing of the sort. I would agree that is sound trolling though.
The irish running results are interesting but neither probative nor germain to this argument. Races from 1970s/1980s were self selecting non-randomized subjects, i.e. generally only good runners entered the race. Now races are full of hobby joggers.
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Ok, here's the proof that no where near 85% of men can run sub 16min 5k. The premise is that Vo2 max is a reasonable predictor for running performance. Now this is not strictly true, runners with the same Vo2 max can have 10k times vary by 1-2 minutes, so 30-60 secs for 5k. But you will see that these variations are so small as to have irrelevant.
Now, the average untrained male has a Vo2 max of 35-40, let's be generous and round up to 40. To run a 16min 5k you need a Vo2 max of about 64-65. About 10% of the population are non-responders for Vo2 max, so you're already taking a large chunk of the "15% can't do it" claim, although some of those non responders may be 15min 5k runners, but not likely. Most crucially, Dr T. Noakes claims that the average person can only improve their Vo2 max by about 10%, which would get them to about 44. This is a 22:50 5k, which in today's hobby jogger world is pretty fast, but absolutely no where near 16min. There you have it, proof QED. Incidentally 16m 5k is equiv to about 55min 10mile, and you can see not many modern running populations do that.
The other proof is simple observation, there are many running clubs with dedicated amateurs out there hammering away (recall previous post about guy running 100mpw can't even break 18min or something like that). And very few break 16k, plain and simple. Their training is far from perfect, but it doesn't take much effort to get 80-90% of the way to your max potential.
I'd be more interested in finding out of a dedicated drug program could get the average male downto sub 16min.