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RE: drug tests -- and drug headlines -- are false <-->
Your mathematical analysis is so narrow-minded that your argument has tunnel vision.
Your ratio of performance suggests that males and females have linear relationship. Which is wrong - Women relative to men have better endurance over longer distances. (women?s mile, 5k world record compared to marathon Vs men show a better adaptation for women towards endurance events).
Your ratio also only implies that 32x difference (which I will show any faster to be wrong) in what you assume to be clean athletes, and clean performances.
If Haile ran 3:31 druggied then that would explain his difference between performances you suggested.
There are plenty examples of people will slow mile times and fast 10k?s ? Ron Clarke world record 10k and never broke 4..
There are also people who have fast 10k?s and slow marathons, fast miles and slow 5k, fast 800 and slow 5k, fast marathon and slow whatever.
You surely get the point some people are suited to different events and train for different events.
?However, in reality this (between 30.73 and 26.2188,) does not happen? - DUH!!!
People also slow down the longer the distances. T2 = T1 x (D2/D1)1.06 T1 is the given time, D1 is the given distance, D2 is the distance to predict a time for, and T2 is the calculated time for D2
Ex. 1mile 5:00? 2mile 5:16 -- 5k 5:32 ? 10k 5:58 ---- marathon 6:28
thus your ratio and difference between increasing distances and pace shows that it eventually becomes 1. Marathon / mile = 26.2188 - Since no one can run their mile pr for 26.2 miles then it must be more than 26.2188. Since no one can run their 2mile pace for 26.2m it must be more than 27.56. Since no one can run their 5k pace for 26.2m it must be more than 28.86. Since no one can run their 10k pace for 26.2m it must be more than 30.16, Thus at this rate someone will run their marathon pace at 32.76 times that of their mile pace. Thus the ratio between pace and distance will be 1. For it will take a marathon pace not a differentiated faster pace to run a marathon.
1. this is why you aren?t going to see some great ratio like you postulated
2. though the slowing down is the counter ?argument I haven?t shown why it happens. I can only say it is the law of physics. Analogy ? you could spend $5 in one second, or spend 500 pennies in one hour. The human body has only so much energy and it is how it?s spent that matters. More time means less expenditure. A druggied athletes just has more to spend. - If you know what I mean
Thus you can never prove by your theory drugs don?t help.
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