# Predict the best mile time?

1. Aug 11, 2008

### futurebird

predict the best mile time??

Now, most people don't run very much and only a few train at all. If you want to know your "personal best" mile time you need to do a lot of training. Let's say that only 1/20 people in a population bother to do this.

We have all of their mile times. Let's say the average is 7:30 and the best is 4:12. The SD is... I don't know, let's say, 1 min.

Now based on the fact that this is only 5% of the population can we predict the world record mile time if EVERY woman trained until she could run her personal best?

2. Aug 11, 2008

### CRGreathouse

Re: predict the best mile time??

I would imagine that most people who have a special ability to run do train -- at least at a local, e.g. high school level -- and so learn how good they are. I don't think adding the other 95% would even double the number of world-class runners. But if it did, you might expect with ~50% probability an improvement in the record. This would likely be a small improvement (probably less than a tenth of a second).

But if you want to treat it as a stats problem, let's assume that each person is chosen from a normal distribution with mean 7:30, and that the current runners were selected arbitrarily (that the other 95%, if trained, would be just as good on average, and equally distributed).

With ~325 million runners who now train, the world record would be 5.81 standard deviations below the mean. This makes the standard deviation ~34.1 seconds. With 6.5 billion people, the record would be 6.29 standard deviations instead. This would improve the time by ~16.4 seconds to an amazing 3:56.

Last edited: Aug 11, 2008
3. Aug 11, 2008

### futurebird

Re: predict the best mile time??

What percentile did you give the top score to get an SD of 5.81 ?

4. Aug 11, 2008

### futurebird

Re: predict the best mile time??

Oh that's based on the population. I see.

How reliable is this? I mean if our data are good (unbiased sample)...

5. Aug 11, 2008

### CRGreathouse

Re: predict the best mile time??

Not reliable at all. It's based on the assumption that runner's don't self-select for a propensity for speed, and I think that's a terrible assumption. The assumption of normality is also a bad assumption, though probably less of a cause of error than the first. Finally, we assume that 5% push their limits far enough to tell if they could be world-class runners; this could be high or low, I have no idea.

I would much sooner guess 0.1 seconds than 16.4 seconds.

6. Aug 11, 2008

### futurebird

Re: predict the best mile time??

Still, the women's world record was like 6:15 in 1920.

7. Aug 11, 2008

### CRGreathouse

Re: predict the best mile time??

And to what do you attribute that change?

8. Aug 11, 2008

### futurebird

Re: predict the best mile time??

Mostly? More women running. It became more socially acceptable.

9. Aug 11, 2008

### CRGreathouse

Re: predict the best mile time??

Yes, and my 'prediction' model doesn't take that into account. Nor does it take better nutrition, improved healthcare, gene mixing ('hybrid vigor'), artificial genetic selection, or a host of other things into account. It just takes a few questionable assumptions and takes them to their logical conclusion.