# Help needed with a Sports Question

1. May 18, 2006

### eldrick

Hi

I hope someone can help me on a question which is one of the biggest posers in athletics.

You may be aware that the 100m record was recently tied & may be broken again. However, one record that seems like it may never be broken ( by general consensus of athletics fans ) is Michael Johnson's legendary 19.32 run at the 1996 Olympics ( although he may have had an illegaly hard track "help" him to that time ) :

Here is the all-time list :

http://www.alltime-athletics.com/m_200ok.htm

Now, I tried a method to predict what the statistical "predicted" 200m record should be & I'd like your opinion on how valid it is & if someone can suggest a better method:

Back in 2003, I took the top 100 performances on that list, worked out the mean & standard deviation of those. The the "predicted" world record should be the value that is 49% away from the mean or 2.326348 standard deviations from the mean ( i.e. it represents the top 1% performance of the population of a 100, which means the world record )

Using this method, the predicted world record then was 19.629s.

The problem with this method, is that we are not dealing with a normally distributed population - this is a heavily skewed population.

Is it still valid to apply a standard deviation method to this skewed population ?

if not, could someone suggest some improvements or a better method ?

Last edited: May 18, 2006
2. May 19, 2006

### Krusty

The best way to look at this problem is using Extreme Value Theory. I know this has been applied to athletics records in the past, but I couldn't find any citations at first glance on prediction of future record. I know that Robinson & Tawn (1995) used Extremes to investigate whether a world record by a Chinese athlete fell within the support of the distribution of possible performances. Their paper might solve your question in explaining how they constructed the distribution of the possible performances.

3. May 19, 2006

### eldrick

Thanks for that. I vaguely recall it, but i can't remember how useful it was.

I'm trying an approach from scratch & looking for the best method by consensus opinion. Mine above was to start the ball rolling. I'd appreciate some input, just from the intellectual standpoint.

4. May 20, 2006

### Krusty

I am currently in the process of writing my Honours Thesis on Extreme Value Theory and was planning to include something very similar to your question as an example of possible applications. A few months before I will have that finished though...

5. May 20, 2006

### eldrick

Could you kindly find the time just to suggest to me a method ? ( a few months is a long time to wait for a method )

It would help settle a lot of sporting arguments

6. May 23, 2006

### Krusty

Well the problem comes down to fitting an Exteme Value distribution to 200m track times. This will let you find the probability that a given time (ie. Johson's record) will be exceeded. There are many ways of fitting the model, but most use the fastest yearly times as the raw data. Probably better for you to read up on it as I don't have a full grasp on it yet. For more info about Extreme Value Theory, I found "An Introduction fo statistical modeling of extreme values" by Stuart Coles the easiest to read. I would also recommend having another read of "Statistics for Exceptional Athletic Records" by Michael Robinson and Jonathan Tawn.

Last edited: May 23, 2006
7. Feb 21, 2007