As a former runner, I’m pretty excited for the Olympics, which start tomorrow. Although I ran the 1600, 3200 and 4800 in high school (and ran slow practice runs in my week adventure into college athletics at LSU), my favorite Olympic event is the 100 meter dash (cue my runner friends shaming me). Usain Bolt set Olympic records in the 100 meter in 2008 and 2012, also setting a world record in 2008. Looking through the final heats for the 100 meter dash over past Olympics, Bolt is far from the only one setting Olympic and world records en route to Gold. Athletes train their lives for this moment and taper their training regimines to be at their very best when the gun fires. Take a look at the final heat times of all Olympic times since 1952 below, I didn’t consider Olympics before the World War II canceled 1944 Olympics (and there was not a complete list of times for the 1948 Olympic 100 meter dash).
We have two big outliers here, which are both due to hamstring injuries. So I won’t consider these in any analysis, I am considering all the caught dopers because although I respect the integrity of the sport, fast is fast. So I’m keeping Ben Johnson’s 1988 Olympic victory over Carl Lewis in this data. Notice that other than the slow times in 1984 who would be beaten by today’s high schoolers, there is a trend of getting faster every year-but at a slower and slower rate. So I want to know, how much faster can we get? Will a person ever break 9 seconds in the 100 meter dash? Before taking a more in depth look at this, let’s take a look at the difference in time of the winners from the previous Olympics to see how much faster people are getting:
The black line here represents no difference between the prior Olympics winning time while the red line is the least squares regression line fitting year to the difference. Although we see an increasing trend, the line doesn’t have significant coefficients for either the slope or intercept so we shouldn’t look too much into this trend.
So let’s look at a Frequentist and a Bayesian approach, first with the Frequentist approach for polynomial regression which based on a general linear hypothesis says that the regression line should have order 3.
The blue line has order 2 and the red line has order 3 in terms of year. They both have a downwards trend at the tail, indicating that we still can get faster with the order 3 model indicating we can get much faster. (I know shame on me for looking outside of observed data for polynomial bounds). Now lets take a Bayesian approach and use a Gaussian process regression.
The black line represents the posterior mean of the Gaussian process regression. We see a trend at the end dipping upwards and in fact if we use this function to predict future race values, this model predicts that 2012 saw the fastest olympic race times. If you take Usain Bolt out of the equation (which might be a factor this year due to his injury) you see that the times aren’t really dropping drastically as of late. Let’s just take a look at the winners here:
Once again, even just looking at the winning times, we see that the Gaussian Process regression model predicts that 2012 was the fastest olympic times on record. Just looking at the raw data, it appears that Usain Bolt is an outlier in terms of pure speed.
Now remember, all models are wrong, but some are useful. From these two approaches, I think we can gather that while we may be able to get faster, we aren’t going to get much faster and realistically, I don’t think anyone will be breaking 9 seconds in the 100 meter dash (unless robots are allowed).
-Andrew G Chapple