September 2004 the well-known scientific magazine 'Nature' published results of a statistical analysis that showed how, should the trends continue, women would run 100m as fast as men in the Olympic games of 2156. (Andrew J. Tatem et al, Nature 431, page 525. The article was not meant to be taken fully serious.) They show a graph extrapolated far into the future. Two linear lines indeed cross in 2156, the women would run 8.079 seconds then, and the men would loose the race with their 8.098 seconds. The problem of these predictions is both in the set of data used for the analysis and in the logic behind the linear model.

An Italian statistician published graphs for the development of all athletic disciplines, using the mean of the top ten of each year. Tatem et al used only the winning times of the Olympic games, which means they were using 40 times less data as the Italian. Using so few data gives erratic results much influence. Unfortunately the Italian site seems to be removed, so I had to do some analysis my self. I started some time ago with the development of high jumping - leading to graphs clearly non-linear. Now I added shot put (even more non-linear) and the 100m to compare with Tatem et al. The 100m for men is closest to linear, but the women's sprint isn't.

The data used come from this tremendous statistical site: http://trackfield.brinkster.net/. (Unfortunately not free anymore.) Blue dots are for the men, dark red dots for women. Regression lines are blueish green.

At first sight it will be clear that the development of high jumping isn't linear, both for men and women. The bending of the graph lies around 1984, so I added linear regression lines for the period 1948-1984 and from 1985 up to this day.

A statistician only having access of data for 1948-1984 could say that high jumping is developing linear, and he (or she) would predict that men and women would jump equally high in 2190. At that moment the two straight lines cross. They would jump 4.17m high then. I suppose no one would take such predictions serious.

In shot put non linearity is even more dramatic. Arbitrarily again 1985 is chosen as turning point, this coincides with the time that doping control increased. Anabolic steroids work very strong in women, so the decline after 1985 is very severe. The mean female top shot-putter now throws 1.5 meter less...

Shown are not the raw data, but times after correction for the difference between hand timing and automatic timing (0.24 seconds is the official correction factor). The men's line is rather close to linear from say 1940 up to the present, but the women's line is non linear with about the same bend as in high jump and shot put. At a closer view the men's line shows the same effect, but only weaker.

A statistician working with 1948-1984 data would predict men and women to run just as fast in 2068. They need only 8.06 seconds for 100m then. On the other hand, a statistician only using data for 1985-2004 would predict that women and men ran with the same speed in... 1791! They needed 11.36 seconds for 100m during the days of the French Revolution. I have indeed heard of people running for their live in those years - nice that husbands could run with the same speed.

Many questions arise. Because the graphs all have a bend around 1985 there have been many cheaters. Who? And how much the cheating will have improved their results?

A more interesting question is what the 'real' development of athletics is, or should have been. It is clear that development in more than a century has not been linear. Both World Wars can be seen. Periods with faster and periods with smaller development can also be seen. After the increase in doping tests decline sets in for some disciplines. When growth hormone (to name just an example) becomes detectable more decline will follow. So there are many factors that make the 'real' development invisible, and I dare not say how development 'really' could have been.

Most likely development goes as for an individual athlete. Adding more training sessions will lead to better results, but every added session adds less improvement. There even is a maximum. Also for the sport as a whole something like that will be the case, but where lies the maximum? Adding training sessions has been done up to the seventies. From then on more sessions could not be added (except with doping), 'only' fine tuning the quality of training sessions remained. The graphs give no hint about the plateau that is 'real'. They only give a hint that ethical standards of top sporters in the mean are not high...

updated october 2007

Weia Reinboud (weiatletiek (@) xmsnet.nl) (More on athletics here.)

And now for something completely different: essay about freedom.