There's been a lot of work into mathematically understanding human performance, especially record-setting human performances. The reason this is interesting is because the limits of human performance involves sampling from the very tail of a distribution, in this case, the most athletic human beings on the planet. How do we deal with this tail, when we are so used to dealing with averages and normal distributions?

Happily, there are whole fields devoted to this, such as extreme value theory. But what about focusing specifically on the Olympics? Can anything interesting be done here? And if so, can we make any predictions for what will happen this summer?

Filippo Radicchi recently set out to do exactly this. In Universality, Limits and Predictability of Gold-Medal Performances at the Olympic Games, he explores the presence of certain universal properties of winning performances at the Olympics. He examines the relative improvement in the gold-medal performance from Olympics to Olympics in a variety of games. These relative improvements approach some hypothetical optimal value (the fastest a human could ever run, for example) and the improvements (but not the performances themselves) follow a normal distribution:

At each new edition of the Games, gold-medal performances get, on average, closer to the limiting performance value. The average positive improvement observed in historic performance data can be motivated by several factors: as time goes on, athletes are becoming more professionals, better trained, and during the season have more events to participate in; the pool for the selection of athletes grows with time, and, consequently there is a higher level of competition; the evolution of technical materials favors better performances. On the other hand, there is also a non null probability that winning performances become worse than those obtained in the previous edition of the Games (i.e., relative improvement values are negative). All these possibilities are described by a Gaussian distribution that accounts for various, in principle hardly quantifiable, factors that may influence athlete performances: meteorological and geographical conditions, athletic skills and physical condition of the participants, etc.

Radicchi finds this pattern to be true for 55 different specialties, and even calculates what the best possible performances could be, based on the model. For example, the limiting time for the men's 100 meter dash is 8.28 seconds (which we are not yet too close to).

You can read the most likely best-possible performances from the chart below, by examining the peak of the asymptotic time curve:

And here are the predictions you've been waiting for, with the right-hand column containing the predicted performances for the gold medalists this year:

Enjoy watching Olympians sample from a probability distribution!

Top image: Paul Hudson/Flickr