Records in athletics through extreme-value theory - Einmahl, J. H. J.; Magnus, J. R. (CentER Discussion Paper Series, 2006)
In this paper we shall be interested in two questions on extremes relating to world records in athletics. The first question is: what is the ultimate world record in a special athletics event (such as the 100m for men or the high jump for women), given today's state of the art? Our second question is: how `good' is a current athletics world record? An answer to the second question will also enable us to compare the quality of world records in different athletics events. We shall consider these questions for each of twenty-eight events (fourteen for both men and women). We approach the two questions with the probability theory of extreme values and the corresponding statistical techniques. The statistical model is of nonparametric nature, but some `weak regularity' of the tail of the distribution function will be assumed. We will derive the limiting distribution of the estimated quality of a world record. While almost all attempts to predict an ultimate world record are based on the development of top performances over time, this will not be our method. Instead, we shall only use the top performances themselves. Our estimated ultimate world record tells us what, in principle, is possible now, given today's knowledge, material (shoes, suits, equipment), and drugs laws.