Archetypal Athletes

Abstract: Discussions on outstanding---positively and/or negatively---athletes are common practice. The rapidly grown amount of collected sports data now allow to support such discussions with state of the art statistical methodology. Given a (multivariate) data set with collected data of athletes within a specific sport, outstanding athletes are values on the data set boundary. In the present paper we propose archetypal analysis to compute these extreme values. The so-called archetypes, i.e., archetypal athletes, approximate the observations as convex combinations. We interpret the archetypal athletes and their characteristics, and, furthermore, the composition of all athletes based on the archetypal athletes. The application of archetypal analysis is demonstrated on basketball statistics and soccer skill ratings.