Eugster, Manuel J. A.
Department of Statistics: Technical Reports, No.113
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.