  Inspired by the Games held in ancient Greece, modern Olympics represent the
world's largest pageant of athletic skill and competitive spirit. Performances
of athletes at the Olympic Games mirror, since 1896, human potentialities in
sports, and thus provide an optimal source of information for studying the
evolution of sport achievements and predicting the limits that athletes can
reach. Unfortunately, the models introduced so far for the description of
athlete performances at the Olympics are either sophisticated or unrealistic,
and more importantly, do not provide a unified theory for sport performances.
Here, we address this issue by showing that relative performance improvements
of medal winners at the Olympics are normally distributed, implying that the
evolution of performance values can be described in good approximation as an
exponential approach to an a priori unknown limiting performance value. This
law holds for all specialties in athletics-including running, jumping, and
throwing-and swimming. We present a self-consistent method, based on normality
hypothesis testing, able to predict limiting performance values in all
specialties. We further quantify the most likely years in which athletes will
breach challenging performance walls in running, jumping, throwing, and
swimming events, as well as the probability that new world records will be
established at the next edition of the Olympic Games.
