  In this paper we bring a novel approach to the theory of tournament rankings.
We combine two different theories that are widely used to establish rankings of
populations after a given tournament. First, we use the statistical approach of
paired comparison analysis to define the performance of a player in a natural
way. Then, we determine a ranking (and rating) of the players in the given
tournament. Finally, we show, among other properties, that the new ranking
method is the unique one satisfying a natural consistency requirement.
