Ranking players in multiple tournaments

This paper examines a generalization of the standard round robin tournament. First we consider a set of tournaments wherein each player competes in each member of the set, and the tournaments can be ordinally ranked in order of difficulty. The data envelopment analysis method is used to obtain a ranking for each player, while taking account not only of the playersʹ strength within each tournament, but also the differential difficulty of tournaments. Second, we extend this concept to the case where each player may only compete in a subset of the tournaments. Hence, any given player may have fewer matches than other players.