A Method of Evaluating Contestants

Various iterative methods based on paired comparisons have been advocated for ranking contestants. H. A. David [1] has discussed many of these methods. Perhaps the best known methods involve reallocating to each contestant the total number of matches won by all opponents defeated by him, or more specifically a(k) = MI, where A is the matrix of aij, the number of wins of each player over each other player, and k is the iteration number. See Kendall [3]. Consider the matrix A = (aij) of Table 1. This table shows the records against each other in 1971 of the four women tennis players generally considered as having a world ranking in the order indicated. (Except for illustrating procedure, more than four players would be considered). The aij indicate the number of matches won by player i from player j. Column a(') is obtained by computing Al, while a(2) is A21. Computing, we find that