Ranking from unbalanced paired-comparison data

Abstract

It is proposed that for ranking objects or players in an incomplete paired-comparison experiment or tournament with at most one comparison per pair, the score of a player, C, be the total number of (a) wins of players defeated by C minus losses of players to whom C lost, plus (b) C's wins minus C's losses. A tied match counts as half a win plus half a loss. More general tournaments can be treated similarly.