Note—Rankings from Round-Robin Tournaments

In a December 1983 article in Management Science, Stephen Goddard studies the problem of ranking contestants in a round-robin tournament. He gives objections to the usual method of ranking contestants by number of victories and proposes both an alternative method for ranking contestants and a criterion for determining the “fairest” ranking. We argue here that his criterion is faulty and, in fact, falls prey to his own objections. We also show that his method, in any event, produces rankings which don't satisfy the criterion. Finally we describe a general class of models of competition which have been proposed to solve this problem and which lead to the usual method of ranking by number of victories.