Measuring the relative efficiency of tournaments

The efficiency of various tournament structures such as knock-outs and round robins has been considered by several authors, and it has been noted that the round robin structure has a higher probability that the best player wins than do the other structures, but it is at the cost of playing a larger number of matches. On the other hand the knock-out tournament requires relatively few matches, but has a smaller value for the probability that the best player wins. Thus, the compromise between the number of matches played in a tournament and the probability that the best player wins that tournament has remained to some extent an unsolved problem. The Masters Tennis tournament, being a combination of two round robins and a knock-out, is one attempt at such a compromise. In this paper the balance between the number of matches played and the probability that the best player wins is addressed, and the efficiency of several different tournament structures is evaluated. It is noted that although the efficiency has been evaluated for just some of the commonly used tournament structures, the approach outlined in this paper can be used for a wide range of other structures