On the Probability of Winning with Different Tournament Procedures

Abstract

Paired comparisons among competing items are analogous to games between contestants and the process of determining the winning item among $t$ contestants is analogous to a tournament. In this paper four different types of tournaments are investigated for the eight-player case. Expressions are developed for (1) the probability that each player wins and (2) the expected number of games required. Examples are presented for comparison of tournament types and to study the effects of (a) the initial draw, (b) mis-classification when using a priori information in initial pairing, and (c) 'byes.' Some generalizations in terms of number of players and replication are developed