The elimination or knockout format is one of the most common designs for pairing competitors in tournaments and leagues, including the NFL playoffs. In each round of a knockout tournament, the losers are eliminated while the winners advance to the next round. Typically the goal of such a design is to identify the overall best team. Despite such a simple set-up, little formal work has been devoted to optimizing the team pairings that maximizes the probability of selecting the best. In this talk, we will discuss the framework of Bayesian optimal design, and demonstrate its use as an approach for constructing playoff schedules. Using a common probability model for expressing relative player strengths, we develop an adaptive approach to pairing teams each round in which the probability that the best team advances to the next round is maximized. The method is compared to other knockout tournament formats based on simulated game outcomes under several data-generating mechanisms, including the standard knockout format used widely in games and sports.
