Seeding, Competitive Intensity and Quality in Knock-out Tournaments

University Higher School of Economics (HSE). Any opinions or claims contained in this Working Paper do not necessarily reflect the views of HSE What is the optimal way to seed a knockout tournament in order to maximize the overall spectator interest in it? Seeding affects the set of matches being played in the tournament, while neutral spectators tend to prefer to watch (i) close and intense matches; (ii) matches that involve strong teams. We formulate a discrete optimization problem that takes into account both these effects for every match of the tournament. With deterministic outcomes and linear objective function, we solve this problem analytically for any number of participants. It turns out that, depending on parameters, only two special classes of seedings can be optimal. While one of the classes includes a seeding that is often used in practice, the seedings in the other class are very different. When we relax the assumptions, we find that these classes of seedings are in fact optimal in a sizable number of cases.