On the comparison between standard and random knockout tournaments

We compare the probabilities of a top-seeded player winning a tournament for a standard knockout tournament and a random knockout tournament. Analytical results are obtained for a two-outlier model, while numerical results are obtained for an alternative model. In both cases, we provide evidence that suggests that the outcomes of the standard knockout tournament and the random knockout tournament may not vary as much as one might expect. A secondary objective is the illustration of probability models that serve in analysing such problems.