The evaluation of seeding rules requires the use of probabilistic forecasting models both for individual matches and for the tournament. Prior papers have employed a match-level forecasting model and then used a Monte Carlo simulation of the tournament for estimating outcome probabilities, thus allowing an outcome uncertainty measure to be attached to each proposed seeding regime, for example. However, this approach does not take into account the uncertainty that may surround parameter estimates in the underlying matchlevel forecasting model. We propose a Bayesian approach for addressing this problem, and illustrate it by simulating the UEFA Champions League under alternative seeding regimes. We find that changes in 2015 tended to increase the uncertainty over progression to the knock-out stage, but made limited difference to which clubs would contest the final.