Tournaments, reward structures based on rank order, are compared with individual contracts in a model with one risk-neutral principal and many risk-averse agents. Each agents' output is a stochastic function of his effort level plus an additive shock term that is common to all the agents. The principal observes only the output levels of the agents. It is shown that in the absence of a common shock, using optimal independent contracts dominates using the optimal tournament. Conversely, if the distribution of the common shock is sufficiently diffuse, using the optimal tournament dominates using optimal independent contracts. Finally, it is shown that for a sufficiently large number of agents, a principal who cannot observe the common shock but uses the optimal tournament, does as well as one who can observe the shock and uses independent contracts.