We derive robust comparative statics for general rank-order tournaments with additive and multiplicative noise. For unimodal distributions of noise, we show that individual equilibrium effort is unimodal in the number of players when it is deterministic. For a stochastic number of players, the unimodality is preserved for changes in the number of players in the sense of first-order stochastic dominance under an additional log-supermodularity restriction. Aggregate equilibrium effort can be increasing, decreasing or nonmonotone in the number of players. The existing results for Tullock contests with stochastic participation follow as a special case. Equilibrium effort decreases as noise becomes more dispersed, in the sense of dispersive order or appropriately defined entropy.