This paper analyzes the impact of input and output spillovers on the expected effective cost reductions in a two-stage model of R&D where all R&D projects are risky. It is shown that, relative to the deterministic case, output spillovers tend to reduce expected cost reductions whereas input spillovers tend to increase investment in R&D and hence expected cost reductions. In particular, the relations between cost reductions in the presence of input and output spillovers known from deterministic models may be reversed under certain parameter constellations.