Water and pollutant fluxes from combined sewer overflows (CSO) have a significant impact on receiving waters. The random nature of rainfall forcing dominates the variability of sewer discharges, pollutant loads, and concentrations. An analytical model developed here shows how sewer network topology and rainfall properties variously impact the stochasticity of CSO functioning. Probability distributions of sewer discharge and concentration compare well with the results from a calibrated Storm Water Management Model in an application to a sewershed located in Dresden, Germany. The model is determined by only four parameters, three of which can be predicted a priori, two from the rainfall record and one from the network topology using geomorphological flow recession theory, while the fourth can be estimated from a short discharge time series. The sensitivity of CSO and wastewater treatment loads to network structure suggests simple topologies may be more vulnerable to poor performance. The analytical model is useful for evaluating various CSO management strategies to reduce adverse impacts on receiving waters in a probabilistic setting.