There is a growing interest in developing stochastic schemes for the description of processes that are poorly represented in atmospheric and climate models, in order to increase their variability and reduce the impact of model errors. The use of such noise could however have adverse effects by modifying in undesired ways a certain number of moments of their probability distributions. In this work, the impact of developing a stochastic scheme (based on stochastic averaging) for the ocean is explored in the context of a low-order coupled (deterministic) ocean–atmosphere system. After briefly analysing its variability, its ability in predicting the oceanic flow generated by the coupled system is investigated. Different phases in the error dynamics are found: for short lead times, an initial overdispersion of the ensemble forecast is present while the ensemble mean follows a dynamics reminiscent of the combined amplification of initial condition and model errors for deterministic systems; for longer lead times, a reliable diffusive ensemble spread is observed. These different phases are also found for ensemble-oriented skill measures like the Brier score and the rank histogram. The implications of these features on building stochastic models are then briefly discussed.