A stochastic method has been developed to evaluate the average performance of an oscillating water column wave energy device equipped with an (assumedly linear) Wells turbine. The wave climate is represented by a set of sea states, characterized by their power spectra, the free-surface elevation being a Gaussian random variable in each sea state. The variance and the probability distribution of the air pressure inside the chamber are computed for each sea state, it being assumed that the chamber hydrodynamic coefficients and the turbine curves are known. This allows the average performance of the turbine and of the plant to be obtained for each sea state and for the annual wave climate. Numerical examples are worked out for given chamber geometry and turbine shape, showing how the turbine size and rotational speed may be optimized for maximum energy production. Controllable rotational speed and the use of a valve system for turbine flow control are considered.