Dispatchability of wind power is significantly increased by the availability of day-ahead production forecast. However, forecast errors prevent a wind farm operator from holding a firm production commitment. An energy storage system (ESS) connected to the wind farm is thus considered to reduce deviations from the commitment. We statistically assess the performance of the storage in a stochastic framework where day-ahead forecast errors are modeled with an autoregressive model. This stochastic model, fitted on prediction/production data from an actual wind farm captures the significant correlation along time of forecast errors, which severely impacts the ESS performance. A thermo-electrical model for Sodium Sulfur (NaS) batteries reproduces key characteristics of this technology including charging/discharging losses, state-dependent electrical model and internal temperature variations. With help of a cost analysis which includes calendar and cycling aging, we show trade-offs in storage capacity sizing between deviation from commitment and storage costs due to energy losses and aging.