We present a statistical method to derive the upper limit of the obtainable fuel savings in simple wind-diesel systems applying fixed control rules. The fuel savings when using the optimal control may be estimated from the statistical properties of the time series of the power balance: wind turbine power-load. The method is validated by comparison with a time step simulation of the system. We found out that the fuel savings which may be obtained with a simple persistence based control are close to the optimal values. Using this method the dependence of the fuel savings on the wind climate and the turbulence characteristics at the site may be obtained easily. These results are also compared to the performance data of systems with energy storage.