Modern FEL facilities such as the European XFEL will serve a large number of users, thus understanding and op-timizing their performance parameters such as the outputpower is important. In this work we describe the statistical approach to such optimization under assumption that the possibility of modelling is limited by uncertainties. We present experience of such statistical optimization of SASE radiation power for FLASH and discuss how the results of empirical tuning can be fed back into the model used in simulations.