One of the main goals of the feasibility study MOSE (MOdelling ESO Sites) is to evaluate the performances of a method conceived to forecast the optical turbulence (OT) above the European Southern Observatory (ESO) sites of the Very Large Telescope (VLT) and the European Extremely Large Telescope (E-ELT) in Chile. The method implied the use of a dedicated code conceived for the OT called astro-meso-nh. In this paper, we present results we obtained at conclusion of this project concerning the performances of this method in forecasting the most relevant parameters related to the OT (, seeing ε, isoplanatic angle θ₀ and wavefront coherence time τ₀). Numerical predictions related to a very rich statistical sample of nights uniformly distributed along a solar year and belonging to different years have been compared to observations, and different statistical operators have been analysed such as the classical bias, root-mean-squared error, σ and more sophisticated statistical operators derived by the contingency tables that are able to quantify the score of success of a predictive method such as the percentage of correct detection (PC) and the probability to detect a parameter within a specific range of values (POD). The main conclusions of the study tell us that the astro-meso-nh model provides performances that are already very good to definitely guarantee a not negligible positive impact on the service mode of top-class telescopes and ELTs. A demonstrator for an automatic and operational version of the astro-meso-nh model will be soon implemented on the sites of VLT and E-ELT.