The moments of the partition function of a disordered system are used to determine the probability distribution of the free energy. The relation between them is essentially given by a Legendre transformation. A cut-off must be introduced to ensure the normalization of the distribution function. The method yields reasonable approximations or even rigorous results for the mean free energy without taking into account replica symmetry breaking (RSB). It therefore represents a conceptually and technically simple alternative to Parisi's RSB-scheme. Investigated examples are the random-energy model and the Sherrington-Kirkpatrick model of spin glasses.