In high-power lasers such as Laser MégaJoule (LMJ), partially coherent beams are used, in order to reduce the impact of laser-plasma instabilities during the interaction with the target. To estimate the effect of certain beamline parameters on the instabilities, it is useful to have a simple statistical description of those partially coherent beams. We propose to use a description based on the Wigner function of the electric field, and on its moments in particular. Notably, we have developed a formalism to express the dimensions of the beams' speckle as a function of those moments.