The equations describing refraction of water waves are based on the geometrical optics approximation, in which wave rays are calculated independently of each other. For this reason the model reacts sensitively to small variations in depth as well as in incident wave frequency and direction. This leads to an uncertainty in the interpretation of the location of individual rays, particularly in cases of large travel distances through regions with weakly irregular bottom topography, as in shelf seas. In this paper, this uncertainty is taken into account from the outset by treating the results of the ray calculations as a case of statistical sampling, in which a tradeoff is made between resolution and confidence. To this end, the area being studied is divided into a number of subregions (bins), in each of which the total wave energy is estimated from the rays passing through it, each ray being considered as a carrier of a certain amount of wave power. The size of the bins determines the spatial resolution. It must be chosen in conjuction with the discretization intervals for ray separation, frequency, and direction, considering also the propagation distance, the length scale of the target area, and the bottom topography. This is illustrated with an example from JONSWAP.