We use Poisson statistics to calculate the mean and variance of the initial bunching factor both in a free-electron laser (FEL) and in a collective atomic recoil laser (CARL). A general criterion for coherent bunching is proposed. We use the statistics of the initial bunching parameter to obtain the scaling laws for the radiated power. This scaling differs markedly from that of current models and is significant in reducing the saturation lengths of short-wavelength (x-ray) FELs starting from noise. We demonstrate the effects of this with relevant examples.