  We study the formation of extreme events in incoherent systems described by
envelope equations, such as the Nonliner Schr\"odinger equation. We derive an
identity that relates the evolution of the kurtosis (a measure of the relevance
of the tails in a probability density function) of the wave amplitude to the
rate of change of the width of the Fourier spectrum of the wave field. The
result is exact for all dispersive systems characterized by a nonlinear term of
the form of the one contained in the Nonlinear Schr\"odinger equation.
Numerical simulations are also performed to confirm our findings. Our work
sheds some light on the origin of rogue waves in incoherent dispersive
nonlinear media ruled by local cubic nonlinearity.
