Abstract. A statistical model for the bifurcation of the radial electric field Er is analyzed in view of describing L-H transitions of toroidal plasmas. Noise in micro fluctuations is shown to lead to random changes of Er, if a deterministic approach allows for more than one solution. The probability density function for and the ensemble average of Er are obtained. The L-to-H and the H-to-L transition probabilities are calculated, and the effective phase limit is derived. Due to the suppression of turbulence by shear in Er, the limit deviates from Maxwell's rule.