The assessment of the efficiency of a storm water storage facility devoted to the sewer overflow control in urban areas strictly depends on the ability to model the main features of the rainfall-runoff routing process and the related wet weather pollution delivery. In this paper the possibility of applying the analytical probabilistic approach for developing a tank design method, whose potentials are similar to the continuous simulations, is proved. In the model derivation the quality issues of such devices were implemented. The formulation is based on a Weibull probabilistic model of the main characteristics of the rainfall process and on a power law describing the relationship between the dimensionless storm water cumulative runoff volume and the dimensionless cumulative pollutograph. Following this approach, efficiency indexes were established. The proposed model was verified by comparing its results to those obtained by continuous simulations; satisfactory agreement is shown for the proposed efficiency indexes.