A rainfall-runoff model is used in conjunction with a probabilistic description of the input to this model to obtain simple regression-like relations for basin runoff in terms of basin and storm characteristics. These relations, similar to those sought in regionalization studies, are computed by evaluating the conditional distribution of model output given basin and storm characteristics. This method of conditioning provides a general way of examining model sensitivity to various components of model input. The resulting relations may be expected to resemble corresponding relations obtained by regionalization using actual runoff to the extent that the rainfall-runoff model and the model input specification are physically realistic. The probabilistic description of model input is an extension of so-called "random-model" of channel networks and involves postulating an ensemble of basins and associated probability distributions that mimic the variability of basin characteristics seen in nature. Application is made to small basins in the State of Wyoming. Parameters of the input variable distribution are estimated using data from Wyoming, and basin-scale relations are estimated both, parametrically and nonparametrically using model-generated runoff from simulated basins. Resulting basin-scale relations involving annual flood quantiles are in reasonable agreement with those presented in a previous regionalization study, but error estimates are smaller than those in the previous study, an artifact of the simplicity of the rainfall-runoff model used in this paper. We also obtain relations for peak of the instantaneous unit hydrograph which agree fairly well with theoretical relations given in the literature. Finally, we explore the issues of sensitivity of basin-scale, relations and error estimates to parameterization of the model input probability distribution and of how this sensitivity is related to making inferences about a particular ungaged basin. ?? 1989 Springer-Verlag.