Local bridge scour, which is defined as the loss of soil particles/mass surrounding a pier foundation due to the flowing water-induced shear stresses, is a primary cause of bridge failure in the United States and worldwide. Current practice of bridge scour prediction is mostly based on the use of deterministic models. Work herein presents statistical models that extend five deterministic approaches reported in literature to predict the expected scour depth while quantifying inherent model bias and uncertainty in view of data scatter. Clear water scour database is used herein and the analyses quantify model scatter by comparatively assessing the computed scour depth versus measured data reported in the database. A relationship between probability of deceedance associated with the predicted scour depth and a modification factor (that is applied into the deterministic prediction) is devised. The modification factor allows for the use of the scour magnitude computed from the deterministic models while quantifying the probability of a computed scour depth being less than or more than a most likely value (per measurements reported in the database). The application of the proposed model is demonstrated with an example and the results are discussed.