Estimates of average default probabilities for borrowers assigned to each of a financial institution's internal credit risk rating grades are crucial inputs to portfolio credit risk models. Such models are increasingly used in setting financial institution capital structure, in internal control and compensation systems, in asset-backed security design, and are being considered for use in setting regulatory capital requirements for banks. This paper empirically examines properties of the major methods currently used to estimate average default probabilities by grade. Evidence of potential problems of bias, instability, and gaming is presented. With care, and perhaps judicious application of multiple methods, satisfactory estimates may be possible. In passing, evidence is presented about other properties of internal and rating-agency ratings.