We consider 1927 borrowers from 54 countries who had a credit rating by both Moody's and S&P at the end of 1998, and their subsequent default history up to the end of 2002. Viewing bond ratings as predicted probabilities of default, we consider partial orderings among competing probability...

We generalize the refinement ordering for well calibrated probability forecasters to the case were the debtors under consideration are not necessarily identical. This ordering is consistent with many well known skill scores used in practice. We also add an illustration using default predictions...