In a binary logit analysis with unequal sample frequencies of the twooutcomes the less frequent outcome always has lower estimatedprediction probabilities than the other one. This effect is unavoidable,and its extent varies inversely with the fit of the model, as given by anew measure that follows naturally from the argument. Unbalanced sampleswith a poor fit are typical for survey analyses of the social sciences andepidemiology, and there the difference in prediction probabilities is mostacute. It affects two common diagnostics, the within-sample 'percentagecorrectly predicted' and the identification of outliers. Partial remediesare suggested.