Dichotomous forecasts are "yes/no" forecasts for the occurrence of a defined event. Verification performance measures for dichotomous forecasts are computed from the entries of a 2 X 2 contingency table of all possible outcomes. Bias is the ratio of the number of "yes" forecasts to the number of "yes" observations. The sensitivity of performance measures to bias has been a matter of concern for many years. The approach here is to derive a quantitative assessment of bias dependency by expressing any performance measure as a function of bias, probability of detection, and event frequency. This formulation quantifies bias dependency in terms of a critical performance ratio (CPR) that ranges from zero to one. Graphical analysis of CPR functions imparts insight into the nature of bias sensitivity for various performance measures, including new "bias adjusted" performance measures. Bias sensitivity is an important consideration in assessing performance of hedged forecasts, bias corrected forecasts, or forecasts verified using spatial techniques.