Hypothetical plots.

The figure shows three hypothetical examples of well-behaved ROC curves when the number of cut-points is large (i.e. tending toward a continuous nature). Panel 2a shows a case of symmetry and a monotonically decreasing gradient where all three estimators provide the same cut-point. Panels 2b and 2c shows how the methods choose different points when there is asymmetry skewing the curve left or right.