How close is my classifier to random guessing?
I need to quantify the inability of a binary classifier to obtain better results than random guessing in a single number evaluation metric.
The random guessing line (RGL) from (0,0) to (1,1) has an AUC of 0.5. But so does the blue curve (grey area).
Wouldn't it be more suitable to use the area between the RGL and the ROC-curve to estimate how "close" a classifier is to actual random guessing?