Most classification algorithms return a classification confidence denoted as f(X), which is, in turn, used to calculate the prediction. Following the credit card abuse example, a rule might look similar to the following:

The threshold determines the error rate and the true positive rate. The outcomes of all the possible threshold values can be plotted as receiver operating characteristics (ROC) as shown in the following diagram:

A random predictor is plotted with a red dashed line and a perfect predictor is plotted with a green dashed line. To compare whether the A classifier is better than C, we compare the area under the curve.

Most of the toolboxes provide all of the previous measures out of the box.