I have 2 binary classifiers and a test set.
For the first of the classifiers I can compute any metrics for any value of a threshold, e.g. I can plot ROC curve and calculate precision, recall, F1 etc at any point of the curve.
For the second classifier the value of the threshold is fixed, e.g. I can calculate all the same metrics but only for one point of ROC curve.
Is there a way to say something about which classifier is better under these conditions? For example, would the fact, that the single dot computed for the second classifier is above ROC curve of the first classifier, mean that the second classifier is better overall?