# Ranking performance measure

I have a system able to produce a ranking of some operations according to their anomalous score. I have N anomalous operations inside the dataset, which I expect to be in the first N positions (best case). This score is computed by a formula which has some parameters. According to the parameters configurations obviously the ranking changes. How can I measure the performance quality of the system? Currently, I am measuring the true positive rate, but I would prefer some measure that shows how much the anomalous operations are concentrated in the first positions. What I mean is that I can have the same TPR but in one case the FNs can be in N+1, ..., N+10 position, right after the Nth position, and another case where the FNs are at the end of the ranking. I definitely prefer the first case.