The following figures show examples of ROC curves:
First of all ignoring the picture, from a logical point one can say: When the cutoff value decreases, more and more cases are allocated to class 1 and therefore the sensitivity will increase (true positives in relation to total actual positives). The specificity will decrease (these are true negatives in relation to total actual negatives and it will decrease, because less and less cases are allocated to class 0 so there will be less true negatives).
I got that and I think it is correct. But I got confused when I looked at the picture.
Lets take this point here:
Now when I decrease the cutoff probability from this point, I move "down" so I get this point as a result:
So I decrease the cutoff value, but one can see clearly that the value of the sensitivity on the y-axis also decreased ($x2<x1$).
Where is my logical error?