Why is there a sharp elbow in my ROC curves? I have some EEG data sets that I am testing against two classes. I can get a decent error rate from LDA (the class-conditional distributions aren't Gaussian, but have similar tails and good enough separation), and so I want to plot the ROC of the LDA predictor against data sets from other subjects.
Here is a typical graph for the predictor tested against a single trial:

I have tried a couple of different packages (pROC and ROCR), and the results are consistent. My question is, what's with the sharp elbow? Is it just an artifact of the projection produced by the LDA, i.e., there happens to be a 'cliff' where the classifier performance plummets?
 A: Although this question was asked about 3 years ago, I find it useful to answer it here after coming across it and getting puzzled by it for some time. When your ground truth output is 0,1 and your prediction is 0,1, you get an angle-shape elbow. If your prediction or ground truth are confidence values or probabilities (say in the range [0,1]), then you will get curved elbow. 
A: I agree with John, in that the sharp curve is due to a scarcity of points. Specifically, it appears that you used your model's binary predictions (i.e. 1/0) and the observed labels (i.e. 1/0). Because of this, you have 3 points, one assumes a cutoff of Inf, one assumes a cutoff of 0, and the last assumes a cutoff of 1 which is given to you by your model's TPR and FPR and is located at the sharp angle in your graph.
Instead, you should be using the probabilities of the predicted class (values between 0 and 1) and the observed labels (i.e. 1/0). This will then give you a number of points on the graph that is equal to the number of unique probabilities you have (plus one for Inf). So if you have 100 unique probabilities, you will then 101 points on the graph for each of the various cutoffs.
A: A perfect ROC "curve" will be shaped with a sharp bend.  The performance you have there is very near perfect separation.  In addition, it looks like you have a scarcity of points making the curve.
