# How to Interpret the ROC Curve?

i plotted the ROC curve for RandomForest Classifier and this is what i get :

The shape looks weird to me , can somebody help me to make sense of it , and is this shape 'common' to not say normal?

thank you.

Imagine you have a blue line drawn from the point (0,0) to the point (0, 0.51). Do you see a common shape now?

That happens because you have few or no predicted probabilities above 0.9 or something close to it, so the point with 0 false positives is never touched.

The ROC curve you are watching is perfectly normal.

Just to give a bit more context to help you understand better, the way a ROC curve is built is by iteratively calculating True Positive Rate (TPR) and False Positive Rate (FPR) based on the updated confusion matrix, for different values of the threshold.

So just to give a very simple example here, imagive you have the following:

• Real labels: [0 0 1 1]
• Predicted probabilities: [0.2 0.6 0.6 0.8]

Trying different thresholds, the TPR and FPR are calculated as:

-Threshold=0, Predicted labels: [1 1 1 1], TPR=1, FPR=1 -Threshold=0.2, Predicted labels: [0 1 1 1], TPR=1, FPR=1 -Threshold=0.4, Predicted labels: [0 1 1 1], TPR=1, FPR=1 -Threshold=0.6, Predicted labels: [0 1 1 1], TPR=1, FPR=1 -Threshold=0.8, Predicted labels: [0 0 0 1], TPR=1, FPR=1 -Threshold=1, Predicted labels: [0 0 0 0], TPR=1, FPR=1

The ROC curve would then look something like this:

This simple ROC curve, like the one in your graph, starts from (0, 0.5). The reason for that (as Juan also explained) is that in the example there are no labels with high probabilities (in our example the highest is 0.8).

For a better understanding of how the ROC curve can be created and interpreted you can have a look at this very well-explained answer https://stats.stackexchange.com/questions/132777/what-does-auc-stand-for-and-what-is-it/132832#132832.