# The value of adding the ROC graph if the AUC is given

I always see in papers that when they want to show how they classifiers performed, they provide ROC graph and the AUC score. Now as far as I know only the AUC tells how well the classifier performed, so what is the advantage of adding the ROC graph? What can one tell from it?

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This isn't really any different from lots of cases where the data are described numerically in the text, but people like to present the information visually as well. –  gung Mar 30 at 20:59

The ROC curve is the specificity/sensitivity plot; the AUC is the Area Under Curve. To be brief, the ROC curve can be interesting because it allows comparison of the sensitivity/specificity behaviour of the model. More simply:

$ROC = (x,y) \in R^2 \Rightarrow AUC = z$ but $AUC = z \nRightarrow ROC = (x,y) \in R^2$

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I still don't get it. What could one use the ROC graph for if he only needs the AUC to really evaluate the performance? –  Alex Twain Mar 30 at 18:08

I usually give the ROC plot but not the AUC: For my applications it is usually clear that either a specific or a sensitive regocognition is needed. The ROC is different for classifiers that are specific but not sensitive vs. sensitive but not specific while the AUC hides this information.

Besides, one can put a whole lot of further information into the plot, e.g. color-coding the thresholds (check whether the classifier is well calibrated if the primary output is posterior probability), model stability (after resampling validation), or confidence regions for a chosen classifier (if one chooses a threshold). Finally, you can even put "extented" measures of sensitivity and specificity which do not require the thresholding @FrankHarrell fights against, e.g. it is possible to extend the concept of sensitivity and specificity and the concept behind Brier's score to yield such measures.

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Is there something about probabilistic decision making that doesn't work in your situation? –  Frank Harrell Mar 31 at 0:11
@FrankHarrell: Well, yes: communication. I spend quite a lot of my working time doing translations: physicist <-> chemist (<-> chemometrician) <-> statistician <-> medical doctor, and I find the art of doing this well has a lot to do with allowing simplifications and finding compromises (and trying to avoid to gross misconceptions). I tackle the "don't throw away information" problem by sneaking in continuous measures (as chemist I prefer MSE/RMSE) which are well (or at least better) behaved, but their names and purpose are familiar. –  cbeleites Mar 31 at 14:40
I feel that probabilities can work well if communication is careful or the problem involves sports or card playing. –  Frank Harrell Mar 31 at 19:34
Only if sensitivity and specificity are helpful. I find them not to be. If we were regressing age on blood pressure we'd never create an ROC curve. Why we do it when $Y$ is binary is beyond me. –  Frank Harrell Mar 30 at 23:34