# Why is the ROC curve two-dimensional instead of three-dimensional?

When I understand it correctly, a ROC curve composes of a lot of ratios of TPR and FPR. Each such ratio is gained, e.g., by scanning/investigating a parameter where the ratio is the result of the used classifier. In other words: I'm interested in how a classifier separates data points according to a frequency interval of 0-100 Hz. Hence I scan this frequency, record all the 101 ratios, put them into the plot and the ROC curve represents these datapoints, finally.

Wouldn't it be much more interesting when the frequency would be used as a third axis? Or is it implicit in the axis? But anyway, I think it would be easier to look at with a third axis?

• Your threshold strictly determines FPR and TPR so it wouldn't add much new information and it'd make the chart more harder to interpret Jun 16 at 14:31
• My question (5 days ago) was closed, because someone else asked the same (2 days ago)? :D
– Ben
Jun 22 at 6:38

## 1 Answer

The ROC curve is two-dimensional because it is defined as the plot of TPR and FPR. Yes, you might be interested in the threshold used to generate the TPR and FPR, and you might want to plot that on a third axis, but then it is not a ROC curve but something else (arguably more informative, arguably harder to draw, arguably so hard to draw that the additional information is not worth the trouble).

• Especially considering it's most likely going to be displayed on a 2-D screen or printed on 2-D paper... Jun 16 at 18:14