What Can Be Learned from Signal vs. Background Efficiency Plots?

[ChrisVer]

What information can one obtain from the plots of the background vs signal efficiency? $\epsilon_{bkg}(\epsilon_{sig})$?
In particular I attach some plots I made by hand and I want to understand how to obtain what each tells us.

 

[mfb]

Your plot should have 1/(background efficiency) or 1-(background efficiency) as vertical axis.

Each point on the curve is a possible selection. As an example, you can randomly take 60% of the events, then you have 60% signal efficiency and keep 60% of the background. That is not a good selection, of course. Your actual one might keep 90% of the signal events and keep only 5% of the background. If you make the selection a bit looser, you get 91% of the signal, but 10% of the background. Make this in a continuous way (with TMVA usually) and you get a curve. With the usual choices for axes, all curves should look like the blue one.