Can someone explain to me why the area under the ROC is 1 to .5 in assessing a prediction in statistics?

I am trying to figure out the advantage this has to correlation coefficient analysis in assessing risk in sex offenders.Can someone explain to me why the area under the ROC is 1 to .5 in assessing a prediction in statistics?
The area under the ROC curve shows how good your test is at discriminating the (for example) re-offenders from the non-re-offenders. So it is binary - i.e. they do or they don't. Hence if you guess the outcome, by chance alone, you would have a 50% chance (or 1/2) out of getting the correct outcome. And if your test gave you that ROC graph, then it's worthless because you might as well be guessing.





On the other hand, if the area under your curve is 1 then it means your test can distinguish a re-offender to a once-off offender _every_ time. So basically, you want a test that will give you an area as close to 1 as possible.





ROCs are different to correlational measures because in your test, you are assuming a cut-off point on some scale. That cut off is essentially the test. Correlations deal with continuum scales (e.g. score on antisocial behaviour scale correlated with illegal activity), whereas ROCs are about measuring 2 different populations who are assumed to overlap a little on some measure.