The area under the curve is an accuracy measure and is literally the area under the ROC curve. If a decision rule has higher precision or higher recall it ends up with a larger area under the curve. A random classifer has an area under the curve of 0.5, wheras a perfect classifier with 100% precsion and 100% recall has an area undet the curve of 1. In general, because of the precision–recall trade-off the value lies somewhere between the two.
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