In my opinion, with 3 boys having gone through boarding school (so, not an expert, but some basis for my opinion) the single best predictor of academic success at boarding school is good time management skills.
Also, just like colleges are familiar with certain schools (boarding, top public etc) the boarding schools are familiar with feeder schools too. Whether they are junior boarding schools or local day schools, the boarding schools know what good grades from those schools mean. Yes, just like with colleges, it disadvantages kids from unknown schools.