If you read enough history, you begin to notice patterns. For example, political legitimacy can function in similar ways in modern Indonesia, ancient Rome, and Imperial China. If history has predictive power, it's probably through these principles.
Combined with Big Understanding, I'm investigating in small ways certain historical principles which I've discerned through my reading. The most promising attempt to do hard cross-cultural work is probably Peter Turchin and the researchers associated with Seshat, which I think is the right approach but one that still suffers from limited data.