I find the Parchment head to head matchups interesting. I’m not sure I trust Parchment, but a reliable comparison of yield for schools that admit the same kids would be another data point. I’m sure it would be easy to come up with a computer-generated ranking of desirability based on these matches.
My ideal ranking would be one with 50 or more factors which the user could weight any way they wanted, resulting in personalized results. I’ve seen this attempted but whenever I’ve tried it I didn’t get results that made sense. You’d probably have to do some pre-weighting of the factors, e.g., academic quality mattering more than good food even if a student said both were of highest importance. Of course this wouldn’t sell magazines.