I agree with your point that additional factors attract students to BYU, and I agree that some of these additional factors are independent from the quality of "outcome measures." But I disagree that these factors are untethered to the quality of school, as you put it--the way to measure the quality of school is the question to be decided, not to be begged. I also think you are wrong that these extra factors that attract students to BYU "drive up some of the most important factors keeping BYU's ranking high". It's an empirical question about which side of the two edged sword is sharper. But is it clear that if there are additional factors that attract students to BYU, that they will only increase BYU's ability to pull in higher quality students by almost any measure (see BYU's incredible matriculation rate). So while it is true that BYU offers its students far more than simple outcomes measures (the mission statement is "to assist individuals in their quest for perfection and eternal life"), those factors will certainly improve the quality of students that end up at BYU. So on your model of the factors that affect student outcomes the most (calibur of incoming students), these additional factors that attract students to BYU ought to be improving BYU's student outcomes, no?