Well, @spayurpets and @VeryLuckyParent, I wouldn’t go so far as to say it’s “hooey” or “garbage”, but I think YTAR has some issues, for the following reasons:
First, I’m not sure what YTAR explains, or how one should interpret it. Stanford’s YTAR is 18.6. Harvard’s is 15.8. Yale’s is 11.0. Cornell’s is 3.7. Does this mean that Stanford is roughly 18% more prestigious (whatever that means) than Harvard, or 1.8x as prestigious as Yale, or more than 5x as prestigious as Cornell?
Second (as previously noted), at the high end, small movements in total applications lead to exaggerated movements in YTAR. Stanford and Cornell get a very similar number of applications (44 to 45 thousand), but an incremental 2,000 applications (less than 5%) increases Stanford’s YTAR by roughly 5x the amount it increases Cornell’s. If both Stanford and Cornell increase their total applications by similar amounts and percentages in a given year, can we really say that Stanford became significantly more prestigious relative to Cornell that year?
Third, as has also been noted, the numerator and denominator are both “game-able” in ways that can have complex effects. Ginning up applications from unqualified students will decrease the admit rate without a direct effect on yield, of course. I think the yield numbers are particularly suspect, though, because (i) they are undoubtedly pumped up at schools with ED programs (particularly if the school fills an outsize proportion of the class early); (ii) they rely on assumptions about targeted class size which aren’t necessarily disclosed by the schools, may change year over year, and therefore are often no more than estimates; and (iii) they don’t take account of how actively/aggressively the schools manage their waitlists, or if they have Z-lists.
Fourth, certain schools have “market niches” that further reduce comparability if one is trying to measure relative prestige. Harvard is the biggest worldwide brand name in education; its total applications and yield are undoubtedly inflated as a result. I think most people would agree that Stanford is the best university west of the Mississippi and has less regional competition than the Ivies, it’s also identified closely with Silicon Valley and engineering, and all this is no doubt pumping up its numbers.
On the other hand, Princeton and Yale, which are of similar size to Harvard and Stanford at the undergraduate level and (according to US News, at least) are of at least equal quality to them, don’t have these differentiators. Accordingly, they get 29 and 31 thousand apps instead of 39 or 44 thousand like Harvard and Stanford, and their yields are 69 percent instead of 82 to 87 percent - even though all four schools have admit rates between 4.7 and 6.5 percent (which makes them fundamentally indistinguishable in terms of difficulty of entry).
This discussion prompted me to graph a scatterplot of admit rate (on the vertical axis) vs. yield at the 10 schools for which @spayurpets provided numbers (the Ivies, Stanford and MIT) and derive a best-fit line (for the nerds among you, y=0.4034e^-2.48x, R-squared = 0.7217). I think this provides some interesting results: (i) Cornell, Penn and MIT seem to have high admit rates relative to their yields; (ii) Brown, Columbia, Princeton and Yale seem to have low admit rates relative to their yields (although the differences from the best-fit line are much less than in (i)); and (iii) Dartmouth, Harvard and Stanford are right where the best-fit line suggests they should be. I’d invite others to chime in if they have thoughts on this.