Various people have done the math, using reasonable assumptions and whatever info is available (in the case of Harvard, there’s a lot more as a result of the court case). When you knock out the recruited athletes and the hooked kids, there’s still a meaningful statistical advantage to applying early, although less than some think. Directionally, it looks to be similar across the SCEA and EA/ED Top 20s. Why might that be?
The early applicant pool is certainly higher-quality on average, in the sense of being able to produce an attractive application. Early applicants are savvier about the process, wealthier and at higher-quality schools with better college counseling on average, enjoying many advantages. So you’d expect applicants in that pool to produce better-looking applications that check all the boxes (including making the case for why they match a particular school), and to be admitted at a higher rate.
Yield is also not insignificant to these schools. They have a certain number of beds and locking down a big chunk of the class early has value, too (some cynically say that locking down the required critical mass of full payers early matters too, even at the supposedly need-blind schools). It’s a little different for the SCEA schools, because you aren’t required to accept the offer, but if you used your bullet there and got in, you’re very likely to enroll. It was your first choice in November, and will probably still be your first choice in March. You might say that HYPS don’t have to care about yield, which is mostly true, but leads on to the final point.
These schools use SCEA and EA/ED as an important tool to shape the class. If they need exactly one elite bassoonist, and you’re one and apply early, your odds are significantly enhanced, because you indicated that this school was your first choice and are very likely (if SCEA) or virtually certain (if ED) to enroll. By admitting you early, the school avoids a potential jump ball with peer schools for elite bassoonists in the RD round.