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Genuine question, albeit probably a very ignorant one: I've been hearing from many people that getting into Harvard is seriously just a stats-based game. But if that's really the case, how can H possibly accept everyone with the right stats? (defining right stats to be both GPA and LSAT at or above the median—but someone correct me if the "right stats" are higher) How does H turn down applicants with the "right stats"? Or do they not?

If anything, I would've guessed that because the Harvard law school applicant is so self-selecting, that the average applicant would have substantially higher GPA/LSATs, and that H would have more "qualified" (again, just people with the "right stats") applicants than available spots in a class?

You have to remember that the number of people who are actually at or above Harvard's medians is already pretty low. But Harvard takes a large class, so unlike Yale or Stanford, they're a bit more predictable. It isn't just about stats, but meeting both median requirements means that as long as you can string words together into somewhat coherent sentences during an interview, you're probably getting in.

It's not. 99 percentile stats are neither necessary nor sufficient

It's not just about stats but H is more predictable than YS, so it is possible to make a good guess based on stats.

I've had kjd friends who didn't get accepted though despite being over medians and the kjd status seemed to be something needing to be overcome in the JS1 interview, so it's not like H ignores other factors.