To the extent that one can affect it, I think it has more to do with selecting the entire friend pool, not picking individual friends (which obviously won't work).
The friend pool at Phillips Exeter's got a higher top-end of friend quality and a higher bottom-end, generally speaking, than your average public school—the best and worst likely cases for your kids' friend groups are both "better", probably—to pick an exaggerated example.
We do the same thing when we choose where to live for the public schools. It's largely about finding better likely friend group outcomes. "Better" kids are easier to teach and their families are more likely to push them academically, so a proxy for that is how "good" the school is (test scores, college readiness, reputation) but it's kinda sorta mostly about the kids with whom your kids will be hanging out 7-8 hours a day.
The friend pool at Phillips Exeter's got a higher top-end of friend quality and a higher bottom-end, generally speaking, than your average public school—the best and worst likely cases for your kids' friend groups are both "better", probably—to pick an exaggerated example.
We do the same thing when we choose where to live for the public schools. It's largely about finding better likely friend group outcomes. "Better" kids are easier to teach and their families are more likely to push them academically, so a proxy for that is how "good" the school is (test scores, college readiness, reputation) but it's kinda sorta mostly about the kids with whom your kids will be hanging out 7-8 hours a day.