Solely on a convenience sample of the cadets I know, most of them went to a public high school. The people who end up here will excel in their environment regardless of where they are.
You will see a disproportionately large amount of D1 athletes having gone to private schools because often times those schools have more competitive sports programs and greater connections with college sports recruiters (I say this from experience on high school travel sports teams and being one of the only public school kids).
I would say the majority of non-recruited cadets are from public schools. Neither provides any visible advantage here.
Unfortunately, I think there is a ton to dive into if anyone really wanted to here. I'm pretty deep into athletics in Texas, and I won't disagree with anything stated here. There are nuances though. I would venture to guess, Football and baseball and possibly basketball may not fit this description of mostly private school recruits. The athletic landscape in some sports (Volleyball, Soccer) absolutely Club Team is recruited WAY more. Some areas in Male soccer, the top leagues literally rules that the player CANNOT play for their public HS team if they want on the team. It infuriates me to take away a kid's ability to show for their school, but that's a long story. Also, regionally, there are schools in the Northeast that are private, recruit, provide scholarships, which I'm torn, I love the opportunity it provides, especially being someone that grew up with a single mom that was a bank teller and waitress at night just to pay the bills (barely). There is not anywhere close to as much of that in Texas, Florida, the whole Southeast. It creates unbalanced teams, and once that starts, all the best athletes go that direction. So any great volleyball player let's say, takes a scholarship or just goes private. Football, the numbers will never let that happen.
Just my rant on D1 athletes coming from HS, and the crazy process of recruiting, ha. It's massively complex for why that is.
I would agree with UHBlackhawk, the genpop from what the WP grad that I'm friends with and he's spent the last 10 years as WP rep in TX, it's all about the individual, and I love that it all matters for these candidates, some get in with great SAT and not necessarily great GPA and vice versa, but they both have to be pretty darn good, and then have all the other things.