Our HS is around 1800 students, they usually get enough for 3 teams of around 16 (freshman, jv, v) with cutting just a few kids. One year recently they only had enough for 2 teams of 20, I think they may have cut more that year, ironically.
The coach ran lots of optional stuff that included middle-schoolers: summer workouts, fall ball for the non-fall-sport kids, and indoor winter workouts for the non-winter-sport kids. We had many baseball-loving kids, most came to these optional events. So by the time he got to actual tryouts, he mostly knew what he had.