If you look at the private school soccer rosters, you only find a handful of year round club players versus 4A schools where you have to play club soccer to make the team - especially in strong soccer club cities. At least on CC team, the majority of the team plays football in the fall, basketball in the winter and high school soccer in the spring. The goals in the upper state playoffs were made by the school's football quarterback, a college recruited football kicker, and one by a year round soccer player. They don't all have club soccer experience but are all excellent athletes and students. Maybe the key difference is the private schools can get good professional soccer coaches who know how to train and develop a good group of athletes to play soccer.
