...the size of the school. When I was in high school, most of the schools in the district were probably the size of "single A" schools, but we played in the AA division. (Virginia had three divisions back then...) The City school played AAA football, but then dropped down into the AA category because they had a small enough student body to do it.

They did have more money, but they also had a much larger student base to draw from when putting a football (or basketball) team on the field (court). They also won most of the contests. If I was deciding the most important factor, would put size of the student population way over available money. Now if a school starts bringing in NFL coaches to hold private training sessions throughout the season...