March Madness: Divisional Matchups

Teachers often complain that it's not fair to compare their schools to other schools, based on differences in student demographics.  I'm not sure I agree with the notion -- and more than a few schools exceed or fail to meet demographic expectations. 

But what about creating NCAA-like divisions (I, II, III)  within public school systems based on student poverty, in order to help someone (educators) get past the poverty- achievement trap and help others (politicos) see that performance varies even with schools with similar demographics?

Under this format, schools in a district or state would match up against other similar schools, like in the NCAA tournament, where schools are organized by size.  Unlike in the NCAA tournament, however, divisions would have to be flexible so that schools would not be limited to certain achievement levels.