According to [Harry Potter Wiki](http://harrypotter.wikia.com/wiki/Category%3aNational_Quidditch_teams), there are 48 National Quidditch teams. This seems like an extraordinarily high number considering the low number of known schools of Wizardry that include Quidditch in their curriculum. Are we to believe the 432 players, 7 per team plus 2 reserve players (unless the big leagues have more reserves), all came from the 3 Magic institutions mentioned in the Goblet of Fire?