In the US, the major team sports are not at all "very thin edge". In fact, lack of parity is a real issue facing several leagues.

Between "tanking" (teams that are deliberately bad in order to get better draft picks), massive budget differences (it's not unusual to see large-market teams with payrolls more than double those of small-market teams), and structural issues in the games themselves, parity can be very very difficult to achieve. 538 attempts to use chess-style Elo ratings to track the major sports, and currently they have:

* ~200-point difference between best and worst major-league baseball team

* ~400-point difference between best and worst NFL football team

* ~400-point difference between best and worst NBA basketball team