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40% of all teams make the playoffs.
8 teams make the playoffs. No wonder you see the same teams. 40% of all teams make the playoffs in the 20 team leagues. Once in the playoffs anything can happen, and usually does. So what if the same 2 or 3 teams make it every year, that still leaves 5-6 spots open. In a number of leagues, teams under .500 have made it. This alone gives everyone a fair chance.
P.S. I would be willing to switch the FA draft to worst record over random chance in the promotion of parity.