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When I say the Federal League is not competitive, I am referring to the quality of play compared to the NL and AL in those seasons. Putting 8 teams worth of players into the NL and AL in those seasons with stats accumulated in different conditions is an issue if playing a historical game. This is not a real issue with random debut leagues.
The National Association is not an issue because it was the only league at that time and many of the players continued to play in the NL formed in 1876. The AA and NL had players moving between the leagues and the AA seems to have the same level of play compared to the NL from 1882-1891.
The Union Association is a different issue. This was never a major league and it ended up in some early baseball almanac and was basically referred to as a major league since then. If you look at the players in the UA in 1884 very few of them ever played in the NL or AA after that. Take a look at Dunlap's batting record after the 1884 season when he played in the NL. He was about a .270 hitter but was a .412 hitter in the UA. He was a good hitter in the NL with a 120 OPS+, but that season in the UA he had a 256 OPS+ and this says something about the comparative quality of talent of the league that season.
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