Here’s something I posted in reply to Brett’s American Association study at the Hall of Merit:
One interesting thing about Brent’s study is that it shows that the gap between the National League and the second-best league in baseball was so great, particularly in 1882-84. When you see the AA’s quality described as “double A,” you might tend to assume that there must have been some triple A quality leagues around; but the AA was almost certainly the best of the rest.
The two best minor leagues in 1883 were the Northwestern League and the Interstate Association. As it happens, the 1883 champions of each league, respectively Toledo and Brooklyn, moved into the 1884 American Association. Toledo declined from 56-28, .667, in the IA to 46-58, .442, in the AA; Brooklyn declined from 44-28, .611, to 40-64, .385.
That’s without taking into account player movements (which I don’t know) that might have affected the quality of the teams—in 1884, of course, overall quality of all leagues was much diluted by the advent of the Union Association and the AA’s expansion. Still, the fact that the champions of the two best minor leagues both moved into the AA and ended up well under .500 gives us a very strong presumption that the AA was much better than the best minor leagues.
The ’82 League Alliance might have been of “triple A” quality, but it had only two teams. One of them, the Metropolitans, moved into the AA in ‘83, finishing at .563. I don’t know whether the other club, Atlantic**, was organizationally the same as the ‘83 IA pennant winners or the ‘84 AA team. Looking quickly at ‘82 box scores, it would appear that only John Cassidy played
on both teamsfor both the ‘82 Atlantics and the ‘84 Brooklyn AA club.

(New York Clipper, May 27, 1882)
See also this post on the Union Association, which also deals with the relative quality of minor leagues and the “lesser” majors.
**-UPDATE 2/17/2007: the other League Alliance club was NOT Atlantic. Rather, it was the Philadelphias, the predecessor of the NL Philadelphia club we know as the Phillies (see comment by Richard Hershberger). That’s what I get for writing from memory, when I had plenty of Clipper box scores and other references to the Philadelphias and the League Alliance sitting right there next to the computer.
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