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Misunderestimated (Brian H.)Mack is rather hard to evaluate -- he's the all-time leader in wins, loses and games (unlikely any of these will every be broken, even though the seasons were shorter in his day). He had a losing record all-time. If longevity is the measure of greatness its hard not to place him near the top. Of course by the end he was also the owner and the GM so his job security was not exactly as precarious as Joe Torre's.
Bill James has a book on Manager that attempts to rank them and also performs the sort of "geneology" you attempted. I forget exactly where Mack wound up but he wasn't first or second.
Mack himself felt McGraw was the greatest ever. Joe McCarthy is also a common selection as greatest ever. Despite his longevity the Hanlon-->McGraw school is often considered the dominant family of great managers.