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Whenever you're crossing eras you have to make some large assumptions, or you end up with one era or another dominating.
You could just have each team do what it did in real life. Three Finger Brown could go out and pitch 300+ innings and use very few relievers. But that ignores the fact that he was pacing himself to do that, and if he tried that approach in 1979 he'd likely get hammered.
You also have to deal with the slope of history. The game gets better every single year. 1906 teams thrown into a pool with 2019 teams would likely get slaughtered. Even the Cubs. Almost every facet of the game and the environment was dramatically more primitive. In 1906 there were no affiliated minors, scouting was limited and ad hoc, information and data was paltry, nutrition and strength and conditioning barely existed, salaries were far lower and players would quit, infrastructure in the Majors was akin to your county fairgrounds, equipment was simpler, segregation was the rule, there were almost no foreign players, an average MLBer was probably 5' 9", 170 pounds. Put Mike Trout in a time machine and he'd probably hit .500 or .600 in turn-of-the-20th century baseball. I really believe that the 1927 Yankees, plucked out of their era and dropped into today, would have a hard time competing in the Japanese Leagues.
But because the distance between best and worst has shrunk over time it was much easier to dominate in the past. So at face value, with no accounting for that, you'd conclude that most of the best players in history played a century or more ago. In the pre-1920 era people would hit .420 with some regularity, and pitchers would throw 340 innings and win 35 games.
You best bet is to set some ground rules that end up with results kind of like what you want and roll with it. If you want to be completely realistic you'll probably end up with the best teams of all time playing in the last 30-50 years.
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