1910 to 2006, no minor leagues but rosters expand, free agency is on but draft pick trading and compensation are off. Used Arod/Garlan's DB.
Check out some of these results with an amateur draft:
16 World Series championships in 21 appearances for the Red Sox. They won 1910-1912, (missed the pennant with a 100-62 record, 1 game back of the Washington Senators) then lost 1914, won 1915 and lost 1916. They won again in 1921 but didn't make another appearance until they lost in '34 and '35. They then won in '45, lost in '46 and won in '47. They had no showings and were a pretty bad team until they won in 1980, '82, '83, '86, '87, '88, and '89. They also win in '98 and '99. They lead the sim in winning percentage with .520, the next closest teams are the Indians and NY Giants at .509.
The Boston Braves lost their first 9 World Series appearances, finally winning in 1992. They lost 3 more mixed in with a win in '97. Every single franchise had at least 2 championships and only the Braves, Brooklyn Dodgers, Philadelphia Athletics and New York Yankees didn't make double figure Series appearances. The Yanks did win 5 of the 6 World Series they were in however.
Ted Williams finished 18th in BA at .334 from 1934-61 though he was frequently hurt. He played for the Boston Braves from '34 to '53 then bounced around between the Cardinals, Indians, Athletics, Dodgers, Yankees, Reds and Tigers. Leads in career OBP at .4656, Mel Ott is in second place at .4448. Has the single season record for OBP and walks, and leads in career walks as well.
Babe Ruth has these single season records: SLG (.830), OPS (1.319), VORP (171.5! as well as 2nd place at 133.39!), total bases (506), homeruns (71), RBIs (183). His career records are VORP (1621.9), Games (3374), ABs (12592), runs (2587), hits (3961), total bases (7648), homeruns (989!), RBIs (2665). He was MVP in 1914, 1916, '17, '18, '19, '20, '21, '22, '23, '24, '25, '26, '27, '29.
If anyone is interested in certain players or leaderboards or anything, let me know. This is the first time I've gotten to look at the stats myself as I let it run overnight.