A few notes:
No caught-stealing records exist for a number of years. Because caught stealing numbers tend to negate much of the value of steals, stolen bases are not counted for players in years their caught-stealing numbers are unknown. This probably hurts the three oldest teams.
Players are ranked at the position at which they played during the majority of their peak years. Thus, Joe Torre is listed as a catcher though the majority of his total career time was spent at other positions.
Reliever totals are skewed by changes, over the years, in the way saves have been determined and relievers used. Because relievers were rarely used before the 50s, a statistically average player is used for the five oldest teams.
A number of players could have represented more than one generation: Musial, Williams, Gehrig, Aaron. Deciding factors included the decade a player was most associated with and who would be the replacement player.