The player I often use to reference this set is Pickles Dilhoefer (1893-1922). Dilhoefer's died of typhoid Feb 23, 1922. His card in the set has him playing for the Philadelphia Quakers, he played 8 games for them in 1918, and finished his career with the St. Louis Cardinals 1919-21.

But the variations in the set also add questions Bob Roth, Maranville, Bancroft, and Jennings. Personally, the exclusion of McHenry suggests all dates prior to 1922-23. Great mystery. My guess is 1920-21.

Many of the accused Black Sox played well into the 1920 season before their alleged involvement in the 1919 World Series scandal became exposed