I count 16 seasons for Bancroft (WaitNSee sitemailed).
Recall that a player who played on two teams in one season, that season counts as two. So in Bancroft's case, 1920 NYG and 1920 Phillies count as two, since both of those versions (partial or combined) are eligible to be drafted.
When doing a search for eligibility, set Season Type = Full/Combined to get the count. Once the draft starts, either the partial or the combined version can be drafted (for each team), but not both.