There are currently 278 members of the Baseball Hall of Fame.
Of them, 8 are Umpires, 16 are Managers, and 28 are Executives. An additional 18 were Negro League players and 12 more were voted in as "players" by a special Negro League commission. None of these 30 players spent enough of their careers in the Major Leagues to be fairly judged against their MLB counterparts, and will not be a part of the "worst" discussion.
That leaves 196 contenders after the first round of cuts. I'm going to separate them into two classes: the 103 voted in by the Baseball Writers, and the 93 voted in by the Veteran's Committee.
In making additional cuts, I'm going to look at OPS+ (OPS compared to the league average of the time) to see how a player compared to his contemporaries as a quick proxy for offense. Fielding statistics are highly imperfect, but I'll try to take defense into account by looking at enough different views to at least separate the really good and the really bad.
No single pitching statistic is as highly correlated to run prevention as OPS is to run creation, so after starting with ERA+ (just to eliminate the really top-tier pitchers from further discussion), really getting to the worst pitchers will be slightly more subjective, but I'll try to avoid making any egregious picks.