What is the toughest position in sports to earn Hall of Fame honors?

Here’s something that my friends and I were discussing a while back: what’s the toughest position in the Big 3 (football, basketball, baseball) sports to earn Hall of Fame honors?

So, I went through their Halls and counted up each position. (The Basketball Hall of Fame, which is a nice website and a cool museum, has a flaw, IMHO: their site’s HoF is not sortable for pros or college only, and you also can’t search by gender, which is bizarre. Like, get real, all the data is there in the spreadsheet that exists behind the pictures, so why not allow users to search by whatever criteria they want?) Anyway, in their respective HoFs (Basketball; Baseball; Football) there are:

• 77 Pitchers
• 70 Outfielders (22 Left, 24 Center, 24 Right)
• 44 Offensive Linemen
• 37 Defensive Linemen
• 32 Centers (NBA)
• 32 Running Backs
• 27 Linebackers
• 26 Quarterbacks
• 25 Wide Receivers
• 24 Shortstops
• 24 Defensive Backs
• 23 First Basemen
• 23 Small Forwards
• 22 Point Guards
• 21 Second Basemen
• 18 Catchers
• 17 Shooting Guards
• 16 Third Basemen
• 16 Power Forwards
• 8 Tight Ends

FYI, for the NBA I just used the player's primary position (I did this by hand, so please forgive any mistakes as user error on my part).

I was looking for scarcity to see if there's one position that's actually the toughest to be excellent at since everyone won't shut up about the QB being the most important position in sports (personally, I think it's catcher since they're involved in every facet of the game, whereas QBs are only offense). Obviously, each sport has different amounts of players who have played, but each league is old enough and with enough Hall of Famers that I figured a straight-up volume comparison was appropriate. If someone out there wants to go crazy and give the percentages for each position, then please do so and either respond in the comments and let us know what you find, or maybe even do a post of your own and tell us if you found anything interesting or surprising. (For example: Rick Mahorn isn’t in the Basketball Hall of Fame. How is that even possible? Why even have a Hall of Fame if you’re not going to include the Baddest Bad Boy of Them All? As with all things, the NBA Hall of Fame Needs More Blaha. Also, donde esta Jon Kitna in Canton? I mean, get real, I know Brandon Inge will get into Cooperstown on the first unanimous ballot in history, DUH, so I ain’t worried about that. But, the other two make me doubt the sanity of literally everyone else in the world.)

Anyway, looks like TEs are the rarest bloom in the Hall of Fame hothouse, but I wonder if that’s a function of their playing time: TEs aren’t on the field for every offensive snap, so they’re closer to part-time players, even though a dude who can block AND catch seems like a dude who should be in on every single play.

Power Forwards have a tendency to also play Small Forward or Center, so I think that explains their scarcity. Odds are that the SF and C positions have poached a few PFs to their respective groups. Third basemen are the rarest baseball HOFers (and remember, there are more baseball players in history to choose from than the others), and then catchers. This surprised me. I wonder if it’s because good third basemen traditionally transfer to first base at some point in their careers and might play longer at that position? Let us know what you think in the comments.