From the
HBD Developer's Chat (back when those were a thing (2009), and I don't think anything on the underlying engine has changed in years):
Q: I wonder if you could lay out for us how players at each position tire. It seems to me that a catcher for instance should tire more quickly over the course of season compared to say a 1B and a DH should hold his stamina better than any position player. After several seasons of playing it seems to me like stamina is almost entirely attached to AB's and nothing else. Not very realistic. (mosley80 - Hall of Famer - 12:44 PM)
A: Catchers fatigue the most, then the other position players, then DH. We're not talking a huge difference here, but it is significant over the course of a season.
The consensus, from those of us who looked at it after this Dev Chat, was that fatigue followed the defensive spectrum (though I don't know if that was ever explicitly confirmed).
Designated hitter – First baseman – Left fielder – Right fielder – Third baseman – Center fielder – Second baseman – Shortstop – Catcher