He's been standing off the whole of South New Hampshire single-handed

[shootingstar]

SI CROWELL; Morning, Howie.
HOWIE NEWSOME: Morning, Si. - Anything in the papers I ought to know?
SI CROWELL: Nothing much, except we're losing about the best baseball pitcher Grover's Corners ever had.
HOWIE NEWSOME: Reckon he was. He's been standing off the whole of South New Hampshire single-handed, looks like.

(Thornton Wilder, Our Town)

Hi, there
Please, what does standing off single-handed mean here. Thanks in advance. I much appreciate your help.

 

[Barque]

what does standing off single-handed mean here.?

Resisting [someone or something] by himself.

He's saying this baseball pitcher has, by himself, been preventing his team from losing to other teams in the area. It looks like Grover's Corners (a town perhaps) plays teams from other places in southern New Hampshire.

It's a bit of an exaggeration in this context of course because baseball's a team sport, but it indicates this pitcher is a very important member of the team.