Green’s Dictionary of Slang

1. any kind of fiercely aggressive and competitive ball game.

1962

K. Kesey One Flew Over the Cuckoo’s Nest (2002) 72: Hey-yah, comin’ at you, guts ball from here on out...

2. any action requiring aggression, courage and determination.

1962		F. Harvey Strike Command 11: ‘Want to turn and run? [...] Or play a little guts-ball and try for the tankers?’ K. P. Green voted for gutsball. And now the sweatout began.
1977		Baa Baa Black Sheep [NBC-TV] Ho boy. Mr. Gutsball, eh? [HDAS].