1. Ball game, an American name for baseball, has formed the core of several colloquial idioms in which it means 'a state of affairs', as in
a whole new ball game. Because of its wide scope of alternative reference, it seems to fit naturally into British English and to be understood perfectly well in other countries where baseball is hardly known:
It was a different ball-game in those days and you bloody well know it—W. J. Burley, 1991.
2. Ballpark, though even more remote culturally, has also entered British English in the idioms
in the right ballpark, meaning 'approximately correct',
in the same ballpark, meaning 'of the same kind' or 'similar'
(It is encouraging to see that the recent total is in the same ballpark—financial website, British English 2003 [Old English (up to 1150)C])
, and
ballpark figure, meaning one that is approximate. Colourful though it is in casual conversation, it is certainly to be avoided in more formal contexts.