ball game

from The American Heritage® Dictionary of the English Language, 5th Edition.

• noun Any of various games, such as baseball, played with a ball.
• noun A game with religious and political significance in some pre-Columbian societies of Mesoamerica, southwestern North America, and the Caribbean, played with a rubber ball in a walled court.
• noun A competition.
• noun A particular condition, situation, or set of circumstances.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• noun Any game played with a ball.
• noun A specific contest or match between teams playing such a game.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

• noun a field game played with a ball (especially baseball)