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In modern day baseball, teams generally have five starting pitchers, and they take it in turn to start a game every fifth day (hence the phrase rotation). Sometimes, if the schedule pans out, a team can get away with a four man rotation, and in the distant past some teams managed a three man rotation.
Since most  major league games average between 250 and 300 pitches, that would  put the ball count at about 40 or 50 balls used per game.  According to the MLB: It says between five and six dozen  baseballs are used during each baseball game, as many as 72 balls..