IT IS TO HELP KEEP THE SUN OUT OF THE EYES SO THEY CAN SEE THE BALL BETTER
AnswerFor the same reason that they must keep their jerseys buttoned and tucked into their pants. It's to maintain a professional appearance and show respect for the game.Improvement:
Baseball separates itself from other major US Professional sports because it prides itself of rich history, tradition, and the respect for the game. Wearing your hat backwards or not at all if you are on the field of play (exception for the catcher) would be considered disrespectful and is not welcomed in the baseball ranks. An example of this would be when the 2009 Milwaukee Brewers after their wins early in the season would all untuck their jerseys as a was of celebration. Although they didnt see anything wrong with it, this caused a rippling effect throughout baseball and followers of baseball. Fans and former players saw it as a sign of disrespect for the game and the players that came before, while current MLB players viewed it as a way of "showing up" the team they just defeated"
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Some do, some don't. If they are scheduled to hit they will get their batting helmets ready and remove their hats. Others remove their hats to mop their heads and faces. Others do so because it is cooler without a hat. Others, especially the manager and coaches do not remove their hats while in the dugout. There is no set rule for or against wearing a hat in the dugout, only on the field, players and coaches must wear their team hats or batting helmet.
Because the game is over. It also keeps them from getting slapped in the head by their team mates during the home plate celebration.