The main objective of the first baseman is to catch the ball. A larger glove or mitt, would be an advantage. Infielders need to catch the ball and quickly transfer the Baseball from glove to hand, to make a throw. A smaller glove has an advantage.
The infielder also needs to have a feel for the ball to help grab the ball or handle tough ground balls. The first baseman's glove or mitt has extra padding and leather to protect the hand from hard throws.
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In a game a first baseman catches most of the balls in a game and therefore would need a bigger glove and it is shapped similar to a catcher's mitt with a deeper pocket size in terms of inches.
To give the first baseman a better chance of digging a throw out of the dirt and controlling it in the glove.