Team owner 'George Beansteiner' is a parody of George Steinbrener, owner of the New York Yankees, who was infamous for frequently firing his managers.
The ending scene of a homerun breaking the lights to win the game is an homage to the ending of the baseball film The Natural.
Brain's fake name, 'Sparky LaBraina', is a nod to former baseball player/manager Sparky Anderson.
The title is a play on the famous baseball poem written by Ernest Thayer titled Casey At The Bat.
Brain: Today I consider myself a mouse trying to take over the world.
A play on the famous farewell speech from baseball star Lou Gehrig, specifically the line "Today I consider myself the luckiest man on the face of the Earth."
Brain: ...the house that Ruth built!
This is a reference to one of the nicknames of Yankee Stadium, home stadium of the New York Yankees.