These aren't purely random. They interest the nerd and mathematician in me. What has always amazed me is how some people carry around in their heads so many Baseball trivia items (see The Trouble With The Curve with Amy Adams). Hopefully, at least one of these will not be on those folk's radar.
Biggest Bat ever used - The average bat in use today is 34-36 oz. Babe Ruth, however used a bat weighing 59oz.
Biggest Paycheck - A-Rod, or Alex Rodriguez, 275 million. I have no doubt this record will be broken soon. Baseball palyers make a butt load of money.
Tallest Player - John Rauch of the Toronto Bluejays. The man was over 6' 11".
Heaviest Player - Walter Young of the Oriels. 322 pounds
Shortest Player - Eddie Gaedel was not only the shortest (3' 7") but also the lightest (65 pounds). St Louis Browns 1951.
Longest Home Run - 643 feet, Mickey Mantle, Yankees
Highest Price Paid for a Baseball - $3,054,000 Mark McQuire's 70th home run ball.
Fastest Pitch - 105 MPH, Aroldis Chapman of Cinninnati Reds. By the way, the reds lost anyway.
Most Number of Teams - Octavio Dotel has been on 13 major franchises.
Most people in attendance at a single baseball game - 115,300; Saturday, March 12, 2008, LA Coliseum: Dodgers vs Red Sox
Longest Game Ever Played in 20th or 21st Century- I know I'm being picky but some games before 1900 went on and on. The longest game in my time span was on May 1,1920. The Boston Braves and the Brooklyn Dodgers. It went 25 innings and ended in a 1-1 tie. They had to quit as the field had no lights and it had gone dark.