Ability to write very legible numbers and letters - hundreds of sportswriters will be reading your work. You must be able to check and double check your work all the time. It's so easy to make a mistake.
Team work is essential.
No one person can record stats accurately. We are constantly talking to each other. Ability to read and understand a technical statisticians guide and make split second judgments during the game. Start getting experience while you are still at school. Volunteer to keep stats for any sport.