From the help page:
Rookie of the Year: Closely mimics the formula used for MVPs for position players and Cy Young for Pitchers. In order to be eligible for the ROY or NOY, a player must not have more than 150 career AB or 50 IP at the current level. For instance, if a player had 87 at-bats at the big league level in season 1 and 90 at-bats at the big league level in season 2, then he will not be eligible for the award in season 3 and beyond.