The prestige of the school may go up or down based on the prestige of your last job. If you're moving up a division, then the school prestige will drop, and if you're moving down a division it may go up. When you're moving within the same division and you are coming from a higher prestige school, your new school may get a small increase in prestige. If you're coming from a lower prestige school (as is most common), you may see a decrease in the school's prestige.
This change accounts for the impact a new coach will have on the national perception of a school, especially in recruiting.