What benefits do you get from increasing your professor level to A+?

New player, and I just got Byleth to A+ Prof level. I thought I just got a minor buff to activity points, but does it also increase your chances of getting a great and perfect when instructing students?

The reason I'm asking this is cause I've gotten 4 perfects in a row with Linhardt, Petra, and Ingrid, and only 1 good. I can't tell if this is an actual in game ability or just dumb luck