Ratings related to the new coach's role. So, if it was a hitting coach, say two points total between con/vsl/vsr/pow/eye and another point between bunt/base running/speed. If it was a pitching coach, same thing. Two or three points total between con/vsl/vsr/p1/p2 and another point or two between vel/gbfb/p3/p4/p5.
Those bonuses could only apply to players at the current level of that coach and would only apply to two or three players selected at random by Simmy, like a DitR.