Strategy buildings how does it works

I have a silly question how does the 39 present of player star quality you get from maxed stragegy buildings works. Let's say speed and stamina is max for my level do it exceed it because of my strategy buildings is maxed or is the attributes that is not maxed get better
i believe it goes beyond max, same as sports shop does
Thx thought as much coz otherwise strategy buildings will be useless for maxed visa players