Let’s think this through: The team’s grade point average is an average, but we want to emphasize that a new player has increased that average. So we call it an average average.
But if we average an average, we still get – you guessed it – an average.
I understand the confusion. We usually think of GPA as something individual. And if we pool several GPAs, don’t we get an average of an average?
Yes, we do. But in this case, writing team grade point average (notice how eliminating the possessive makes a subtle difference) produces a clearer (and tighter) phrase than the team’s average grade point average.
Sometimes, an imperfect solution – do I dare call it average – provides better results than technical perfection.