I am not sure about this, but this is how I THINK it works:
when you play a game the fan survey module checks a number of trues and falses. If the question : was the game against a rival is true, then the module will calculate it's formula to set the number of basketballs based upon the result of the game. If the answer is false, then the current result is used and will slowly evoluate towards a standard value (wich I guess to be 2,5 balls, not good, not bad).
IF it works like this, the answer to your question is this: last game against your new rival doesn't count, last game against your previous rival does count, but the longer it has been, the less bad/good it will do to your fanopinion on that subject.
It is possible it is resetted at the season start, or possibly not, I do not dare to take a guess on this... I guess we will find out soon enough.
And finally, I think (again not sure) that PO games indeed do count.
They are not your friends; they dispise you. I am the only one you can count on. Trust me.