[ErickX2]

Here's what I think so far. Hints don't necessarily allude to the game itself, and as such while I agree baseball could be a major part of the hint, I don't think it's about the game theme. Rather, it could be about the way baseball is played, which simply put is teams taking turns as they try to score.
At first I though this sounded somewhat hard to manage, but looking back this is something that was alrady used by FIRST in the game Aim High.
Of course I could be completely wrong, it's just my thoughts on it so far.