short answer, pay from pocket...

long answer, Your insurance would pay from your liability extension from your home owners policy for their window. You're the one who did it, you're liable. Their insurance may cover the costs upfront then surrogate(sue) against you. Contact whomever you have homeowners insurance with, ask about personal liability extension and if you're covered for breaking someones window playing a game(if you have this extension then you would be covered).... If you rent and only have renters coverage you most likely do not have a personal liability extension. auto liability will not cover.

even longer answer, Was this game part of some league play or, did you rent the ball field for play? Under joint and several liability,others may be held liable, including whoever rented you the diamond. Depends what contracts exist, and hold harmless clauses. If you rented this from the city you have 15 days to file notice, unlike other liability, and get out and take pictures of the missing fence/other issues asap. Its amazing how fast things get done when they are served, literally watched them come and chop down tree bits blocking a stop sign as i was taking pictures of the visual obstruction... they tried to claim it was clear, i showed them the pictures of themselves cutting it down. They are crafty fuckers.