I always think of the "break-even" point of an AP to be about 9-10 days considering park entrance/hopping only. This formula is taking the cost of the AP (my last one was just under $500) and comparing it to how much $500 would get you on a Magic Your Way ticket. On last check a 10 day that did not expire would be only be slightly less than an AP.
I also kind of try to factor in room discounts, but you CANNOT count on them. On 5 of 6 trips since becoming a passholder I have been able to secure a room discount that when compared to rack rates made the AP pay for itself. For example, had an AP rate at AKL savannah for $179 per night, checked disney.com for same nights and it was $340. So basically - 3 nights with the discounted room rate paid for my AP and more since i didn't have to buy a theme park pass!! However, remember the discounts are limited. On my December trip, for the dates I wanted I could not get an AP at a deluxe but was able to get CSR for $99 per night.
So - in my opinion, since you are going to be there 12 times, I think the AP will be worth it for you.