I agree with zbravian. To me honestly as a person who repairs their own phones; apples warranty is useless to me since I can fix everything on this phone for a fraction of what apple charges, and a battery replacement will take me at most 5 minutes to do on my desk and cost 10 bucks. Meanwhile a restore and blah blah blah will take probably a good part of a day to do and I need my phone to work. I will report back with ibackupbot data and when the new battery arrives.
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I'm guessing with over a year of heavy usage it probably just is slowly dying. This was my battery life within the first week of getting the phone (just checked my photos, another reason I refuse to erase and restore) using the same backup I'm using now.