In addition, I have turned off 4G/LTE and am just using 3G. This I think is also playing an enormous factor.
Do you notice your phone switching from 4g to 3g a lot? I was, and I think this constant changing drained my battery. My house is near 3 towers and they are not all 4g, so it just kept changing. If your phone is doing that I'd really suggest switching on 3g for a whole day and see what happens for you. If it is still bad definitely go get a new one.