I watched my battery steadily degrade month to month as well even while rooted. Then I stumbled upon clean master, its just a simple cache cleaner but it seems to have improved my battery life. Having not run a cache cleaner in 5 months of getting phone I was able to free up almost 2gb of usable storage space as well. I dont know if this will help you but its free so why not? You can alway root later.
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I rooted anyway and noticed a difference after the first day. I can go a night without charging if needed now. Before, I'd be getting a battery alert. At least I don't have "charging anxiety" now, lol. Even processing (going from app to app to home) is more fluid and faster. I don't know why I waited so long to root this one.