I thought of a new battery saving tip today. I have a new action in Llama that says "If I'm at work and I turn the screen on, turn on 4G", plus the opposite when I turn it off. I don't need it to use data when it's off, because I have a computer for that. I'll probably add another rule "when I'm at home, between 6am and 10pm, turn WiFi on when I turn the phone on". You need secure settings and root.
Things like this mean my 3 ish year old S4 with the original battery only uses 20 - 40% of the battery each day, even with a bit of email checking, a few calls, Facebook, notes, etc. I'm not a heavy user though.
Note that Llama does location based on the cell tower you're near, not GPS, so it uses essentially no battery.