I think I may have a fix for the OP and others who have this issue! Finally one solution to battery problems that I know works lol. My battery usually lasts between 12-15 hours with moderate use, but yesterday the battery drained in 9 hours with very little use (barely touched it, I was in my classes.) I think it has something to do with LTE connection, because my phone consistently overheated yesterday when looking for signal in my school building, which gets no signal whatsoever. It would overheat every half hour or so, and that battery would just draaaain. Today I did a soft reset on my phone and turned off background tasks, and my phone stayed cool all day! Battery saver didn't kick in until I was 17 hours into the charge. If you have background tasks constantly trying to update live tiles in an area with no connection, that battery suffers.
So my advice: Perform a soft reset, and turn off background tasks in areas with poor coverage. (I mean really, I'm sure you don't need the latest weather every thirty minutes.)