Battery saving tip
When I'm not going to use my tablet for a while, e.g. a few hours or when I sleep, I do a clear-all recent apps. That has worked well. For example, last night before bed, my gpad was fully charged, I long-pressed the home button to bring up recent apps, did a clear-all, turned off the screen and went to bed. I woke up this morning and found the battery at 98%. I streamed some news for 5-7 mins or so. Before I left the house around 6:40am, I did a clear-all again and shut the screen. I came back around 5:50pm. The battery was at 96%. I hope this helps your battery during idle too.
PS: every so often I do a reboot esp when I feel battery is draining peculiarly fast. I do that with my Note 3 every few days also.