For the record my screen is on quite a bit as I read Flipboard a lot, MR, YouTube and do quite a bit of google searching and use it to control my Apple TV. I also use SBP Mobile to touch up artwork between my ipad, iPhone and Mac mini. Either way I still think if you can't get 8-9 hours of normal use and be at 10-20% there is something wrong! wether it be the the actual hardware or some kind of software drain somewhere.
Also there are other things I do to preserve battery, alerts don't repeat, screen @ 30-40%, no push or fetch accept on things I need. app refresh only ones I use. notifications only on things I need/use. This works for me as I check my phone regularly and don't need to see everything that everyone is doing on FB , twitter etc...
I full charge my battery, and full drain it and use battery doctor for full cycle at he end off every month (app reminder).
Maybe I'm just lucky, my Touch ID works 99.9% of the time! my ipad air has a perfect screen and I'm getting upwards of 12 hours use out of it even with some gaming, the mini retina I bought had a perfect screen and good battery life, and safari doesn't crash on me.
I'd try some reboots, restores and if that doesn't work I'd go see a genius. My ip4s was struggling to get 8 hours and would get warm/hot, I took it in showed how the battery was dropping pretty quick and received a replacement. After that I was getting 8-10 hours easy with same settings off restore. I did have to remove FB and reinstall it, it was doing something to the phone idk.
I don't want you to be jealous I want to help you solve the problem. Part of that is me sharing my experience and results, and giving suggestions. I'd go see about a new phone or replacement.