I'm not going to say it's flat-out impossible for an app to drain your battery that fast in the background, but it's not far off. If you want to be really sure, though, enable Battery Saver mode immediately after unplugging the phone (at full charge) and don't use it. Battery Saver prevents all background app activity, so there won't be any apps running and therefore they *cannot* be affecting the battery.
I'm pretty sure that, given the rate of drain and the fact that it persisted through a hard reset, you have a hardware problem. The good news is that it might just be a bad battery - that is a thing which happens, and it's even fairly common on batteries a couple years old - in which case it's a good thing you have a phone with a user-replaceable battery! The way I'd test that is to swap your battery into somebody else's ATIV S and see if the problem persists. If so, it's the battery; if not, it's your phone. Alternatively, you could just buy a second battery and see if that helps.
One other thing to check: if the battery really is still working and the phone is draining it that fast, it'll be dissipating a lot of energy as heat. Does the phone stay abnormally warm while the battery drains like that? That would be a sign of a problem with the phone or the OS, as opposed to the battery itself.
Oh, and I'm pretty sure there are some battery diagnostics and charging statistics located in the Diagnosis app (##634# in the dialer). I forget the code for them but I have all of the codes written somewhere; alternatively, you could do some searching. You could compare the reported battery capacity there with the expected (design) capacity.
Win8/Windows RT projects:
List of desktop apps for hacked RT devices
Native Access WebServer and Libraries
WP8 Interop Unlocks
Storage Cleanup tool
XapHandler, Root Webserver, OEM Marketplace XAPs, Bookmarklets collection (Find On Page), Interop-unlock hacks.
Do not private message me with questions that should have been posted on the forum!
Not only are you wasting your time - I'm not going to bother writing an answer to such a question for only one person - but I will probably block you from PMing me in the future as well.