While the *usual* tips about tweaking settings and such can help maximize battery life, losing 10%/hour when idle isn't normal even all that stuff is turned on...so let's start there.
It seems obvious that the OP may have already made up his/her mind, but just in case others find this thread when searching for their own issues, here's my advice...
9 times out of 10, excessive battery drain like this is caused by 1 of 3 things:
1. Poor signal. Not a lot that can be done about this, but if your phone is in a place where there is little to no cellular reception (and no wifi to connect to), the battery is gonna drain. fast. Of course, this will be a problem regardless of whether we're talking about an S4 or an iPhone or [insert any other device here], at least if they are all on the same carrier. Sure, some devices have better radios than others, and therefore you may have better luck with one device over another in some places, but if there's no signal, there's no signal. This is usually pretty easy to rule out as an issue, so if a person is on the forums trying to resolve their issue, it's more likely to be...
2. An app (or apps) that is consuming more resources than it should. Generally, if you've had your phone for a while and the excessive battery drain only started recently, the first culprits should be any apps you've recently installed. If it's a problem that has always been there, it can be harder to weed out which apps may be causing a problem, and that's where checking battery stats may help. Also, if you've installed any kind of "task killer" apps, try uninstalling those -- while there are some good ones out there (like Greenify), many of these apps are actually counterproductive because the processes they kill take more power to start up again, which the system will attempt to do automatically.
3. An OTA software update. I won't go on about how much I dislike the current delivery method for system updates, and how easily it could be improved (that's a different subject), but the fact is that many phones take a performance hit after doing an update and/or start to have worse battery life. (This is actually true on both the Android and iOS platforms). On Android, if you think this is the problem, the best thing to do is to perform a factory reset. A tradional factory reset will NOT uninstall any updates, but it will wipe ALL internal data, so you will want to do a back up first. Yes, this process can be a major PITA, but in almost all cases of post-updated related issues, this will get things running right again.
The other 1 out of 10 times? Probably a hardware issue, such as a bad battery. If possible, you may want to try swapping batteries with another S4 to rule this out, but if that's not available, it's usually easier to rule out the software first.
Honestly, I've had my S4 since launch, and I have GPS and BT turned on all the time, several apps that sync regularly, keep my screen brightness fairly high, and in general simply don't believe in crippling my device and sacrificing features I use just to gain a bit more life from my battery...and on normal days my phone EASILY makes it all day on a single charge, if not more. I do try to research the apps I install, and if I find one that drains more power than I like (and/or more than I'm willing to live with to keep using the app), I remove it. I do use Snapdragon battery Guru, and I'm rooted so I also have Greenify setup, and those do help a bit, but you really should still be able to get decent battery performance even without those.
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