first off, the conscencous on S4 battery life has been generally been very good, personally 15-17 hrs/day with 30%+ reserve on fairly heavy use is the norm for me and seems to be pretty typical results on these forums! While there is always those few that have problems with battery life on the S4, this is typical of any device since battery life is SO dependent on usage, signal strength, 3rd party apps and sinc/update habits!
Normally, your early battery life is going to be relatively poor due to battery conditioning and the initial heavy usage from setting up the phone and all the apps that you load initially...after a few charge cycles this tends to improve dramatically as the phone/battery "settles".
In my personal experience, one other result of this may be several 3rd party apps, OEM apps, and carrier installed apps all trying to sinc/update in the backround and while your phone is in standby, effectively killing your battery without you even knowing it!
I stumbled into this early on with my S3 last time around when my data usage was going through the roof! After a little digging I found several apps powering up in the backround to update/sinc on the net, a carrier loaded wifi app was a huge offender constantly polling for wifi networks!
After freezing the unneeded/unused apps, I put all the remaining apps on a diet/schedule and actually update some manually. This resulted in cutting the data usage by more then 50% and dramatically increasing the battery life!
Now this is a normal part of the setup process of all of my new devices!
It sounds like this may be at least part of your issue and may be worth a little time to explore!
Cheers