I think one of the apps that I have used that did indeed help save battery was greenify. For this app you will need root, but let me explain how it works. There are some apps that run in the background on most devices, some people will tell you they eat up memory but thats not even a big deal as we all know in android using more memory is actually a good thing. However, these apps wake up and use a little battery to update and other things. When you use greenify it keeps those apps from running in the background for example when your screen is off and you're not even using the device. The result is getting less battery usage because there are less wakeups. Hope that helps a little.