Spotting Cause of Excessive Battery Drain
GSam Battery Monitor is an excellent program that will give you an extremely detailed report of what is using your battery and to what extent. 
However, what I believe this may be is the Mobile Radio Active bug. It is one of the most starred Android bugs in existence. Essentially, when apps that use data are turned on (such as Facebook or Skype), the Android system forgets to turn off the radio until the app that asked for the radio in the first place is force stopped. Google has acclaimed that the issue is fixed in Android M, but I do not believe they have plans to fix it for Lollipop. (I am looking for a source of proof and will edit this when I find it)
In the meantime, Greenify will automate the process of force stopping apps when you don't need them, however, you may stop receiving notifications from these apps.