You can try the "battery spin test" to see if your current battery is bad.
1. Shut down your phone normally.
2. Remove back and take out battery and place it flat on a table (or similar surface)
3. See if you can easily spin it (put your finger on a corner and give it a flick) like a top.
4. Healthy batteries won't spin due to the friction created by the flat sides. But "dying" batteries often "bow out" in the middle as they die which pushes the sides out and causes them to spin really easily. You'll know if it is spinning easily...they spin for a long time (I have two cheap dead ones). If you aren't sure, then youtube it. There are videos.
I also used GSAM battery monitor app and Better Battery stats to figure out which apps were eating up my battery. It helps. For my battery drain (and it seems to be different for everyone), it was a wakelock issue where the phone didn't go into deep sleep. I got a free app called Deep Sleep Battery saver, and it has made a night and day difference. It just about tripled my battery life. But it shuts down all my apps when my phone turns off. For my issue, that was what I needed. Something kept activating in the background, and I couldn't pin it down.
K--