How do I know when a cell phone battery is bad?

I just got the new Droid phone, sorry I’m really not trying to brag. Anyways, I just got it and I expected it to have a shorter battery life than my old phone because of the screen obviously and the other functions it can do. But I had it plugged in all night and used it from 9am until about 1pm and thats when I shut it off because the battery was down to like 15%. So 2 things I am thinking. Either I am a noob and left a bunch of apps running while I was just sitting in class and it drained the battery really fast. Or the battery is a dud. The only thing that made me think the battery is a dud is that it heated up really bad the last couple hours and that made me think maybe it was the battery. But I really don’t know. So what do you guys think?