Battery drains overnight with computer shut off

My MacBook Air drains the battery when Shut off (not sleeping) overnight. I am thinking of replacing the battery on a MacBook Air. Currently the battery lasts for about two hours with the machine unplugged. The battery will charge full from empty in about 3 hours. Have you ever seen a situation where replacing the battery fixes a drain problem? Or, is it more likely that there is a fault somewhere else, logic board etc.? Any tips for looking for drain faults?

Thanks