What you're describing doesn't sound normal. If you have Fast Boot enabled the phone isn't really shutdown it is merely hibernating. That is why it boots so quickly. Even in hibernation it may be using some small amount of power but it should not be enough to drain the battery overnight. If you do indeed have Fast Boot turned on, try disabling it and then shutdown overnight to see if it is still draining. If it is not drained there may be a phone problem. If it is drained you probably have a bad battery that wont hold a charge. If you were to charge the battery and then remove it from the phone and let it sit for 8 hours and it drains you can be sure that it's the battery. I had that problem with an after market battery before.