I had this happen to me when I first got my iPhone 4S...I had played Rage for a little while and hit the home button. I pulled my phone out of my pocket and it was really warm and it had drained about 30%...I went into the multitask tray and killed the Rage process and it cooled off and went back to normal battery use....so it seems some high CPU apps can persist in the background, even tho they aren't supposed to be able to.
I seriously doubt its calendar stats....I always have mine running and I get a lot of notifications....with the latest update I am getting incredible battery life!
I think (by default), the Location Services arrow is hidden.
On many devices with battery drain, a lot of times something is keeping location services active. If you don't see the arrow, you will have no idea why the battery is draining.