I've broken two phones in my life; both of them had on robust cases. The first time, I knocked my phone off of my desk at work. It fell three feet to the carpet and shattered the screen. The second time, I missed my pocket and dropped the phone 2-3 feet. Completely shattered the back glass and sent a hairline crack through the screen.
I've dropped my phones so many other times, in much worse ways (sometimes with no case), yet in these two instances they break. I'm almost at the point of not using cases, but I know my anecdotal experiences don't reflect reality.