Contrary to the previous definition, this is and has been widely used throughout the United States military to describe the 0000-0400 watch and is. It unique to any maritime academies. It is a widely used term.
I had the balls to 4 watch last night, I'm really tired.
Midnight (0000 in Military time) to 4 watch. The first watch of the day's rotation. NOT unique to any maritime academy. In fact, it is a pretty common term in most branches of the military. I've also heard it called the Balls to Forever watch.
I'm going to go hit the rack early. I've got to get up for the Balls to 4 watch.