This can be used to define times when a guy does something that requires a great deal of nerve and skill, but he is truly lacking in skill and ends up hurt, humiliated, and/or dead. Alcohol is considered the main accelerant to this condition.
Roz looked down from the 58 foot cliff that overlooked the shallow, rock-filled lagoon. While diving to his imminent death, he knew that his balls were bigger than his brain.
Bobby “Why is that guy riding a motorcycle with no helmet at 130 mile per hour (209 Kilometers per hour)?”
Brandon “That’s because he has a bad case of Balls No Brains”
Example with huge balls
Bobby “damn! That guy just punched one of the robbers in the face, too bad he’s about to get shot.”
Brandon “That guys got a serious Balls No Brains way of thinking.”