Baby-Daddy Material is mainly used towards "Pretty Boys" or in other words, "Very Attractive Men". A young man who has beautiful features as in: eyes, lips, hair, and skin. These are the type of men just to have beautiful babies with and nothing more.
"He is so fine! He has long flowing hair, green eyes, soft pink lips, and he's light-skinned! Oh yea, definitely baby-daddy material!"
It is said of the situation where a person has the bad luck to make contact with his testicles against an undefined surface or object, intentioned or not.
Given the nature of the word, it is more appropriate to design cases where the interaction is made with a moving object, for example, a ball.
Although it is extremely painful for the victim, it tends to be considerably funny to people who witness it.
Today in the baseball game the pitcher took a nutshot; the baseball hit him in the nuts.
Man, I just watched the funniest nutshot video ever.