The "Kukoc Cup" is the middle of the three cups in a power I or straight line in a game of beer pong. Toni Kukoc was an NBA basketball player who, although tall, had a good long range shot. Unfortunately they were mostly in meaningless situations. The middle of the three cups is statistically the worst cup to make because it separates the remaining two cups. Thus this meaningless cup was deemed the Kukoc cup.
Brandon - "Maybe you'll hit a cup besides the Kukoc cup."
DJ - "Probably not."