Brain Game: Balls Galore!

On his Web page at New Jersey's William Paterson University, author/editor/professor Stephen R. Shalom posted five Sports Stumpers that included the following trivia gem. As baseball rolls on (with the NFL season still in jeopardy) we offer it as the Think Thursday challenge here at the mentalfloss.com Brain Game. Good luck!

What are the most balls
(that is, pitches called by the umpire as balls)
that can be called in one scoreless half inning of baseball?

Here is the ANSWER.