I hate hate HATE articles like this one. The author--and readers--are searching for some magic point where a statistic (in this case, BABIP) suddenly gains credibility. One might as well ask how many dates you have to go on before your girlfriend spontaneously switches from 'gold-digging whore' to 'future Mrs. Sabermetrician'.
In a way, I feel the linked post is the best of its kind, because rather than pretending to be scientific, it admits (albeit in the last paragraph) that it has been a waste of the reader's time:
"This isn't a very functionally useful finding for evaluating players or predicting what they will do."
Translation: forget everything you just read, you'll never use it. Pizza Cutter should pitch a new book idea to Michael Lewis: "Chaosball: The Art of Not Predicting a Random Walk".