Intermediate School 318, a public middle school in Brooklyn, has an unusual distinction. Not only does it have a chess team, but the team dominates national competitions the way UCLA used to dominate college basketball. It’s won 26 national chess titles. “In 318,” the school’s principal proudly says in “Brooklyn Castle,” “the geeks, they are the athletes.”

Katie Dellamaggiore’s lively and affecting documentary introduces us to a cast of characters that’s very winning (in both senses of the word). John Galvin, the assistant principal, has a Noo Yawk accent and savvy demeanor that’s part monsignor, part cop on the beat. Elizabeth Vicary, the coach, has the slightly otherworldly intensity (and underfed physique) of Patti Smith. “The total brains of the operation,” Galvin calls her. Vicary is as much an avatar of chess as Smith is of rock ’n’ roll. The biggest complaint about “Brooklyn Castle” is that there’s not enough of her. A presence as magnetic as Vicary’s demands more screen time. How did she come to chess (a notoriously male-dominated game)? How did she come to 318?