Falcons trivia: Name the season the team scored exactly as many points as it allowed

As we wind down our trivia series for the summer, I thought I’d ask about one of the most unique seasons in team history. You see, exactly once in their history, the Falcons managed to score exactly as many points as they allowed in a single season, and in typically quirky Atlanta fashion couldn’t quite manage a .500 season out of that balance.

It’s sort of remarkable and certainly rare that the team managed to do this. They’ve had plenty of .500 seasons and close calls—under Norm Van Brocklin, they allowed three more points than they scored and five more points than they scored in consecutive years—but only once have they managed an even ledger. What year was it?