In 1971, the Boston College football team won nine games. It went undefeated at home with a perfect 5-0 record and ended the year by beating five consecutive opponents by a 106-42 aggregate score. In the last two games of the season, the Eagles crushed local opponents by a combined 56-7 advantage.
Joe Yukica's Eagles had a better overall record than Houston and Arkansas and finished better than Notre Dame and LSU. Yet all of those schools finished the season ranked, and all four of those teams earned bowl invitations except for the Fighting Irish, who announced prior to the final game of the season (against LSU) that they would not accept a postseason game.