In New York City, elderly Father Burke is informed that church authorities will close St. Anthony's college, where he studied as a young man and is now the rector. Determined to keep the college open by raising money, Burke offers former bigtime coach Steve Williams a job building up the school football team into a winning program. However, Steve, who has fallen into disfavor with his colleagues and now keeps solvent as a bookie in a billiard hall, is uninterested until probation officer Alice Singleton shows up, investigating complaints by his former wife, Anne McCormick, that Steve has been neglecting their young daughter Carol, who lives with him. Steve's cheeky response irks Alice, who admits that Anne wants sole custody of Carol. Steve is later approached by Anne, and her behavior convinces to him that she is using Carol as a means of revenge. After accepting Burke's offer, Steve takes up residence with the tomboyish Carol in rooms under the campus belfry and resigns himself to St. Anthony's decrepit sports facilities. Later, when Alice announces that she has awarded Anne visitation rights, Steve remembers how, five years earlier, he found Anne romancing wealthy Harold McCormick, while Carol slept in a room upstairs. Meanwhile, Burke naïvely schedules the team to play the following fall against several big schools. Convinced by Carol not to give up and quit, the overwhelmed Steve works quickly, and after convincing two former gridiron assistants to join him, entices good players with dubious academic credentials to enroll at St. Anthony's and reap the rewards of a "cooperative football team." Steve acquires good equipment from a sports store manager, who takes kickbacks and rents a polo field by threatening the manager with bad publicity. To get around League rules, the players sign up for summer school and begin training. On the day of the first game, Alice takes Carol to visit Anne, who is now married to Harold, and they walk into a children's party in progress. While Carol unhappily tries to fit in, the McCormicks secretly agree that dealing with children is distasteful. Finally, Alice rescues Carol from the taunts of the other children, and together they attend the football game, where Alice proves to be surprisingly conversant in the sport. After the party, the McCormicks listen to the end of the game on the radio, and hear St. Anthony's victory. Later, although the game makes a $31,000 profit for St. Anthony's, Burke cancels the remainder of the team's schedule and prepares to close the school. After looking over the football players' records, Burke accuses Steve of dividing profits among team members, forging records and, referring to an older Canadian student, buying semi-professional players. Unashamed, Steve argues that the student in question had been drafted to fight in Korea, and thanks to St. Anthony's, finally has an opportunity for a college education. Later, Steve drunkenly confronts Alice, accusing her of tipping off Burke, then after suggesting she find a man, kisses her. Alice denies talking to Burke and angrily tells him that she, too, was reared as a tomboy without a mother, and hopes to keep Carol from becoming a misfit like she was. Feeling defeated and knowing that Anne does not really want Carol, Steve goes to the McCormicks' to compromise and offers to send her away to school. However, Anne wants to humiliate Steve by having Carol witness the hearing. After Harold admits that they tipped off Burke and that he is not fond of Carol, Steve slugs him and the police are called. Later at the hearing, where Steve's many mistakes are being aired, Alice refutes her previously written report citing Steve's "degrading influence" on Carol, as she has come to realize that Anne is using Carol against Steve. However, when Anne's attorney gets Alice to admit her love for Steve, the judge reassigns the case and makes Carol a ward of the court. Back at the college, Carol reminds Burke that Steve only did what was asked of him. Later, after learning that his superiors have decided to keep the school running, Burke announces at chapel that St. Anthony's will continue its tradition of providing financial aid, but that he is resigning as rector. Burke explains that he asked a man to do the impossible and when the man accomplished it in the only way he knew how, both St. Anthony's and the man almost lost what each valued. Later, Burke informs Steve that the football team will return to its former, lusterless state, but that Steve will remain as coach. He refers the surprised Steve to the fine print in his contract, written in Latin, which gives the school power to retain him. When Alice then arrives to take Carol away, pending the court's final decision, Carol and Steve signal to each other that Alice will make a good mother for Carol, and the three look forward to a happy future together.