Henry Wiggen, the smooth-talking pitcher of the New York Mammoth baseball team, rooms with catcher Bruce Pearson, a dim-witted and uncouth country boy who chews tobacco and wears a greasy pompadour. Although initially disdainful of Bruce because he is an average player, Henry softens when Bruce confides that he is dying of Hodgkin's disease, a blood cancer, and wants to keep his illness a secret, at least for the season. Before spring training, Henry accompanies Bruce to the Mayo Clinic in Minnesota, then on to visit Bruce’s parents in Georgia, where Henry’s wife Holly joins them. When they return to the hotel in which the team is lodged, manager Dutch Schnell, concerned that Henry is showing unexplained interest in Bruce, demands to know the details of their trip together, but Henry easily outwits Butch. Before the season begins, Henry, having heard a rumor that Bruce is being fired, surprises Butch and the team’s two owners when he accepts a lower contract figure on the condition that Bruce be allowed to play on the team for the entire season. Dutch accepts Henry’s terms but questions his motive, sarcastically suggesting that the two are lovers. Back in the hotel room, Henry, who sells the players life insurance and runs a card racket, suggests that Bruce fake confidence in order to bluff the other team. When Henry tells Bruce that he will remain on the team for the season, Bruce’s childlike glee fills Henry with satisfaction. Meanwhile, call girl Katie, knowing of Bruce’s prognosis, agrees to Bruce’s naïve marriage proposal on the condition that she be named as his life insurance beneficiary. When Bruce begs him to change the policy, Henry stalls by claiming that his office demands more paperwork. As the season opens, the Mammoths appear to have the skill needed to win the pennant, but divisiveness among the players holds them back. The team members aim their derision at the gullible Bruce, mocking his clothes, manners and playing. Unable to understand Henry's sudden concern for Bruce, Dutch continues to question Henry. When Henry claims their trip to Minnesota was for hunting, Bruce merely nods in agreement, but soon Henry is forced to spin more elaborate tales in order to keep Bruce’s secret. Meanwhile, Bruce, who is usually poor at bat, plays consistently better, making several base hits. In an effort to cheer Bruce, Henry invites him to play T.E.G.W.A.R., his card racket, with unsuspecting fans in the hotel lobby. Team coach Joe Jaros, who runs the game with Henry, refuses to play with Bruce, complaining that his slow wit will ruin the racket. During a pre-game pep talk, Dutch delivers a rousing speech, saying that they will be unable to catch the opposing team, which he refers to as flies, unless all their fingers are working in unison to squash the little fly. Dutch states that they are too busy insulting each other to be capable of beating their opponents, but his warnings goes unheeded. Henry then approaches player Goose, who is the most antagonistic toward Bruce, and offers to help him financially if he will stop harassing Bruce. To win over Goose, Henry reveals Bruce’s condition. While Bruce continues to improve on the field, the pressure of keeping the secret hampers Henry, who threatens to expose Katie’s call girl service to stop her scheme to marry Bruce. After being pulled from an August game, Henry flies into a rage in the locker room, smashing every object he can find out of frustration and sadness. Days later, hotel operator Tootsie unknowingly reveals to Henry that Butch and the owners have discovered Bruce's illness. Going straight to Butch’s office, he watches helplessly as Butch calls in catcher Piney Woods to replace Bruce if he should die mid-season and ex-star catcher Red Traphagan, to coach. In the locker room during a rainout, Piney sings “Bang the Drum Slowly,” a lament about a cowboy’s death, while the players look at Bruce, now aware of his illness. The team rallies around Bruce that night, joining him in his room for a night of drunken celebration, during which Joe invites Bruce to join their T.E.G.W.A.R scam. Only Katie has no sympathy for the dying man and hangs up on him when she finds he has not changed his insurance policy. Having put petty squabbles aside, the team pulls ahead. On the last game of the season, Henry, seeing Bruce’s waning strength, warns the coach and others. After Bruce fails to see the direction of a pop fly, a baseman runs in to catch it, a play that wins the game. When Bruce stares on blankly, oblivious to the team rejoicing the win that places them in the pennant series, Joe and Henry pick up his hat and glove and escort him off the field. Shortly after, Red, Joe and Henry bring Bruce his tobacco and belongings at the hospital, where Bruce is checking out. When Henry takes Bruce to the airport to return home to Georgia, Bruce vows to be back in the spring, but they both know they will not see each other again. As Bruce boards the plane, he asks Henry for the series scorecard. That winter, Henry is the only team player to attend Bruce’s funeral. Learning humility through Bruce’s death, Henry vows that he “rags nobody” from now on.