MLB Hall of Famers Ernie Banks, Bob Feller, Harmon Killebrew, and Duke Snider make cameo appearances in this film.
After losing a game, Roy Dean is released by the Steamers. He goes to the stadium and starts throwing balls at the backstop until he collapses dead of a heart attack. During the game following Roy Dean's funeral, Tyrone punches out Randy, who is immediately released by the team. Years later, Tyrone is a member of the Chicago White Sox, and he uses Roy Dean's best pitch to get batters out.
Set in California in 1957, Roy Dean Bream (William Russ) is a minor league baseball player who is near the end of his career. His team, the Tri-City Steamers, are perpetually at the bottom of the standings, and they are always losing money, according to their owner Peter LaPorte (Jeffrey Tambor). He believes that cutting the highly-paid Roy Dean will help ease their financial burden, but Steamers manager Clyde Bigby (Noble Willingham) refuses to do so. Clyde says that Roy Dean has more heart in him than the rest of the team combined, but Peter only cares about the amount of money the team can earn him.
At the start of the season, the Steamers are joined by their first African-American player, Tyrone Debray (Glenn Plummer). His new teammates don't care much for Tyrone, especially star pitcher Randy Keever (Scott Plank), who is outright hostile towards him. But Roy Dean takes a shine to Tyrone and decides to take him under his wing and show him how to be a pro. Since both of them are pitchers, Roy Dean shows Tyrone some of the things he's learned over the years, including how to throw his best pitch, the "Bream Dream". As the season goes on, Roy Dean and Tyrone are spending all their time together, and that bothers Randy. He goes to Clyde and tells him that the team has a problem with Roy Dean and Tyrone, but Clyde just tells him not to worry about it.
During a road game, a Steamers batter gets deliberately hit by a pitch. Clyde orders Tyrone, who's pitching that night, to hit the first batter he faces. He reluctantly does so, which sets off a bench-clearing brawl. Tyrone is getting beat up by the batter he hit, but Roy Dean comes up and punches out the batter, then tells Tyrone that pitchers stand up for each other. In that same game, Roy Dean loses the game by throwing a wild pitch, allowing the winning run to score. Afterwards, Randy overhears Peter ordering Clyde to release Roy Dean. On the bus ride home, Clyde doesn't tell him that he's done, but he does tell Roy Dean that he should start seriously thinking about life after baseball.
The next night, Peter is throwing a party for the team, and Roy Dean invites Inez Brice (Deirdre O'Connell), the barmaid from his favorite hangout, to join him and Tyrone. At the party, Inez overhears the other players' girlfriends talking about her, and Randy pulls aside Roy Dean to say he'll be missed. Suddenly feeling uncomfortable, they leave the party, but Peter pulls aside Roy Dean and tells him his days as a Steamer are over. Roy Dean drops off Inez and Tyrone at her house and goes for a drive into the desert, where he cries his eyes out. Inez later tells Tyrone that she likes Roy Dean and she wants to see him again. Roy Dean eventually drives out of the desert and goes to Tri-City Stadium, where he goes to get his Steamers uniform. Instead of leaving, he puts on the uniform, grabs a bag of balls, goes to the mound and starts throwing at the backstop, reliving his career in his mind. As Tyrone is walking home, he sees the lights on at the stadium, and Roy Dean's car in the parking lot. He goes in and sees Roy Dean collapsed on the mound. Tyrone runs over to check on his friend, but he is dead of a heart attack. The next day, Tyrone is clearing out Roy Dean's apartment when he finds a prescription bottle. It's for Roy Dean's high blood pressure, something he never told anyone about.
Clyde, Tyrone, and Inez attend Roy Dean's funeral, and they are the only ones there due to the Steamers having a game at that time (Peter is managing the game). Upon arriving at the stadium, Clyde sees that Randy started the game but is pitching badly. Clyde immediately replaces him with Tyrone, and Randy is furious. He tells Tyrone sarcastically to win one for Roy Dean, and Tyrone responds by punching out Randy. Clyde then tells Randy that he is being released by the team, and to clear out his locker right now. On the mound, Tyrone uses the "Bream Dream" to get the first batter out. The movie ends years later, with Tyrone pitching for the Chicago White Sox, and he again uses the "Bream Dream" to get a batter out.