“My All American” is an earnest, ultimately heart-tugging sports drama: nothing fancy and nothing many moviegoers won’t see coming from a football field away. That’s especially true if they’re familiar with the true story the film is based upon.

In 1969, University of Texas Longhorns star safety Freddie Steinmark helped his team reach the Cotton Bowl, where the Longhorns defeated Notre Dame. Tragically, Steinmark didn’t join his teammates that day in the game he’d worked so hard and long to bring them to.

“My All American” is mostly about what happens in the years before the Cotton Bowl game, including Steinmark’s college football years at UT in Austin. The film introduces him as a determined kid who grew up playing football under the encouraging guidance of his father.

Finn Wittrock (“American Horror Story”) plays Steinmark, the optimistic, devoutly Catholic young man who dreams of winning a football scholarship to Notre Dame. But Steinmark has a big disadvantage, in college as well as pro football. He’s a little guy.

Despite his size, Steinmark is a great competitor and teammate for his Wheat Ridge High School football team in suburban Denver. And he works constantly with his dad (Michael Reilly Burke), engaging in grueling training sessions off the school grounds.

Writer-director Angelo Pizzo (“Hoosiers,” “Rudy”) based “My All American” on the book “Courage Beyond the Game: The Freddie Steinmark Story.” The film scores underdog points by exploiting Steinmark’s unlikely entry into college football. The whole family, including Steinmark’s mom, Gloria (Robin Tunney), experiences suspense and disappointment around the telephone on the wall in the family kitchen.

The family’s hopes rise when University of Texas coach Darrell Royal requests a campus visit by Steinmark and his fellow Wheat Ridge High teammate Bobby Mitchell (Rett Terrell).

Aaron Eckhart, the biggest name in the “My All American” cast, co-stars as Coach Royal. The aged Eckhart who’s first on screen is disconcerting, but once the film returns to the late 1960s, Eckhart comfortably assumes the role of a driven but caring coach who’s genuinely fond of Steinmark. Eckhart and Wittrock, as player and mentor, strike up a credible on-screen connection.

“My All American” features lots of football action, cheering crowds and painfully clichéd announcer scenes. Shot entirely in Texas, the film gets an authentic look through locations such as the UT campus in Austin, the Alamodome in San Antonio and The Cotton Bowl in Dallas.

The script plays like a by-the-book underdog sports story until Steinmark begins experiencing pain in his left thighbone. Fiercely devoted to the game as he is, he doesn’t quit or complain. What comes next takes “My All American” in a poignant direction, the impact of which is aided by Eckhart’s and Wittrock’s thoroughly professional performances. But other than the moving conclusion, this is a largely mediocre drama.