Chuck Wepner tried to do a lot with his fifteen minutes of fame.

The journeyman boxer stunned everyone by going fifteen rounds in a 1975 title fight against Muhammad Ali, even knocking him down at one point. His million-to-one shot helped inspire “Rocky,” which sanded off some of Wepner’s rougher edges as it punched its way to the top. Wepner struggled with his fictionalized alter-ego, embracing its Oscar success and befriending Sylvester Stallone before engaging in long-running litigation against the actor and writer.

In “Chuck,” an upcoming indie biopic, Wepner is casting off his Rocky Balboa alter-ego. The boxer is brought vividly to life by Liev Schreiber, who capturers the Jersey bruiser’s tender side and his dangerous attraction to the limelight. Schreiber got involved in the project because he felt that Wepner represented an important cautionary tale about celebrity, and that his life story was a way for him to process the greater notoriety he’d achieved as the star of Showtime’s hit drama “Ray Donovan.”

“Chuck” screened as part of the Tribeca Film Festival and opens on May 5. Schreiber, who boxes for fun in real life, spoke with Variety about what drew him to the project, what’s next for “Ray Donovan,” and how he almost appeared in “Logan.”

Why did you want to tell Chuck Wepner’s story?

After having a couple of kids and being on a television show and in everyone’s living room for a couple of years, it felt like kind of a cautionary tale about fame and celebrity. It was a trip down the rabbit hole of narcissism and identity, things that drive a lot of us who end up in the spotlight. He had a precipitous fall. The way he responded to it and the way he recovered from it was inspiring to me. It says a lot about his character as a person and a fighter — he was constantly moving forward, but there was an innocence to him. He kind of won me over. When I had kids, I felt very paranoid initially about fame and celebrity. It was something that had been on my mind a lot.

What do you fear about fame?

If we believe the essential lie that I think is at the heart of fame, which is that we’re the most interesting person in the room, it’s a fairly dangerous assumption. Everyone is drawn to that kind of anonymous adoration of the mob. We’d all love to have, but I don’t think many people get to experience it, so they don’t know what a double-edged sword it can be. When you have kids, you want to find ways to teach them to appreciate the world rather than have expectations of it. The problem with fame is that it really does set up impossible expectations for children

Why do you enjoy boxing?

I don’t box. I train-boxing. I’m trying to learn how to box. I spar, but I’d never compete. I’ve always had a terrible fear of being punched in the face, when I began training it was to get over that fear. I thought it would be therapeutic. I may have gone a bit far in playing Chuck Wepner, because there are very few people who have been punched in the face as much as Chuck Wepner. On top of that, I had this very amateurish idea that we need to have real contact in the boxing scenes. I felt like it was important for me as an actor to experience being hit.

Did you get hurt?

I never broke anything.

Did you talk to Sylvester Stallone before you did the film?

We had a couple of conversations both about Chuck and his own process in writing “Rocky” and where he was coming from. “Rocky” for him was a kind of metaphor for his experience as an artists and an actor and a writer. That fight was his fight as an artist. His relationship with Chuck has had different incarnations. He was somebody who tried to help Chuck and then was at odds with Chuck, but knew him very well and loved him and appreciated him and respected him. He had some great insight into Chuck’s tenacity.

Do you have a favorite boxing film?

“Rocky” is an incredible boxing film. “Raging Bull,” the first time I saw it, it blew my mind. There’s something about the intensity of those 15 rounds that are a kind of existentialist microcosm. There’s something so moving, so intense, and so dramatic. The trials and tribulations, you just imagine no one could ever survive them, yet they somehow do. It reminds us of our ability to withstand punishment and pressure and pain. There’s something celebratory about the human spirit at the end of a prize fight both in victory and defeat.

Critics have called you the greatest stage actor of your generation and the greatest American interpreter of Shakespeare. How do you respond to such intense praise? Is there a downside to it?

I remember a certain New York theater critic who shall remain nameless who said I had like a watermelon and was a somnambulistic actor, so I have to believe that I have a head like a watermelon if I also believe I am the greatest stage actor of my generation.

I’m lucky that stuff happened to me early enough in my career that I developed the kind of kevlar. Having those reviews and having things said about me and buying into them at an early enough age was important to have gone through before I was on a television show and saw what real notoriety was like. It was one thing to have the New York Times say something like that about a theater actor. It’s another thing to be recognized everywhere you go.

The film’s title changed from “The Bleeder” to “Chuck.” Did you have a preference between them?

I probably shouldn’t admit this, but I did like the title “The Bleeder” because I thought it really embodied that thing about Chuck and how far he willing to go for people’s attention and love. Having said that, I think folks felt it wasn’t a true boxing film. There were people who felt that we wanted to move away from that and find a different way to define the film.

You’re going into the fifth season of “Ray Donovan.” Do you have any idea of how much longer the show will go on?

I have no idea. I’ve been at odds with it for a long time. It’s a hard thing to do. The schedule is really, really difficult. Having said that, I’ve also accepted that this is my job and these people are my family. I’m lucky to have a job, and I’m lucky to have such a talented family. I guess as long as I can manage it, it’s a great job.

I’m grateful, but it’s hard. It’s six months of the year. There’s nothing quite like the one hour drama for attacking your schedule.

Are you still discovering things about Ray as the seasons progress?

Yes. Unfortunately they are just getting darker and darker and darker.

Did you watch “Logan” and was there ever any plans to have Sabertooth, the character you played in “X-Men Origins: Wolverine,” appear in the film?

There was an invitation early on from Hugh [Jackman] and [director James Mangold] and I would have loved to work on it. It was very difficult given “Ray Donovan’s” schedule, and I think they went a different direction as well with story.

I think it’s a terrific movie. I’m just very proud of Hugh and the way that he handled himself with that franchise and that character. It was a great experience to be involved with one of them and to get to work with them. I had mixed emotions when I heard that he was going to retire.