Costner, an avid grid iron fan who's better known for his baseball movies, plays the general manager of the Cleveland Browns as he races the clock to acquire the No. 1 draft pick.
Reitman and his cast shot at the real draft last year, held over three days at Radio City Music Hall, and included a cameo with the man himself, NFL Commissioner Roger Goodell.
For her role as the Browns' salary "capologist," Garner told reporters in a ballroom of a midtown hotel taken over by the NFL for Sunday's game that she modeled her character on the team's legal affairs director, Megan Rogers. She took photos of Rogers' desk so she could recreate it down to the Post-Its.
"I have a great deal of respect for any woman who will enter the world of little boys, of sports," Garner said to laughs. "No offense, but I mean have you been out there? It's like little boy heaven."
Megan Rogers aside, the movie includes real players, including Arian Foster of the Houston Texans, wearing real jerseys on screen. The April release from Summit Entertainment took out a TV spot during this year's Super Bowl matchup between the Denver Broncos and the Seattle Seahawks to help cement its authenticity.
Reitman said he signed on after reading the script when it first surfaced as written by Scott Rothman and Rajiv Joseph, who was born and raised in Cleveland but initially focused the story on the Buffalo Bills.
"I read it in the middle of the night and I said, 'Oh my, this is really an amazing script, except it really can only be made if we get the National Football League involved,'" Reitman said. "It wasn't one of those movies where you sort of made up the names of the teams and the players and everything. It had to live in the real world and, you know, we sent the script to the NFL and the good news is they liked it as much as we all did."
There were Hollywood liberties taken, of course, including a toning down of recent boos from the crowd at the actual draft when the commissioner walks in.
Costner cautioned, "We're a movie, not a documentary," but he was drawn to the project's "level of grit" that, hopefully, will bring the game and the draft alive.
Most importantly, Reitman said, the movie is about the rookies, the potential draftees "who spent their entire lives trying to be football players, somehow dreaming that one day they're gonna get to play in the NFL, and most of them don't."
The "tension that's put on them, and the pressure and the emotionality of that moment is something that we can all understand," Reitman added.
Tracy Perlman, vice president of entertainment marketing for the NFL, helped oversee the league's participation, including use of its own film crews during the actual draft last year, on down to helping Reitman re-create such things as the credentials worn by officials.
And deals were done, from trademark agreements to production agreements, but she called the dollar worth "minimal" to the NFL.
"To us the value is in the outreach beyond the avid fan," she said. "We think we're going to touch a lot of people with this. There's a love story in the movie, there's the strategy of football, there's the everyman story of everything going wrong on the biggest day of your career."
For his part, portraying the Browns coach, Leary entertained the media crowd Friday with salty F-bombs and said: "I just wanted to be in a Costner movie. I just wanted to be in a sports movie with Costner."
Chadwick Boseman, who played Jackie Robinson in the baseball movie "42," portrays the sought-after football player this time around and Terry Crews, once an 11th-round draft pick, also appears as a Browns legend attempt to get his son drafted.
"The NFL got me ready for entertainment," Crews told reporters, "because sometimes you get knocked out cold and you gotta get back up."
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