Image Kenny Bell Credit... Matthew Ryan Williams for The New York Times

“Video games were for a long time the cart, but now they are becoming the horse,” said Carl Goodman, the executive director of the Museum of the Moving Image in Queens, which has assembled an exhibition on the history of Madden NFL. “It’s a double-edged sword, because the experience at home is so good, it’s another reason not to go to the stadium.”

Madden’s hyper-realism is partly a result of increasingly sophisticated game consoles and software. But the game is also inextricably entwined with the league. Madden NFL is known informally as “the 33rd franchise,” because its developers are sent the same game footage that the coaches on all 32 teams receive every week during the season.

“Especially the last 10 years, EA has been among our best partners, not just in total dollars, but in the fans they bring in and the fans they retain,” said Tim Langley, the director of consumer products at the N.F.L. “It’s very important to us, because we anecdotally see time and time again people who said they didn’t really follow the N.F.L. ‘but then I started to play Madden.’ ”

While EA Sports has an exclusive license to use names, plays and other elements of the league, the N.F.L. has editorial oversight. Mr. Langley and others vet thousands of pages of recorded scripts and delete inappropriate dialogue, like the harshest trash talk. Chop blocks, helmet-to-helmet hits and other illegal plays are not permitted in the video game — even with accompanying penalties — despite the other efforts at realism. This stems not only from the league’s fastidiousness about its image but also from Mr. Madden’s insistence that the game be exciting and educational. He still helps developers at EA Sports identify trends to add to the game.