The ritual is the same every Saturday before the Marine Corps Marathon. First, the runners and their families, a group numbering about 50, shuffle into a conference room. They mingle, pick up their long-sleeve T-shirts, munch on cold-cut sandwiches and cookies, and wait for the video projection machine to play.

There, in grainy black-and-white celluloid, they see the young Marine, the first lieutenant in his “U.S.A.” tank top, taking the lead on the gun lap of the 10,000-meter Olympic final in Tokyo.

They let out a small gasp when he is bumped, nudged to the outside by the world-record holder from Australia. They groan when he drops to third and then fourth behind the Tunisian, just as the runners are about to round the backstretch.

And at that jarring moment when Billy Mills re-enters the camera frame, now high-stepping the last 100 or so meters as he sprints past the Olympic favorites and the defending champion — never having won a major race before, his time in the preliminaries almost a minute slower than the favorite — the room thunderously applauds, as if everyone were watching a live sporting event.

During the replay, they laugh at the sound of the stunned NBC analyst Dick Bank, shouting, “Look at Mills! Look at Mills! Oh my God!” — now a YouTube favorite. And they applaud again at the final image, of the only American to ever win Olympic gold in the event, who puts his hands on his head in utter disbelief over what he has done.

They clap again, in 2011 — for the man in the footage from 1964.

Serene, regal, a full head of brownish hair to help him pass for barely 50, he walks to the front of the room. Billy Mills, 73 and three Octobers away from the 50th anniversary of his victory, tells them who they are running for Sunday and why.

“Who did you beat?” someone says.

You want to raise your hand, blurt out “Ron Clarke and Mohammed Gammoudi.” But Billy’s answer is always better.

“Who did I beat?” he replies. “I beat the demons within me.”

Even the people in the room who have heard his story for seven years now — since 2004, when Mills’s Running Strong for American Indian Youth charity began using the Marine Corps Marathon as its major annual fundraiser — become quiet, instantly enraptured.

“The greatest challenge we face is perception,” he says.

When his mother had died of tuberculosis and diabetes at the age of 43 on the Pine Ridge Indian Reservation in South Dakota, the perception was of sadness, self-pity and anger. He was just a boy of 9 — his entire identity formed by the Oglala Lakota Sioux on the Res.

That’s when his father said, “Son, you have broken wings.” He proceeded to draw a circle around Billy in the Pine Ridge dirt. “He told me to step inside and close my eyes.”

“He said, ‘If you follow what I share with you now, some day you may have wings of an eagle. Look inside your heart, mind body and spirit. You will see anger and hate, the emotions that will destroy you.

“He told me to look deeper where the dreams lie. And he said, ‘Find your dream, son. It’s the pursuit of the dream that’ll heal you.’ ”

Orphaned at 12, Billy seized that mantra until his junior year at Kansas, where, he admits, “perceptions finally broke me.”

Named all-American three times, he said three different photographers told him the same thing each year. “You, the dark-skinned guy. We want you out of the photo.” Or, “You, the Indian guy, we’re going to take one without you in the photo and one with you in it.”

When it happened again at a cross-country meet, he went back to his hotel room and got on a chair, near the window. “I told myself, ‘Just let go. Just let go. It will be all over.’ ”

The audience in the room, this year inside the Chastleton at 16th and R Streets in Northwest Washington instead of at the charity’s headquarters in Alexandria, holds it breath.

Billy says at the moment he was about to jump and commit suicide he heard the word, “Don’t,” several times. “I didn’t hear it through my ears; I heard it through my skin. I thought it was my dad’s voice. I thought it was the Creator sending me my father’s voice.”

He got down from the chair and, now inspired, wrote down on a piece of paper for the first time, “Gold Medal, 10,000 meter-run. BELIEVE. BELIEVE. BELIEVE.”

Rounding the final turn that wet, muddy day in October 1964, he says, a West German runner he was about to lap moved aside when he looked at the figure on his singlet. “The eagle, their national emblem. I can see it out of the corner of my eye. And I get a flashback to my father’s words — ‘Some day, you’ll have wings of an eagle.’ I knew I could win at that moment.”

“I saw him after the race and looked at his singlet again — there was no eagle,” Billy says. “I think there was one on his warmup sweats, but not on the singlet. Where did I see that eagle? A perception, one that didn’t destroy me but created that moment.”

The listeners applaud again.

Peggy Wellknown Buffalo, whose Center Pole foundation on the Crow Indian Reservation in Montana is directly helped by Billy’s generosity, blesses the gathering with eagle feathers, cedar and buffalo hair. A song of prayer is sung by Stephen Hill, whose son Nicholas Gibbs-Hill is running the Marine Corps 10K on Sunday. And Billy, who flies in from Sacramento for the pre-race celebration and honoring every year, later signs shirts and speaks with the people who run for his charity.

Bud Greenspan, the late documentary filmmaker who was to the Games what Ed Sabol is to the NFL, once called Mills’s upset the second-greatest Olympic moment of all time, trailing only the Miracle on Ice in 1980.

As the runners and families applaud at the conclusion of the video, as some tear up as Billy rises and speaks, it’s hard to argue even five decades later.

“I think he switched up a couple parts this year, I liked it,” says Melvin Taliman, a Navajo marathoner from northern Arizona who has run the past seven Marine Corps for Running Strong. “I’ve heard varieties of the same one every year, and every year I feel the same way: It’s still the best story I’ve ever heard.”