The Oglala Lakota—also known as the Oglala Sioux—consider South Dakota’s Black Hills to be their spiritual homeland, and on a Tuesday in mid-December, a record snowfall had turned their pine-covered peaks white. In the Rushmore Plaza Civic Center, in nearby Rapid City, a former tribal president named Bryan Brewer stood on a hardwood court and told a few hundred teen-agers the origin story of the basketball tournament they would play in over the next four days, the thirty-ninth Lakota Nation Invitational. Brewer wore a turquoise vest, a yellow beaded bolo tie, and black Nikes. The kids sat in their warmup suits and ate Pizza Hut in the bleachers.

“After Wounded Knee, no one wanted to play us,” Brewer said. He was referring to the occupation of the town of Wounded Knee by the American Indian Movement, in 1973, when Brewer was a basketball coach at Pine Ridge School. The A.I.M. wanted the U.S. government to reëxamine scores of treaties, which, they believed, had been broken. The occupation, which included the site of the 1890 massacre, set off an intense dispute between A.I.M. supporters and a private paramilitary group funded by the existing tribal leadership, whom the A.I.M. had accused of corruption. In the three years following the seventy-one-day occupation, stabbings, shootings, and beatings related to the conflict became common, and by 1975, the impoverished Pine Ridge reservation, roughly the size of Delaware and Rhode Island combined, had the highest murder rate in the United States. Athletic directors from school districts across South Dakota refused to let their athletes play ball there.

Bryan Brewer. Photograph by Dan McMahon Photograph by Dan McMahon

Brewer, unable to schedule a full slate of games for his team, got on the phone and pleaded with coaches from native schools as far away as Kansas to play in a tournament on Pine Ridge. Seven schools signed on, and the first all-Indian tournament was a success. The tournament moved to Rapid City in 1979, its third year, and became the Lakota Nation Invitational; since then it has evolved into one of the premier showcases for “rez ball,” the run-and-gun, offense-first style of play that first caught on at reservation high schools in the nineteen-eighties. Over the years, the L.N.I. has widened its scope to become a winter homecoming of sorts for Native Americans all across the Dakotas, and a vital platform for fostering Lakota culture.

“This tournament started because of racism,” Brewer told the kids. “We wanted to work on reconciliation. What we’ve got now is something that’s much more than basketball.”

This past year, racism almost pushed the tournament out of Rapid City. On January 24, 2015, the Rushmore Plaza Civic Center was host to one of the uglier moments of the year in American sports: chaperons ushered fifty-seven elementary-school kids from the Pine Ridge reservation out of a minor-league hockey game, after white businessmen allegedly hurled racial slurs (“Go back to the rez,” and “You’re Indians, you should be louder”) and sprayed beer on them from a party box above. A trial was held over the summer; the one man who was charged was found not guilty. (If convicted, he faced a maximum fine of five hundred dollars, for disorderly conduct. Some on and off the reservation wanted the incident tried as a hate crime.)

Native Americans in Rapid City have lodged complaints about racism and racial profiling by the police for years; in one notorious incident, from December, 2014, a thirty-year-old Native American man was killed by a white police officer a day after marching in an anti-police-brutality rally. (The shooting was later ruled justified, and described by the Rapid City police chief as “suicide by cop.”) But the ugliness at the hockey game was a tipping point of sorts. After a chaperon named Justin Poor Bear posted about it on Facebook, and received attention across the Native American community, the Associated Press covered the story. The Rapid City Journal then ran a front-page headline asking, “Did Native students stand for National Anthem?” as if to offer a justification for the alleged harassment. (Two days later, the Journal’s editor apologized for the headline.) Citing safety concerns, the Oglala Sioux Tribal Council passed a resolution in February requesting that the L.N.I. be moved out of Rapid City, and the tournament’s board publicly announced that they were looking at moving to other cities. But it became apparent while talking to Brewer that some board members, at least, never seriously considered moving the L.N.I. elsewhere. Taking the tournament away from Rapid City and the Black Hills—which the Lakota people still want returned to them, citing a treaty broken in 1877—would set a bad precedent for Native American youth. The board decided to stay put.

“This is our home,” Brewer said. “They can’t run us out.” All of the schools in Pine Ridge ended up sending official representatives to the tournament—except for American Horse, the school attended by the “Lakota 57.”

I spent four days watching the Lakota Invitational from the bleachers, and I saw enough lob passes, breakaways, and uncontested layups to develop a love for the fast, loose, and improvisational offenses of rez ball. For weeks after the tournament, N.B.A. basketball still seemed halting and strange. In rez ball, set plays are scarce. Most teams run zone defenses instead of slower man-to-man, and relentless full-court presses and traps speed up the opposing offense. It’s an endurance game. At a morning matchup between the Red Cloud and Crow Creek girls’ teams, the sound of footsteps firing up and down the court drowned out the noise of the small crowd, and during one particularly fluid and unbroken stretch of play it felt as though I were watching an indoor half-marathon. The games feature a shot clock, adopted in 2006, which is a relative rarity for high-school games—but you never hear its buzzer, because somebody always shoots well in advance of the thirty-five-second limit.

When you do get to a rare break in play, you can pore over the players’ names in the program and wonder about the events that precipitated them. A few to ponder, from various schools: Noah Comes Flying, Robert Looks Twice, Shyann Gray Grass, Jordan Rattling Leaf, Wiconi Walking Eagle, Louis Her Many Horses, JoDean Fast Wolf, Hoksila Moves Camp, Stevie Lone Dog, Adam Rough Surface, and Adriano Brings Him Back. When players were called out on the public-address system, their last names were often compressed. “Foul on No. 22 Roughsurface” or “Bringsimback” or “Comesflying” or “Movescamp.”

Meanwhile, cultural events took place in meeting areas spread across the convention center. One room was the setting for a language bowl: kids won points by repeating an English vocabulary word back to judges in its Lakota translation. I watched a match between teams from two “immersion schools,” one from the Standing Rock Reservation, in North Dakota, and another from the Cheyenne River Reservation, in South Dakota. The Lakota language is endangered; one organizer told me that only a handful of people under the age of thirty-five can speak it. Immersion schools, or “nests,” are an attempt to revive the language through instruction by fluent speakers. In the language bowl, some words thrown at the kids were more obscure than others: the six- and seven-year-olds offered furrowed brows at “dried corn” and “chokecherries.” But their legs swung excitedly under their chairs at softballs like star (wičháȟpi), tickle (yuš’íŋš’iŋ), fire (pȟéta), and winter (waníyetu).

A colorful scene in the stands at the Lakota Nation Invitational. Photograph by Dan McMahon Photograph by Dan McMahon

Outside, the civic center’s hallways were filled with the patter of teen-agers and trinket-sellers. There were tables set up where you could buy the New Lakota Dictionary, or declare your interest in signing up for the National Guard, or purchase a five-dollar raffle ticket to win a white 2005 Chrysler Sebring, which was parked out front and had new tires but some rust on the frame. A small choral group set up near a food court; I walked by as a teen-ager wearing a black Nirvana T-shirt sang “Silent Night” in Lakota.