The show, said the L.A. Times, drew “possibly one of the highest-wattage front rows in New York Fashion Week history.” The New York Times said it “certainly had the front row of the year.” Glamour said, “It was like, seriously packed.”

On a Thursday night in February, Jay Z, Beyoncé, Rihanna, Sean (“Puff Daddy”) Combs, Vogue editor Anna Wintour—“and no fewer than six Kardashians,” by the New York Post’s count—squeezed elbow to elbow into a SoHo event space to see Kanye West debut his “Kanye West x Adidas Originals Yeezy Season 1” collection. (Justin Bieber was there too, but apparently couldn’t get a seat in front.) As a lone trumpet solemnly blared, 45 models marched out in a mélange of blousy sweatshirts, bomber jackets, and flesh-toned bodysuits. The buzz wasn’t about the clothes, though. Hardly. It was about the sneakers.

The rapper followed his models on the catwalk sporting a pair: gray suede high-tops that fell somewhere on the fashion spectrum between mukluks and moon boots. These were the new Yeezy Boost, rumors (and sightings) of which had swirled around the web for months.

That night, not far from Madison Square Garden, West switched effortlessly from fashion designer to megawatt rap star, kicking off the NBA’s All-Star Weekend—the world’s most high-profile sneaker showcase—with a free concert, co-hosted by last season’s league MVP, Kevin Durant. West praised Adidas from the stage and told the crowd to shun archcompetitor Nike: “We ain’t wearing that other company no more, right?” The very next night he was busting onstage at a Drake concert, handing the fellow superstar his signature sneaks. (Drake set them atop a speaker, where they remained for the rest of the set.) The next morning West was delivering pairs of the shoes to surprised fans at an Adidas store in SoHo.

KANYE WEST x adidas NY Launch The collaboration with Kanye West has given Adidas plenty of buzz. Whether it will bump up sneaker sales is more doubtful.Photograph by Leandro Justen—AP Images

By Sunday’s end the “conversation” about Adidas and Yeezy Boost had lit up social media, with social analytics firm Networked Insights recording 141,077 related posts—20% more than the sum of posts about Nike NKE , which had likewise set up a flotilla of big-dollar marketing events for the All-Star celebration. Sure enough, the Yeezy Boost was a bona fide hit with sneakerheads, bloggers, and urban fashionistas everywhere. When the shoe, priced at $350 a pair, finally went on sale online days later, the first run of 9,000 sold out within minutes. You can now find them on eBay selling for as much as $7,000.

“This was an Adidas weekend,” Herbert Hainer, the longtime CEO of the German sports apparel company, declares in a sprawling interview with Fortune at the company’s home base in Herzogenaurach. “It was all about Adidas.” Brand chief Eric Liedtke, an American who works at the headquarters in Germany, is more gushing (if less family-friendly): “We had no right beating Nike on that. But we’re getting our shit together, that’s why.”

Corporate marketing teams the world over live for launches like this, of course. The question is, What exactly is Adidas launching into?

The $16-billion-a-year sports apparel and footwear company, at long last, has some news to crow about. In the latest quarter, global revenue for the corporation—which, besides the Adidas brand, owns Reebok and the venerable golf name TaylorMade—rose 17% year over year and was a first-quarter record for the company (though the increase drops to 9% if you remove the effects of currency fluctuation). Much of the gain comes on the strength of its flagship Adidas brand—or, rather, a segment of it called Originals. The success of Originals, a lifestyles brand within a brand, has in turn been driven by collaborations with West and Pharrell Williams—the Grammy-guzzling hip-hop artist and well-liked coach on The Voice.

It’s a music-fashion-celebrity thing, and it has yet to translate into credibility in the main area in which Adidas competes: sports. That wouldn’t be such a bad thing, except that in the case of sports footwear and apparel, almost all the money is in, well, sports. The “sport performance” segment accounts for 70% of global sales for the Adidas brand.

Here, Yeezus wheezes.

Nike Inc., with its namesake brand, Air Jordans, and Converse, has scooped up a nearly 50% share of the U.S. athletic footwear market. Adidas Group’s slice is a mere 9% and has declined every year since 2011. The strong first quarter aside, the company’s overall revenue has fallen in back-to-back years when measured in U.S. dollars, with 2014 net income ($593 million) sinking to its lowest level since the recession-racked 2009. (The company, which reports its financial results in euros, says currency fluctuations make its recent sales and profit numbers look worse than they are; it says its 2014 net sales of 14.8 billion euros were actually up 2% from 2013.)

To be sure, Adidas still dominates the sport that dominates much of the earth. Its share of the global soccer market is an estimated 39%. But here, too, Nike is closing in fast. A warning shot if ever there was one: Nike’s sales in Western Europe, Adidas’s home turf, grew three times as fast last year as Adidas’s.

It is in the States, however, where the battle royale is. Here is the place where some 40% of the world’s sports apparel and footwear sales are made. Here is where, for decades, Adidas was the cleat to beat. And here is where, today, nine of the 10 top-selling sneakers in the U.S. belong to Nike. The one holdout, meanwhile, isn’t even an offering from Adidas, but rather a shoe from Under Armour UA —whose sizzling growth rate has lifted the company to the No. 2 rank (behind Nike) in the sports apparel category in the U.S. That dropped Adidas to No. 3, for the first time this century.

Don’t count on Kanye to change that roster anytime soon. Nobody is going to play street ball in Yeezy Boosts. As one morning radio DJ told West when he came to plug the shoe: It looks “like a papier-mâché project.”

Hainer, Herbert - Manager, CEO of Adidas AG, Germany CEO Hainer acknowledges that Adidas has “not been present enough” in American sports.Photograph by Albert Foss—Getty Images

Hainer says he understands the company has “not been present enough” in American sports—and to succeed in the U.S., Adidas needs to remind Americans that it is a running-shooting-scoring brand first and foremost. All of which sets up the company’s recent success with Originals as an awkward challenge of its own. The bigger it gets in lifestyle and fashion, the less it may be seen as a cutting-edge sports company. And once that goes, there may be no going back.

If you want a road map for how Adidas ended up in this spot, look no further than its relationship with Derrick Rose. Rose was the No. 1 pick in the 2008 NBA draft, when the 19-year-old quit the University of Memphis for the Chicago Bulls. At 22, the 6-foot-3 point guard became the league’s youngest-ever MVP. Rose was poised to be the new king of basketball. So it must have seemed like a coup to many when, in February 2012, Adidas extended his endorsement contract into a “lifetime” deal reported to be worth up to $260 million over 14 years, including achievement bonuses. (Adidas won’t confirm the figure.) The brand made Rose the global face of the company, with billboards, social media blitzes, television ads, and of course a signature basketball shoe.

Then he got hurt. In an April 2012 playoff game, he fell to the court, wincing in pain. He had torn the ACL in his left knee. After surgery that May, he missed the entire 2012–13 season. It appeared Rose would come back for the 2013–14 season. Adidas went all in, launching a campaign it dubbed “The Return,” complete with a web series documenting his recovery. Again, both player and brand got unlucky. Rose came back only to injure his other knee just four weeks into the new season, forcing him to sit out another year. This season he played in 46 games (his most since 2010) before hurting his knee yet again in February, undergoing major surgery, and finally returning for a short run in the playoffs.

It was nothing but bad luck that hit Rose. It was bad luck (and perhaps bad judgment) that Adidas bet the farm on one marquee player. “God, they gave him too much,” says Bob Dorfman, sports marketing adviser at Baker Street Advertising. Hainer, for his part, understands the brutal calculus of endorsements: “We suffer with the player,” he says, shrugging his shoulders helplessly. “Obviously, if he’s not playing, he’s not as visible as we’d like, and it hurts us.”

The bad luck didn’t stop with Rose. Adidas seemed to have a knack for inking endorsement deals with the wrong players. It signed a multiyear deal with Dwight Howard, a former No. 1 draft pick who later won the NBA’s Slam-Dunk Contest in a Superman cape. But Howard, who jumped from Orlando to Los Angeles to Houston, seemed to make as many enemies on and off the court as he did rebounds—or enough, anyway, to fill SB Nation’s “A History of Hating Dwight Howard”—which generally doesn’t translate into marketability, says Dorfman. called Howard’s signature line for Adidas “perhaps the most underwhelming in the history of basketball shoes.”

In the end, it is numbers rather than names that best capture Adidas’s awkward run with the NBA: $400 million and 96%. The first figure is what the German company reportedly spent in 2006 to be the league’s official apparel provider, getting the chance to have its three stripes on all NBA merchandise (though not game jerseys) for 11 years. The second is Nike’s current share of the basketball footwear market. After nearly 10 years of sponsorship, Adidas is little more than an asterisk in basketball shoes, with less than 3%.

Last month the company waved a white flag in the sport, announcing it would not seek a renewal when the deal expires after the 2016–17 season. (Nike has reportedly picked up the contract.) By then, Adidas will no longer be the official sponsor for any of the big three American sports leagues. The German company’s two mighty rivals, Nike and Under Armour, have done a lot right, says Stifel Nicolaus analyst Jim Duffy, “but both have benefited from Adidas just not even showing up.”

As much as people talk up the Adidas rivalry with Nike, it has been Under Armour’s streak of a rise that has execs in Herzogenaurach scared. Falling to No. 3 in sports apparel market share in the States raised alarm bells, insiders say. “It’s always this way with niche challengers,” says Mark King, the former TaylorMade CEO, who was just promoted to run Adidas’s North American business. “There’s two points here, there’s three there, and pretty soon that 3% for Under Armour turns into freakin’ 30.”

Liedtke, Adidas’s global brand chief, is even more candid. He says Adidas needs to “reset” everywhere, not just in the U.S. Evaluating the brand, Liedtke is as brutal as the critics, acknowledging that young athletes aren’t looking to the three stripes the way they did a decade or two ago. “I think a lot of times we’re not even in consideration,” he says of sneaker shoppers. “That’s what breaks my heart.”

Formerly based in Portland, Ore., as vice president of North American brand marketing, Liedtke moved to Germany in 2006 and last year became global head of the brand, a huge step up. The 48-year-old is rumored, as is the 55-year-old King, to be a strong candidate for the top job when Hainer is slated to retire in March 2017. (King says of Liedtke: “Whether he’s the next CEO or not, that forward thinking, that we-need-to-push-the-envelope thinking—that’s what he represents.”)

adidas Mark King (left) and Eric Liedtke are tasked with turning around Adidas’s U.S. business.Photograph by Chris Hornbecker for Fortune

Liedtke is now spearheading a massive reorganization that he says has this year directly affected 40,000 of Adidas Group’s 54,000 employees. The company moved a handful of key executives from Herzogenaurach to Portland, including its global design chief. It demolished its old chain of command, a traditional hierarchy with heads of divisions reporting to managers. Liedtke eliminated 30 vice president positions and now has 16 people reporting directly to him. Previously, if, say, football cleats weren’t selling well, he had to talk to six people to find out why. “Now I have one single guy responsible for winning football,” he says. “And if he doesn’t do it in the next 18 months, I have to make a change. Sorry, guys, but it’s a performance culture now.”

Liedtke added sports clocks in meeting rooms to stress the theme of speed, a touch he picked up from Google GOOG . He read up on Pixar’s corporate culture. He brought two busloads of Adidas folks to Google in Zurich for a field trip. “We did it all very radically—we went faster than we’ve ever done before,” says Liedtke. “There’s going to be despair, there’s going to be denial and complete frustration, and then there’s awakening.”

One of the brand chief’s biggest goals was borne out of his own frustrations. Having worked in both Portland and Herzogenaurach, Liedtke says it has often been “a huge divide.” King concurs. Both men describe instances when German employees would complain about the Americans, and vice versa.

In Liedtke’s first visit back to Portland after relocating to Germany, he told employees to raise a hand if they had not recently complained about the Germans. No hands went up. “When you think of the Germans, think of me now,” he told them. “I’m the guy. Do you picture me, or is it some 1944 reference? I’m the German guy now. There’s no more bogeymen.”

Running the Wrong Way

The problem hasn’t been just one of comfort and compatibility. King blames that Euro-American culture divide, in part, for the problems in U.S. sports. He surmises that Adidas’s strategy for years was to dominate soccer and assume that the halo of soccer would drive growth in other sports. That worked for a long time in other countries, but it hasn’t worked in America—and isn’t likely to. He volunteers the way he imagines past conversations went between execs in Germany: “American football? They only play that in America. Let’s not worry about it. Baseball? Americans don’t even like baseball anymore. Lacrosse? What’s that?”

Adolf “Adi” Dassler, a cobbler, founded Adidas in his hometown of Herzogenaurach in 1949. Before that, Adi had a shoe company with his older brother Rudolf. One of their first shoes was a track spike, famously worn by Jesse Owens in the 1936 Olympics in Berlin. In 1948 the brothers split, and Rudolf created rival Puma. Six years later the German men’s team won the World Cup wearing Adi’s cleats. Many consider it Adidas’s true debut.

With such pedigree, Liedtke is hardly off base when he calls Adidas the “original sports brand.” It is, in Liedtke’s I-can’t-believe-my-dad-said-that phrasing, the Original Gangsta: “We are the OG. And kids respect the OG. So we need to tell people,” he says.

And yet instead of sports, many consumers in the U.S. associate Adidas with hip-hop culture. That dates back to 1986, when rap trio Run-DMC released the song “My Adidas.” Before long, items like track jackets and the shell-toe Superstar sneaker were surging in popularity, prodding management in 2000 to split its apparel division into two segments: sport performance (athletic gear) and sport style (fashion, which includes Originals). Under the latter, it has partnered with designers like Jeremy Scott and Yohji Yamamoto, outfitted pop sensations like Katy Perry, and designed signature shoes with even little-known rappers like Big Sean and Pusha T.

ADI.06.01.15.timeline Courtesy of Adidas

“I think it’s fair to say that sport has transcended into fashion, into lifestyle, into streetwear,” explains CEO Hainer. “I would guess that 80% of all sold basketball shoes will never see a court. They are worn just to build status and be cool. So sport has a connection to lifestyle, which I think is good. Within Adidas, of course we want to benefit from that.”

But even with hitmakers like Kanye West and Pharrell, the strategy might be a dangerous one. For better or worse, it has redefined the company Adi Dassler built.

Some analysts say that Adidas pushed Originals too hard. “You have to pick your lane and decide who you want to be,” says Matt Powell, a widely followed apparel analyst with NPD Group. John Horan, founder of Sporting Goods Intelligence, puts it this way: “Think of it like a glass of beer. Your fashion business should be your foam. The performance business has got to be the beer. What they have is a lot of foam and not enough beer.”

Hainer acknowledges the company’s recent fumbles on the sports side, but insists fashion isn’t the cause. “If we might be seen in America as a hip-hop or street-fashion brand,” he says, “it is not because we do too much hip-hop and celebrities. It is because we did not do enough sport.”

He adds forcefully that Adidas will always stay true to that heritage. “When you look at our new brand campaigns in America,” he says, “this is sport, sport, sport!”

Maybe so. But then the $500 Yeezy duck boot hits stores later this summer.

This story is from the June 1, 2015 issue of Fortune magazine.