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The timing could not be more ideal. Days after President Obama fired the CEO of General Motors, and instructed GM and Chrysler to fix up fast or drive headlong into bankruptcy, college basketball's annual bonanza, the Final Four, has arrived in the Motor City to provide a much-needed distraction. What's even sweeter: Michigan State University, located just 90 miles west of Detroit in East Lansing, made the national semifinals this year, giving the locals more reason to cheer (unless, of course, they bleed the University of Michigan's maize and blue and wouldn't dare root for an archrival). For a few days at least, the city can lose itself in the rah-rah world of college hoops. (Read TIME's special report: "Is This Detroit's Last Winter?")

And for a few days, more importantly, the Final Four will jolt the local economy. Thousands of fans have flocked to Detroit for the big games, and they'll spend money in the city's downtown hotels, restaurants, bars and retail shops. The games are being played at Ford Field, the downtown home of the Detroit Lions, which will seat some 70,000 fans. Fan-festivals and free concerts throughout the weekend will also draw visitors downtown. The NCAA anticipates that the Final Four will generate anywhere between $30 million and $50 million in new direct spending for the ailing area. (Hear Dick Vitale's Top 10 NCAA Tournament Moments)

Detroiters are optimistic that it's the beginning of a turnaround. "We think this will have a long-lasting effect for the city's economy," says Renee Monforton, communications director for the Detroit Metro Convention and Visitors Bureau. "The people who visit here will want to come back again, either as leisure tourists or for a meeting. And people watching on television will see Detroit as a viable place to live, work and visit."

To economists, however, blissful predictions like these are bunk. "I don't believe it's that big of a bonanza, frankly," says Smith College sports economist Andrew Zimbalist, who predicts an economic impact of about $15 million. "It's kind of silly to suggest that it is." Festive fans of North Carolina, the University of Connecticut, and Villanova University — the other three teams that made the Final Four — will likely have a nice time in spruced-up Detroit. But it's a stretch, Zimbalist says, to figure they'll suddenly think of Detroit as a repeat destination — and even more of a stretch to hope that television viewers will be impressed. "People aren't going to sit there and think, 'Oh my God, I'm going to Detroit for my next vacation,'" says Zimbalist. "Corporate executives aren't going to say, 'I need to open an office in Detroit.'"

History would seem to side with the economists. In 2006, Detroit hosted the America's most gargantuan sports event, the Super Bowl, also at Ford Field. Fans gave the area a $274 million boost, according to one economic research firm. Over 90 million people watched the face-off between the Pittsburgh Steelers and Seattle Seahawks on television. Did the game lift Detroit long-term? Well, Detroit's unemployment rate is 13%, worst in the country among major metropolitan areas. The city's bonds have junk ratings. Because its school system has run up a $305 million deficit, the city may have to close up to 50 schools. Thanks for the help.

One misconception is that every dollar a fan spends in a host city directly benefits the city. Some of the money coming into Detroit will leave it just as quickly. Take hotels, for example. The Marriott and Sheraton may be full, but a chunk of that revenue flows to corporate headquarters outside of the city. The same holds for national restaurant chains like McDonald's. And the NCAA takes about 65% of the revenues from game tickets.

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Some of this year's Final Four spending won't even stay in the country. More than half of the several thousand college basketball coaches who flock to the Final Four for their annual convention will be lodging across the river — and border — in Windsor, Ontario. Don't underestimate the financial clout of the coaches, who wander around the host city in their schools' sweat suits (Look, there goes Coach K from Duke! And over there, an assistant coach from Le Moyne!), angling for job gossip and drinking lots of beer. We're talking buckets of beer. And since both Detroit and Windsor have casinos, many coaches will end up drinking and losing their money in Canada, not in Michigan. (See the most important cars of all time.)

Perhaps the cruelest irony is that while the press has portrayed Michigan State's berth as a gift to a troubled city, from an economic point of view the Spartans' success may actually hurt Detroit. Yes, since a Michigan team is playing in the game, more fans will be crowding Detroit's bars and shops than there otherwise would have been. But since Lansing is a neighbor, a reduction in local hotel stays could offset this revenue. Fewer out-of-towners also means less spending at the airport and on transportation (cabs, rental cars, and so on). Also, it's safe to assume that a portion of the Michigan State basketball fan base would have spent money in Detroit even if the team had not made the Final Four. The event is a huge draw for hoop-heads who just want to soak in the festivities. Many Lansing residents and other Michigan State basketball fans from outside of Detroit would have made the trip and maybe even gone to the game, regardless.

From the state's perspective, the school's appearance is definitely a drawback. "Financially, the state of Michigan would have been happy if there were four teams out of state," says Jason Winfree, a University of Michigan sports economist. If, say, UCLA had made the Final Four instead of Michigan State, thousands of the school's fans would have flown to Detroit to spend money. All of that cash is a windfall to the struggling state — without the Final Four, none of those Californians and UCLA fans throughout the nation were heading to Michigan to hang out for the weekend (OK, a handful might have family or some other reason to make the trip). For the Michigan State fan who spends a couple of hundred extra dollars at the Final Four, that's money he would have spent somewhere in the state at some point anyway. He might have even spent the same amount this weekend, doing something else.

So the Final Four isn't a magic pill that will make Detroit all better. But still, it is at least a temporary boost, especially in these grim times. "This economic injection is real and important," says Rodney Fort, a University of Michigan economist who also specializes in sports. "It's just not permanent." Beyond dollars, we shouldn't discount the intangible perks a major sports event delivers to a city. Detroit families can discuss the big game instead of the plant closing, maybe catch a free concert downtown. And though Michigan State's run may cost the state some extra cash, a national championship will lift the state's spirits, and who's to say a few hours of celebratory hysteria are worth less than a few bucks from out-of-towners? "People here now have a respite," says Fort. "Detroit is a focal point for a good reason, not a bad reason. That's very, very valuable."

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• Sean Gregory