Given how poorly many seem to understand private equity and how companies like Bain operate - this is a good case study.

When private equity firms go shopping for a takeover, they look for certain qualities. Weak management. Underachieving revenue. Opportunities to expand by taking on debt. Problems that are driving down value, but could be solved by a fresh set of outside managers.

Sound like any professional sports you know?

Private equity firms like to buy distressed properties, and right now the National Hockey League—fourth of the four pro sports, nonentity on SportsCenter, and days away from its second work stoppage in seven years—is as distressed as it gets. Fans have long fantasized about new league management (booing Commissioner Gary Bettman has become a tradition at the Stanley Cup ceremony), and the idea of private equity swooping in to the rescue is actually not as far-fetched as it sounds. In early 2005, with players and owners at an extra-bleak moment of a season-ending labor dispute, Bain Capital made a surprise offer to buy out the entire league for $3.5 billion.

Three men—Stephen Pagliuca of Bain, and Robert Caporale and Randy Vataha of Game Plan LLC, a sports consultancy—made the pitch to a meeting of the NHL’s board of governors at a New York hotel that spring. By buying out all 30 teams and combining them into a modified single entity, they argued, they could streamline operations, boost TV revenue, and negotiate down player salaries from a position of absolute strength.

“They actually clapped at the end of the presentation,” Caporale says. “Which was interesting, because part of the presentation, the part that my colleagues asked me to give, was the one where we said, ‘You’re running this business all wrong.’”

The bid failed after a number of owners made it clear they were unwilling to part with their franchises—which, to some, hold far more emotional value than real worth. Still, the episode offers a useful window into how private equity operates: spotting troubled entities, using leverage to buy them out, and renovating the business. Then, and again today, the NHL is a surprisingly good fit.

“This certainly fits all the characteristics of what a distressed asset is,” says Tobias Moskowitz, author of Scorecasting and a finance professor at the University of Chicago’s Booth School of Business, where students are fond of blowing off exam steam on the ice.

With more capital, the NHL could use the National Basketball Association’s template for expanding into Europe and other markets, Moskowitz says, and outside managers could drive a harder bargain on player salaries. Not surprisingly, salaries are the league’s highest cost, but at 57 percent of league revenue they are also higher than those of the National Football League (47 percent) and the NBA (about 50 percent). Meanwhile, “the NHL certainly has cash flows that it will spin off almost immediately. You’ve got merchandising, you’ve got ticket revenue. So I think that would make this very attractive.”

Private equity is no stranger to hockey. Phil Falcone, the founder of Harbinger Capital Partners, skated for Harvard before playing professionally in Sweden, and today owns a minority stake in the Minnesota Wild franchise. The St. Louis Blues were until recently owned by TowerBrook Capital Partners, a private equity firm with offices in London, New York, and San Francisco. Providence Equity Partners, a Rhode Island firm, considered a bid for the Toronto Maple Leafs last fall, Bloomberg reported. And Kohlberg & Co. took equipment giant Bauer (BAU), whose skates are worn by two out of three players, public in January 2011 after three years of ownership.

Susan Chaplinsky, who teaches private equity at the University of Virginia’s business school, says a buyout firm that found itself in control of the NHL would be able to wring value out of everything from selling off assets to buying goods—peanuts, pucks—at scale.