The Washington Nationals are off to a magical start this season, with a sold-out house Monday witnessing a pair of home runs by star outfielder Bryce Harper and a seven-inning shutout by pitching ace Stephen Strasburg. There were even commercial victories, including expanded sponsorship deals with athletic-wear company Under Armour and MedStar Health, both with prominent new outfield signs — right behind Harper.

But the team’s owners, the family of Ted Lerner, have yet to make their big commercial home run: a long-term stadium naming-rights deal, expected by some to soar as high as $15 million a year over several decades.

“The maximum timing for the stars to be aligned [for a naming-rights deal] may be this year or next year,” said Mark Tuohey, a lawyer and former chairman of the D.C. Sports and Entertainment Commission. He played a key role in bringing the Nationals, formerly the Montreal Expos, to Washington. “If you couple a successful season with the potential for playoff and World Series success . . . this year or next year will be maximum timing.”

The Lerners, who bought the team in 2006 from Major League Baseball, have rarely spoken about naming-rights possibilities, and they declined to comment for this article. Although they retained a Los Angeles firm several years ago to explore naming rights, nothing came of it.

Andrew Zimbalist, an economist at Smith College and an expert in sports business, said the Lerners are patiently waiting for the right pitch.

“The stadium came on line during the recession,” Zimbalist said. “They didn’t want to compromise what would be a secure and healthy long-term deal just to be able to have some naming-rights revenue in the short run. What they have been doing is waiting for the market to firm up a little bit and waiting for the right company at an attractive price.”

With the Nationals expected to compete for a playoff berth and possibly a World Series title, and with a lineup of stars led by Harper, Zimbalist said, companies may be itching to grab the naming rights, and the television and media exposure that goes with them.

Naming-rights deals have been soaring since the Washington Redskins signed a $205 million, 27-year pact with FedEx in 1999.

MetLife signed a 25-year, $400 million deal for the home of the National Football League’s New York Giants and New York Jets. The Houston Texans signed a 32-year, $320 million naming-rights deal with Reliant Energy; and CitiGroup agreed to a reported $400 million deal to put its name on the New York Mets’ ballpark, which caused a stir because the financial services company received government bailout money during the financial crisis.

Zimbalist estimated that a Nationals Park naming-rights deal would bring $10 million to $15 million a year for 20 years or more.

There are not many companies that can afford the kind of outlay and still get a return for their shareholders. The Washington area names most frequently mentioned include hospitality group Marriott Worldwide, financial firm Capital One, Chevy Chase-based insurance giant Geico, Baltimore-based Under Armour and the big local defense contractors, including Lockheed Martin, General Dynamics and Northrop Grumman.

Most of those companies have disclaimed any interest in a Nationals deal. Historically, apparel and hospitality companies have not signed naming-rights deals because of the difficulty in justifying a return on the investment.

But Capital One’s founder and chief executive, Richard D. Fairbank, is a big sports fan and a partner in Ted Leonsis’s holding group, which owns Verizon Center and its tenants, the National Basketball Association’s Wizards and the National Hockey League’s Capitals.

A Capital One spokesman declined to comment on the naming-rights speculation. The McLean-based bank has a raft of sports sponsorships, ranging from local deals to national ones, including college football’s Capital One Bowl and ESPN’s Capital One Bowl Week. Locally, Capital One owns the naming rights to the University of Maryland’s football field, which the company inherited with its purchase of Chevy Chase Bank.

“The Lerner ownership group is being extremely careful,” said Lisa Delpy Neirotti, a professor in sports management at George Washington University. “They do not want repeated name changes like other teams, such as the San Francisco Giants and the [Arizona] Diamondbacks have experienced at their parks. And they don’t want a Hooters ballpark. They are being patient for the right price and the right partner for a long-term marriage.”