Patrick Murray tries to win voters at an Arlington County GOP booth in September, 2012. (Astrid Riecken/The Washington Post)

Of all people, Allan Lichtman should have known better than to run for Congress.

An American University political historian who has accurately predicted every president since 1984, he understands the harsh realities of congressional elections: Outsiders rarely win, especially against incumbents.

He ran for Senate in Maryland in 2006 anyway. In the end, it got him another mortgage, which he used to lend his campaign $250,000, an arrest record for protesting his exclusion from a televised debate and exactly 1.2 percent of the vote.

“I’m still paying off the mortgage,” he said recently.

Every election cycle, congressional races across the country include candidates like Lichtman — long shots who know the odds but choose to run nonetheless. They are guided by hope and faith and, in some cases, ego. Some are Mr. Smith innocents driven by the belief that American democracy confers a real chance. Others are hopefuls inspired by the Truman-defeats-Dewey upsets.

Of the dozen House and Senate races in the Washington region this year, only two are considered competitive by nonpartisan analysts. Yet all of them include challengers who are waging spirited and, in some cases, costly campaigns. Among them are major and third-party candidates who have well-funded, professionally staffed campaigns that are airing television ads. Others are far more modest, featuring candidates who write their own news releases and may generate as much pity as support.

As for his decision to run, Lichtman said, “I thought I had something important to say.”

He paused a moment, then added, “It also involved a lot of illusions.”

‘We can do it’

In any year, the biggest reason that so few congressional races are competitive is the same: the power of incumbency. The average reelection rate since 1990 is 87 percent for senators and 94 percent for members of the House. First-time winners tend to be candidates who were fortunate enough to have run for an open seat or who worked their way up through lower public offices, building name recognition, political connections and a fundraising base.

The odds are not enough to discourage Patrick Murray.

After spending 24 years in the Army and retiring as a colonel in 2009, the Alexandria resident could have easily snagged a lucrative job close to home with a federal contractor. Instead he ran for Congress against the 21-year incumbent in Virginia’s 8th District, well-known Democrat James P. Moran, who has won each of his last seven elections with more than 60 percent of the vote.

After losing by 24 percentage points in 2010, Murray, a Republican, is trying again this year. Yes, he is aware of the downside: He might again spend all that time and energy — and money — for a campaign that may come up short. But he doesn’t dwell on that; he can’t, he said. It would be counterproductive.

“You just can’t say, ‘We can’t win, so why try?’ ” he said.

So he tries not to give too much weight to incumbent reelection rates or what the analysts say. He tells himself what he tells voters: that he can win, that he will win.

What some might find quixotic, even foolish, he sees as the embodiment of the American way: It’s the voters who decide, and if you work hard enough, anything can happen.

He has gained a lot of name recognition from his previous campaign, he’ll tell you. And redistricting has given Republicans a better shot at winning.

Upsets, he knows, do happen. Just look at how financier John K. Delaney beat Maryland Senate Majority Leader Robert J. Garagiola (Montgomery), who had the party’s backing, in the Democratic primary this year.

Plus, Murray thinks Moran’s time has come.

“If I thought Jim was doing a good job,” Murray said, “then I wouldn’t be running.”

It’s a message he sought to drive home at the recent Clarendon Day street fair, where he, his campaign manager and a handful of volunteers spent the afternoon passing out yard signs and talking with potential voters.

“It’s still an uphill battle,” Murray told two 20-somethings who seemed eager to chat. “But we can do it.” With a mascot in an elephant costume dancing behind him, he said that although the 8th District leans blue, redistricting has helped, and his campaign is working hard to pick up votes in new neighborhoods.

“Really,” Murray said, “this is about getting someone in office who can do better for the people of this district.”

Not everyone was interested, though. Some pretended not to hear him when he said hello. Others said they were Democrats and kept moving. One grumbled dismissively, “Good luck.”

Murray seemed unfazed as he wiped perspiration from his brow.

“It’s a tough business,” he observed.

He said his decision to run a second time was not made lightly. He looked to friends, family members and advisers and deliberated for months, choosing to try again only after becoming convinced that he could win.

Among the biggest factors that convinced him are the parallels being drawn between 2012 and 1980, when Ronald Reagan unseated President Jimmy Carter and Republicans made huge gains in Congress. One person who argued the similarities and encouraged him to run again, he said, was his friend Frank R. Wolf, Virginia’s 10th District congressman.

A fact that Murray has been careful to point out: It took Wolf three tries before he won.

‘An insurgency’

Some candidates simply won’t admit how long the odds are and focus on how anything is possible, especially in the digital age, when even the most seasoned candidates can implode quickly.

Kristin Cabral, Wolf’s latest Democratic challenger, is a former federal prosecutor who has never run for elected office before. Her opponent has been vanquishing challengers since he was first elected in 1981, the year Reagan took office as president. Wolf crushed his last challenger by 28 points, and as of June 30, his campaign had $456,000 in the bank, about eight times what Cabral had on hand.

Still, she fervently believes that career politicians such as Wolf aren’t doing right by the country and that bringing in non-politicians is the answer.

“Congress is broken,” Cabral said.

Asked why she believes she’ll beat Wolf, she said flatly, “Because he’s out of touch.”

Newcomer Ken Timmerman, a Republican who is taking on a 10-year incumbent in Maryland’s 8th Congressional District, said he also gives little consideration to forecasts.

“I don’t consider this an underdog campaign. I consider this an insurgency,” he said. “I’m going to win with votes of Democrats and independents.”

Rob Sobhani, a businessman who is running for U.S. Senate in Maryland as an independent, is so confident of his chances to unseat Benjamin L. Cardin (D) that he has spent more than $1.7 million of his own money.

The cash has allowed him to run television ads, even in the expensive Washington area market, which has raised his name recognition after a late entry into the race last month. The effect? A recent poll shows that Sobhani is in a dead heat for second place with Republican Dan Bongino, who has been campaigning for more than a year.

But both challengers are still far behind Cardin.

Nonetheless, Sobhani is convinced that he’ll pull ahead by Election Day: “If I wasn’t, I wouldn’t be spending all this money.”

‘I’m contributing’

Not everyone is running to win.

“I expect to lose,” real estate agent Bruce Majors said cheerily after spending the better part of a recent afternoon hanging campaign signs in the heat. The Libertarian is challenging Del. Eleanor Holmes Norton, the District’s non-voting representative in the House. Rather than winning, his aim is to score at least 7,500 votes, the number needed to earn permanent ballot status for his party, which would spare future libertarians the hassle and expense of collecting signatures.

More so than any other group, third-party candidates have used losing campaigns to introduce new ideas into the mainstream, said Mark Rozell, a political analyst and public policy professor at George Mason University. The abolition of slavery, prohibition, women’s suffrage and the minimum wage all were advanced by such candidates. Others have used elections to draw attention to causes including campaign finance reform and the legalization of marijuana.

Mark Gibson, an independent candidate in Virginia’s 11th Congressional District, made his Web site himself, writes all his own news releases and has no staff. But he, too, has a cause aside from his platform, even if it is a little old-fashioned: democracy.

He defines himself as a centrist who sticks to the issues and maintains civility. True, he probably won’t win, but he thinks voters should still have a choice to pick someone who rejects all the finger pointing.

“That’s enough for me,” he said. “I think I’m contributing.”

So he’s set a goal different from most. Victory, as he’s defined it, is 10 percent of the vote.

Ben Pershing contributed to this report.