A common cognitive bias in political analysis is what Daniel Kahneman calls the availability heuristic: the tendency to focus on recent or familiar examples as opposed to the broader course of history and the richer volume of precedents.

There is some risk of this in Massachusetts, where the Democrat Martha Coakley lost a special United States Senate election in January 2010 to the Republican Scott Brown. The state is holding another special Senate election in June, in which the Republican candidate, Gabriel Gomez, is drawing comparisons to Mr. Brown, and Republicans are hopeful that they can win again.

The problem with using the 2010 race as a precedent is that it may have been an outlier. Republicans won a net of 63 seats in the House of Representatives that November, but none came in places as blue as Massachusetts. (The one comparable G.O.P. victory was in a Senate race in Illinois, where the Republican Mark Kirk defeated the Democrat Alexi Giannoulias.) Mr. Brown himself was defeated in 2012 by a Democrat, Elizabeth Warren, whose margin of victory, 7.5 percentage points, was reasonably large for a non-incumbent candidate. A number of unusual factors may have come together to allow Mr. Brown to win in 2010.

My purpose here is not to dismiss Mr. Gomez’s chances. The most recent poll shows a fairly close race in Massachusetts, with Mr. Gomez trailing the Democratic candidate, Representative Edward J. Markey, by just four percentage points. But I want to examine Mr. Gomez and this special election in a broader context. The 2010 Senate race in Massachusetts is one point of comparison — but so are the 2012 elections, and so is the evidence from the dozens and dozens of Senate races across the country in recent years.

Our model for forecasting Senate races looks at a number of “fundamental” factors along with the polls. As the election date draws closer and the volume of polling increases, the model puts more weight on the polls, even if they are in defiance of the fundamentals. Early in a race, however, when the campaign has not begun in earnest, the polls may not be very reliable.

The fundamentals calculation is based on an analysis of all November Senate elections from 1990 to 2010. It includes seven factors, although two are specific to elected incumbent candidates and do not apply to the Massachusetts race. Another factor reflects a coattail effect from presidential voting in the state, which is also not applicable in a midterm or special election, when there is no presidential race. A fourth factor is the national political environment, as measured by the generic Congressional ballot. However, this environment appears to be roughly neutral right now: neither party has had a consistent lead on the generic ballot.

That leaves three factors to consider: the candidates’ ideological positioning relative to the voters in their state, their fund-raising totals and their history of being elected to public office.

The bad news for Mr. Gomez is that these factors suggest he is a significant underdog in the race. In fact, the fundamentals calculation would project him to lose the special election by about 15 percentage points — considerably larger than his current deficit in the polls.

The good news for Mr. Gomez, in addition to the fact that the fundamentals calculation gets its share of close races wrong, is that this is a preliminary estimate. Two of the three factors are malleable to some degree: he has time to raise more money and build a better infrastructure, and he may have more room than most candidates to calibrate his ideological positions. His lack of experience running for elected office is a problem, but it’s possible that Mr. Gomez has other strengths that might outweigh it. Let’s examine each of these factors in more detail:

Fund-raising. Of the 15-point lead that the fundamentals model assigns to Mr. Markey, eight points are attributable to his edge in public fund-raising. Mr. Gomez reported raising about $600,000 in individual contributions before the special primary. By contrast, Mr. Markey reported raising $4.2 million in individual contributions as of April 10.

Mr. Gomez, a successful private equity investor, loaned about $600,000 to his campaign in addition to his public fund-raising. Our models for forecasting Congressional results, however, focus on public contributions only, as opposed to self-financing, independent expenditures or transfers from other candidates or party committees.

The reason for this is that, in addition to enabling candidates to spend more money on their races, fund-raising totals are a useful indicator of their overall strength as a candidate. Robust individual contribution totals are a measure of grass-roots support in a way that self-funding is not. Candidates who rely heavily on self-funding have a poor electoral track record. In addition, raising large amounts of money from individuals usually requires a professional campaign infrastructure, so these public funding figures can serve as an indicator of a campaign’s organizational strength.

This is not to say that Mr. Gomez’s ability to contribute money from his own pocket will be of no help to him. But if there is one thing to watch in the next couple of weeks, it will be how much financial support he receives from rank-and-file Republicans. In 2010, Mr. Brown’s fund-raising was spectacular after he became the Republican nominee. He had raised about $15 million in individual contributions by the special election date, roughly double Ms. Coakley’s $7.3 million. That was a sign that something special was going on.

Electoral Experience. Our analysis of Senate races suggests that electoral experience has some predictive power, even after controlling for other factors like fund-raising. Specifically, the model rates candidates on a four-point scale based on the highest office they have been elected to in the past. The highest tier is for candidates who have been senators or governors. The second highest tier is for United States representatives like Mr. Markey and for holders of elected statewide offices other than governor, like secretaries of state and attorneys general.

The lowest rank is for candidates like Mr. Gomez who have never won elected office. (Indeed, Mr. Gomez has never run before.) In the fundamentals model, the experience gap is worth roughly five percentage points for Mr. Markey.

Republicans can hope that Mr. Gomez is a quick study. But his inexperience increases the risk of gaffes and missteps, and he will be under more pressure now that the race is attracting more scrutiny. There are some attractive components to Mr. Gomez’s biography: in addition to his business experience, he is a former Navy SEAL. Still, there have been plenty of candidates with impressive military credentials (like retired Gen. Wesley K. Clark) or business credentials (like the former eBay chief executive Meg Whitman) who fell flat on the campaign trail. Mr. Gomez’s favorability ratings are good so far — in part because of his biography, no doubt — but he might not maintain them if he struggles through interviews, stump speeches or debates.

Ideological Positioning. Isn’t all of this focus on Mr. Gomez’s fund-raising and experience obscuring a more basic problem: that he is a Republican seeking election in Massachusetts?

Certainly, Mr. Gomez would have little chance of winning if he were running on a conventional Republican platform. However, he has quite explicitly positioned himself as a moderate: he has endorsed same-sex marriage, for instance, and taken views to the left of much of his party on gun control and immigration reform. By contrast, Mr. Markey is a fairly conventional Massachusetts Democrat, which means that he is quite liberal.

The way we evaluate a candidate’s ideological position is by comparison to the voters in his state. In each state, we calculate an “ideal point” — where a candidate would position himself on the left-right spectrum if he wanted to maximize his chances of winning the general election, other factors being equal. (The ideal point can also be thought of as an estimate of where the median voter is in the state.) The further a candidate is from this point, the more harm he does himself.

In Massachusetts, the ideal point is quite a bit to the left of the rest of the country. Still, it is slightly to the right of Mr. Markey and most other Democrats. In more precise terms, we estimate it to be -0.277 on the scale used by the statistical system DW-Nominate, where a score of negative one represents an extremely liberal candidate and positive one an extremely conservative candidate.

Our method of calculating Mr. Markey’s ideology, which reflects a combination of DW-Nominate and two other systems, puts him at -0.458. This isn’t especially far from the median voter in Massachusetts, but Representative Stephen F. Lynch — the more conservative Democrat, with a score of -0.349, whom Mr. Markey defeated in the primary — would have been somewhat closer to it.

What about Mr. Gomez? Only one of the three systems that we use to evaluate ideology, his public statements as evaluated by the Web site OnTheIssues.org, is available in his case, and it puts him in the exact middle of the ideological spectrum. Mr. Markey is slightly closer to the Massachusetts ideal point, but the difference is minor, and translates into only a two-percentage-point advantage for Mr. Markey, other factors being equal.

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We need to acknowledge, however, that Mr. Gomez’s ideology is hard to pinpoint. As I mentioned, only one of the three statistical systems is available in his case, and that score is based on a relatively thin record of public statements.

In some ways, this makes Mr. Gomez’s task easier than Mr. Brown’s was last year, and more like Mr. Brown’s in 2010. Mr. Gomez does not have a Congressional record to defend in a state where almost any history of Republican party-line voting could harm him.

So how can Mr. Gomez win? First, he needs to continue to run toward the center, or even the center-left, of the ideological spectrum. Next, he must overcome his inexperience and avoid gaffes on the campaign trail. Finally, it would be a positive indicator if he had at least some of the fund-raising surge that Mr. Brown had in 2010. Mr. Gomez is very unlikely to match Mr. Brown’s $15 million, but if he were able to bring in one-half or one-third of that amount, it would be a sign that he was tapping into some of the same enthusiasm as Mr. Brown. It would also help him achieve more parity in advertising and, perhaps, build more of a voter targeting and turnout operation.

This is not an easy set of tasks for Mr. Gomez. Among other problems, positioning himself more toward the center-left could make it harder for him to win financial support from Republican activists.

But what Mr. Brown’s victory in 2010 shows is that Republicans can win Congressional elections in blue states if just about everything goes right. That Mr. Brown’s election also came in Massachusetts, or that it also came in a special Senate election, is not especially relevant: the same principle would apply to a November Senate election in Illinois or to a House race in a Democratic district in California.

However, these instances are rare. Mr. Gomez is capable of winning, but his roughly five-point deficit to Mr. Markey in the polls now could also prove to be a high-water mark.