In early May, when we last checked in on the Massachusetts special election for United States Senate, I noted that while the Republican nominee, Gabriel Gomez, had an outside chance of upsetting the Democrat, Representative Edward J. Markey, the fundamentals ran strongly against an inexperienced candidate in such a blue state. Instead, I wrote, the roughly five-percentage-point deficit that Mr. Gomez had against Mr. Markey in the polls at that time “could also prove to be a high-water mark.”

In fact, Mr. Markey now leads by margins ranging from 7 to 11 percentage points in a series of recent nonpartisan polls. With the vote to be held in just eight days, on June 25, Mr. Gomez’s chances for a victory are even slimmer than before.

How likely is a candidate to overcome a polling deficit in the range of nine percentage points with so little time remaining in the campaign? I searched through our Senate polling database, which covers all November elections for Senate between 1990 and 2012, looking for those candidates who overcame the largest deficit in the polls with 10 days to go in the race. (I limited the search to cases where it was actually possible to construct a polling average rather than relying upon a single poll — meaning those where there had been at least two polls in the field late in the race.)

The award for the largest comeback belongs to Paul Coverdell, the Republican candidate in the Georgia election for Senate in 1992. Mr. Coverdell overcame a huge polling deficit to defeat the Democratic incumbent, Wyche Fowler Jr., having trailed him by 24 percentage points with a month remaining in the campaign and by roughly 19 percentage points in the polling average with 10 days to go. However, Mr. Coverdell’s win requires an asterisk of sorts, as Mr. Fowler took the narrow plurality of the vote on Nov. 3, 1992, triggering a runoff that Mr. Coverdell won three weeks later.

Another large comeback in 1992 involved the Republican incumbent from New York, Alfonse M. D’Amato, who trailed the Democratic candidate and state attorney general, Robert Abrams, by nine percentage points in the polls with 10 days remaining. But with Mr. Abrams fighting a series of campaign missteps, Mr. D’Amato held his Senate seat.

In Georgia’s Senate race in 2002, the Republican candidate, Saxby Chambliss, trailed the Democratic incumbent, Max Cleland, by eight percentage points in the polling average with 10 days remaining in the race. But Mr. Chambliss wound up winning by a clear margin, roughly seven percentage points. (It’s possible that this reflected a case of social desirability bias as some voters were reluctant to tell pollsters about their plans to vote against Mr. Cleland, a triple amputee and war hero.)

So such last-minute comebacks are not impossible. But they are unlikely — these results are plucked from a database that covers approximately 400 Senate races. From an actuarial perspective — based on an analysis of the accuracy of the polling average in each of the several hundred races — the probability of winning a race after trailing by nine points with 10 days to go in the campaign is on the order of 5 percent.

All of these results, however, are from general elections in November, and not special elections that are held at odd times of the year. There are some reasons to think that special elections are associated with more uncertainty in the polling. First, special elections often have low turnout. As a rule, the lower the turnout, the higher the probability of a polling error, because the polls are more likely to misidentify who actually shows up to vote.

Second, special elections typically take place within a compressed time window, so voters may be slower to make their decisions and more reactive to developments late in the campaign.

In the Massachusetts special election for Senate in 2010, the Republican candidate, Scott P. Brown, pulled into a one-point lead against the Democrat, Martha Coakley, in a poll with 10 days to go in the race. However, Mr. Brown had trailed Ms. Coakley by margins ranging from 9 to 17 percentage points in polls just a week or so earlier.

In the 2010 race, however, there was at least one important indicator that testified to Mr. Brown’s potential even before he pulled ahead in the polling average. That year, Mr. Brown had raised $15 million in individual contributions as of the special election date, considerably more than Ms. Coakley’s $7.5 million.

This year in Massachusetts, Mr. Gomez reported just $2.1 million in individual contributions as of his June 5 Federal Election Commission report (not counting donations that Mr. Gomez made to his own campaign). That compares unfavorably against Mr. Markey, who had brought in $6.8 million as of the same date.

Our fundamentals-based model, which evaluates the public fund-raising totals along with other factors, like the ideological positions of the candidates relative to the state, would now project Mr. Markey to win the contest by roughly 12 percentage points, not far from the recent polls.

By contrast, the same model would have seen the 2010 race as a tossup by this point in the campaign on the basis of Mr. Brown’s superior fund-raising totals and the national political environment, which had already come to be Republican-leaning. This year, while President Obama’s approval ratings have been under some recent pressure, it is less clear that this has implications for Congressional races. The most recent “generic ballot” polls have shown either a rough tie between the parties in voter preferences for Congress, or Democrats very slightly ahead.

In short, it is difficult but not impossible for a Republican to win a Senate seat in Massachusetts in a normal political environment. And it is difficult but not impossible for a candidate to overcome a nine-point deficit in the polls at this point in the campaign. For a candidate to do both things – when the fundamentals and the polls both point against him — is more unlikely still. Although some news accounts had been describing the race as a tossup until recently, Mr. Gomez’s odds of prevailing are remote — probably no more than 10 percent even under optimistic assumptions for his campaign.