Depending on how you slice the numbers, Herman Cain may now be leading, or tied for the lead, in polls of Republican primary voters.

Polling averages still have Mr. Cain in third place, slightly behind Mitt Romney and Rick Perry. That obscures, however, a substantial shift toward Mr. Cain over the course of the past two weeks.

Pew Research, for example, had Mr. Cain with just 8 percent of the vote and Mr. Perry at 23 percent in polling conducted from Sept. 22-25 immediately after the most recent Republican debate. But Mr. Cain was up to 18 percent of the vote, with Mr. Perry down to 15 percent, in polling over Oct. 1-4.

Treating these Pew surveys as separate polls and combining them with other credible polls of Republican voters (including the Economist/YouGov poll but not another Internet-based survey that does not have a scientific methodology) shows clear evidence of a trend toward Mr. Cain. If you draw a simple linear trendline based on these surveys, he’s now at about 21 percent of the vote, tied with Mr. Romney, with Mr. Perry having fallen to about 12 percent.



As Mr. Romney’s numbers are essentially the same as they were before the Sept. 22 debate, Mr. Cain’s gains have come at Mr. Perry’s expense. A day or two after the debate, I wrote that I thought Mr. Perry’s problems were a bit overblown. That looked like a wise conclusion initially, as the first two polls released just after the debate — a CNN survey and the first installment of the Pew poll — had Mr. Perry with a healthy 23 percent of the vote. The near-continuous chatter about Mr. Perry’s performance in subsequent days, however, has taken a huge toll on his numbers — to Mr. Cain’s benefit.

The bettors at the political futures market Intrade are not sold on Mr. Cain’s surge, however. At this writing, they have him with a 9 percent chance of winning the G.O.P. nomination. That’s up significantly from before the last debate, when Mr. Cain’s chances were implied to be under 1 percent. But Mr. Cain still lags significantly behind Mr. Romney, who is given a 58 percent chance of winning the nomination, and Mr. Perry, who is assigned a 20 percent chance.

It’s probably right for these bettors to take a longer-term view of the nomination process. Newly won support is often soft, so a poor performance in one of the next two debates, or some sort of gaffe on the campaign trail, might send Mr. Cain’s numbers back down again. And polling has been unusually volatile in this election cycle so far. Believe it or not, there have been 10 G.O.P. candidates who have led at least one poll of Republican voters since Jan. 1: Mr. Cain, Mr. Romney, Mr. Perry, Sarah Palin, Chris Christie, Newt Gingrich, Michele Bachmann, Donald Trump, Rudolph W. Giuliani, and Mike Huckabee.

In May, another point in time when Mr. Cain’s numbers had looked to be on the upswing, I had written a long piece explaining why his chances of winning the nomination should not be dismissed. The article noted that Mr. Cain was polling reasonably well despite limited name recognition, a sign of upside potential for candidates in past primary races.

That remains true today: Mr. Cain is now polling in the high teens or low 20s despite name recognition of only about 55 percent. If the remaining half of the Republican electorate likes him as well as the half that has gotten to know him so far, he could be quite formidable.

At the same time, Mr. Cain — having never held elected office and having run for it just once — lacks the credentials of a traditional nominee. One can make a case that this is an asset as well as a liability, given the across-the-board distaste for traditional politicians of any kind right now, as well as the fact that having served in office gives voters more of a track record to pick apart.

There is reasonably persuasive evidence, however, that endorsements from party officials have a significant amount of predictive power in determining the identity of a party’s nominee, even after accounting for polling. On that score, Mr. Cain is doing quite poorly. As of Sept. 23, Mr. Cain had just a handful of endorsements, versus dozens for Mr. Romney and Mr. Perry.

So here is one test to see whether Mr. Cain is a long shot — or a big shot. Will he begin to receive more endorsements from Republican elected officials, and key party officials in states like Iowa and New Hampshire, in the coming days?

Mr. Cain has begun to get more attention from Republican opinion-makers: The Wall Street Journal had an editorial that was favorably disposed toward him on Wednesday, for instance. Writers and talking heads, however, can change their opinion on a moment’s notice, and can usually count on their readers and viewers having short memories. A formal endorsement is more of a commitment, and Mr. Cain has seen very few of those so far.

The other litmus test is Iowa, where there have been few credible polls conducted in recent weeks. But the former leader in Iowa, Mrs. Bachmann, has since seen her numbers slump badly in national polls. Tim Pawlenty has dropped out of the running, meanwhile, while Mr. Romney has yet to fully commit to the state for fear of raising expectations.

That would seem to open the door for Mr. Cain. Mr. Cain has also sought to play down expectations in the state after a disappointing fifth-place finish in the Ames Straw Poll in August. But if a candidate that fits Mr. Cain’s profile — nontraditional, insurgent, but conservative — has any real chance of winning the Republican nomination, you would think that they also ought to do well in Iowa, which has historically rewarded candidates who fit that description.

Mr. Cain’s winning Iowa would be a potential game-changer. Iowa has not historically been as important for Republican voters as for Democrats, but a win there would give rank-and-file Republicans — many of whom like Mr. Cain but are not convinced that he is viable — confidence that a vote for him would not be wasted.

Also, although I don’t mean to bring race into the equation any more than is necessary, voters in one of the nation’s whitest states picking an African-American man to be their presidential nominee would be a big deal — echoing, in some ways, the lift that Iowa Democrats gave Barack Obama in 2008.

If Mr. Cain does not win Iowa, though, someone else will. If that person is Mr. Romney, he will probably also follow it up with a win in New Hampshire, making him an overwhelming favorite in the nomination race. But if that person is Mr. Perry, we might see a long, drawn-out contest between him and Mr. Romney — something that seemed very likely a few weeks ago and remains reasonably likely now. In either case, Mr. Cain would again be reduced to the second tier of candidates, at best.

One can imagine a situation in which Mr. Cain finishes a strong second in Iowa behind a candidate like Mrs. Bachmann, Ron Paul or Rick Santorum, then rebounds to win South Carolina or Florida. But this is a much harder path than winning Iowa outright. So look to the Iowa polls, and to the endorsement scorecard, to get a better sense for his chances.