Arguably for most of the referendum campaign the polls have served to take some of the energy out of the referendum campaign.

After all, although they persistently disagreed significantly about how far the No side were ahead, all the polls agreed that a majority of Scotland's voters were minded to vote to stay in the Union.

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But those days are over. As polling day began to loom last weekend, one company broke from the consensus and put the Yes side narrowly ahead. The result has been panic in unionist-supporting newspapers and the biggest grin yet on Alex Salmond's face.

Not least of the reasons why the polling that put Yes ahead has created waves is that it came from a company, YouGov, that hitherto has been one of the most pessimistic so far as the prospects for the Yes side are concerned.

As recently as the beginning of August the company suggested that, after undecideds were excluded, just 39% were going to vote Yes while 61% were backing No. Indeed YouGov was the only company during the summer to put the Yes vote below 40%.

But then in a sequence of three polls conducted later in August and into early September, the estimated Yes vote in YouGov's polls increased to 43%, then 47%, and finally 51% at the weekend. So, far from being an isolated reading that perhaps could easily be dismissed as a 'rogue', the weekend poll was one of a sequence that suggested the Yes camp was continually gaining significant ground.

That, and the fact that the poll came from a company that had hitherto tended to paint a pessimistic picture for the Yes side, inevitably meant that it was widely interpreted as demonstrating that the state of the referendum race had fundamentally changed from a one horse race into a contest that is too close to call.

Seemingly to underline the point another polling company, Panelbase, reported at the same time that Yes were on 48%, No on 52%.

True, that reading implied the No side were still ahead, but only by less than the margin of potential error associated with any poll. In short, this poll too was telling us that the referendum now looks too close to call. However, this poll also directly contradicted YouGov's in one important respect. Hitherto the company that had tended to paint the most optimistic picture for the Yes side, Panelbase had already suggested in the middle of August that the Yes side were on 48%. Indeed, they had first come up with that figure as long ago as June. In other words, Panelbase had failed to detect any movement to Yes during the last few weeks at all!

However, yesterday another of the companies that previously was also suggesting that No were well ahead, TNS BMRB, now also agrees that the two sides are evenly matched, with both Yes and No on 50%. That represents an eight point swing since the company's previous poll in July, only a little less than the swing registered by YouGov. In part what may be happening is that previously divergent polls are simply be converging but even so, what they are coming to agree on is that the race is now very tight.

Consequently the prospects for the Yes side have never looked brighter. Altogether five of the six companies that have been polling regularly during the campaign, in their most recent reading put the Yes vote on at least an equal record high. In the other case, Yes support was only a little below that company's high.

Thus, as our first graph shows, at 46% the average level of support for Yes in all of the polls conducted since the first of the two televised leaders' debates at the beginning of August is two points higher than at any previous period during the campaign.

Mr Salmond's stumble in the first of those debates has certainly not proven to have inflicted any long-term damage on the Yes campaign while his more assured performance in the second debate may perhaps have even helped boost its support.

But why have the Yes side apparently made such progress?

Previous research has found that nothing seems to matter more in persuading voters to choose Yes or No than their views of what the economics of independence would be.

And according to YouGov at least, many a voter has changed their mind on that issue in recent weeks. As recently as June, just 27% thought that Scotland would be economically better off under independence, while no less than 49% thought it would be worse off - figures (as our second graph shows) not dissimilar to what the company had found on various occasions during the course of the last three years.

Now, however, almost as many people (40%) say the country would be better off as believe it would be worse off (42%). Certainly, if the Yes side is to make further progress and move securely past the 50% mark there is little doubt that this is an argument that they will have to carry on winning.

It is, of course, an argument that the No side thought it could win by its insistence that an independent Scotland would not be able to keep the pound as part of a monetary union with the rest of the UK.

However, as much as Better Together insists this would be the case, its claim is widely and perhaps increasingly disbelieved. Last month Survation reported that just as many (40%) believe the claim is a 'bluff' as think it is not (39%). Now YouGov say that the proportion who think it is a bluff has risen to 51%, after having been no more than 39% shortly after George Osborne made the original announcement back in February.

Perhaps the lesson for both sides is that the most precious commodity in a referendum that invites voters to choose between two uncertain futures is credibility - and that therefore the temptation in the final days of the campaign to make ever more lurid claims about what would happen following a Yes or a No vote may be best avoided.

Otherwise, the voters may just stop listening.

John Curtice is professor of politics, University of Strathclyde, and chief commentator at whatscotlandthinks.org, where a comprehensive collection of referendum poll data can be explored.