In the wake of his improved debate performance, President Obama’s recovery is now apparent. It is most clear when viewed in terms of the Meta-Analysis of state polls. Over the last four days, the Popular Vote Meta-Margin – the amount of swing it would take to create an electoral near-tie – has moved by over 1.0%. Today, the President’s effective lead, using Electoral College mechanisms, is Obama +1.8%. A rapid move like this can continue for a few days as polls catch up with the nation’s mental state.

But why do national polls continue to look so close, and in about half of cases good for Mitt Romney? To answer that, let’s take a look back at the effects of all three debates so far.

This is a graph showing the average national margin during a 4-week period when 50 national polls were taken. (If you wonder why poll aggregation is needed, that fact alone answers it.)

The graph is easier to interpret than most aggregates (compare with RCP and Pollster). To calculate it, I spread out each poll’s data across days when the pollster made contact. For example, the ARG Oct. 11-14 poll is split across four days. To capture the Debate #1 change, I left out a few polls where contacts were equally spread before and after October 4. The gray zone is the 1-sigma confidence interval.

The post-debate-1 correction was a nearly five-point swing. It was complete within one day. This means that the post-debate-day media meltdown could not have caused the swing – though it certainly helped cement perceptions.

What caused this crash? Considering the polarization of voters this year (only a small fraction are persuadable), it seems likely to be caused by a change in morale on both sides: hope among Romney’s supporters and despair among Obama supporters, and a consequent change in whether they meet the criteria for being a “likely voter.” Imagine that an Obama supporter was 60% likely to vote before Debate #1, and then 57% afterward – and vice versa for a Romney supporter. That could fully account for the change.

There could also be some fraction of voters whose minds were changed by suddenly-moderate-Mitt and stumbling-Barack.

Since that time, there’s been a reversal in the direction of change. On October 5, Romney had a narrow lead, about 1.0%. Today, President Obama is back in a razor-thin lead at the national level – about 0.5-1.0%.

Because the race is so close, individual polls will inevitably be all over the place. And news organizations love the outlier data points, like the Gallup poll showing Romney +6%. I find this to be a particularly unattractive trait in media coverage. It was what led me to start the poll meta-analysis in 2004.

But here is something interesting. National polls do not match the state polls – and it is state races that determine the outcome, via the Electoral College. In the Meta-Analysis that Andrew Ferguson and I report on this website, Obama has been ahead all along.

You can see this especially clearly in the Popular Vote Meta-Margin, which I have defined as the amount of voter swing needed to create a tossup as defined by the Electoral College. It is an extremely sensitive measure, precise to within 0.2-0.5%.

Here is what it looks like. I shifted it one day to the left to match the national-poll data. The general pattern is clear: viewed through polls that focus directly on electoral mechanisms, Obama performs 1-2 points better than in national polls.

The likeliest cause of this discrepancy is that in states where it matters most such as Ohio, Nevada, and Colorado, the two candidates are genuinely overperforming/underperforming. Also, as I noted in 2008, winners in non-swing states often outperform polls. So there is some question about the accuracy of likely-voter screens when a local result is very unequal. Which leads us back to state polls as a better measure of the race.

In this graph the Meta-margin appears to be a lagging indicator. However, it’s not an apples-to-apples comparison, since I am showing the calculation as it unfolded, day by day. It can move quickly if more state polls are reported – as has occurred since Debate #2.

I will be interested to see if on Election Day, the national vote and the electoral vote count still show this discrepancy. If both are accurate, President Obama’s re-elect probability is about 90% – but his probability of winning the popular vote is lower, about 70%.

Update: for hobbyists, the MATLAB source code is here.