A week after the news broke of the American raid that killed Osama bin Laden, bettors at Intrade, a political futures market, are barely any more likely to think that President Obama will win re-election.

As of this writing, Mr. Obama’s Democrats are given a 60.3 percent chance of winning next year’s presidential election. By contrast, the day before Bin Laden was killed, the market’s estimation of the Democrats’ chances had been 59.7 percent. That’s less than a full percentage point worth of improvement. Is this the appropriate reaction?

The “bounce” in Mr. Obama’s approval ratings has been fairly small — probably about 5 or 6 percentage points on average, although with some variability from survey to survey. I had been expecting a somewhat larger reaction.

At the same time, as I’ve repeatedly advised, the bounce is not necessarily the right lens through which to perceive the long-run electoral impact of the news.

The attraction of bounces is that they seem easy to quantify. Mr. Obama’s approval rating in the Gallup tracking poll improved from 46 percent before the Bin Laden announcement to a peak of 52 percent, before ticking down to 51 percent, where it remains now. A few other things have been going on — the release of Mr. Obama’s long-form birth certificate, the tornadoes in Alabama, various economic reports and so forth. But the Bin Laden coverage (rightly) has dominated the news, and there’s no doubt that most of the movement in Mr. Obama’s polling is attributable to it.

As time passes, however, the bounce will become blurrier, for two reasons. First, its magnitude will become smaller. And second, other events will intervene, and will either favorably or unfavorably affect Mr. Obama’s numbers.

Perhaps if we were able to control for all the other factors, the bounce would look something like this:

That is, Mr. Obama’s approval rating would initially spike by 5 or 6 percentage points, before gradually reverting back, after some weeks or months, to almost where it had been originally. But it would not quite come all the way back; instead, Mr. Obama would realize a small, but essentially permanent, 1-point gain in his approval rating.

Things won’t look quite this neat in practice, however. Imagine, for example, that within the next couple of weeks, Greece defaults on its debt and this sets off a major, 2,000-point selloff in the Dow Jones Industrial Average. This negatively affects Mr. Obama’s numbers. If so, the trajectory of his approval rating might look something like this:

If this scenario transpires, pundits will no doubt conclude that the “Bin Laden bounce” has been short-lived. What they can’t know, however, is what Mr. Obama’s numbers would have looked like had he not caught Bin Laden. Perhaps they’d be even worse still — and look something like the red line in the chart below.

It’s also possible that Mr. Obama will get some good news instead. Perhaps NATO forces will capture Col. Muammar el-Qaddafi. Perhaps he will “win” the confrontation with the Republicans over the federal debt ceiling. And then, once we reach the second half of the year, the economic figures come in a little stronger than expected. If so, the trajectory of his approval rating might look like this:

In this scenario, the conventional wisdom would be just the opposite. Killing Bin Laden would be regarded as the turning point of Mr. Obama’s entire presidency, and the bounce would look as though it had never faded — when in reality, killing Bin Laden will have been a relatively minor factor, and Mr. Obama’s approval rating would have been bound to improve with or without it:

Because of ambiguities like these, we’re never going to have an exact idea of the impact of Bin Laden on Mr. Obama’s re-election prospects. I’m not sure that we’ll ever even have an inexact idea — there are too many other factors to untangle.

Nevertheless, I think a fairly straightforward case can be made that betting markets like Intrade are underestimating the political impact of Bin Laden’s death. It goes something like this:

First, Americans think killing Bin Laden is a reasonably big deal.

Second, the vast majority of Americans give Obama at least some credit for having initiated the special forces mission that resulted in his death.

Third, foreign policy and national security issues do affect presidential voting decisions. Their impact will probably be muted in the 2012 election because of the focus on the economy, but that doesn’t mean they’ll have no impact at all.

Fourth, there is almost no American voter who will think worse of Mr. Obama for having killed Bin Laden. Nor is it likely that killing Bin Laden could boomerang around to hurt him. (It could, I suppose, set off a retaliatory terrorist attack, but it’s not obvious what the electoral impact of that might be.) Electorally speaking, it represents pure upside.

Fifth and most importantly, small but permanent changes in Mr. Obama’s approval rating could make a relatively large amount of difference in his re-election odds.

I’ve hypothesized — and to be clear, this is just a guess — that killing Bin Laden might provide Mr. Obama with a permanent gain of one percentage point in his approval rating, which will be left over after the initial bounce fades. Since almost all people who approve of a president vote to re-elect him, this would increase Mr. Obama’s share of the vote in November 2012 by one percentage point, while decreasing his Republican opponent’s share by roughly the same margin.

In the 35 presidential elections since the Civil War, there have been 9 elections (1876, 1880, 1884, 1888, 1916, 1948, 1960, 1976, 2000) in which the losing candidate would have won the electoral vote had he received 1 percentage point more of the vote in each state, and his opponent 1 percentage point less. That’s a pretty frequent occurrence — it’s happened 26 percent of the time.

What this means is that if a presidential candidate were spotted an additional 1 percentage point “bonus” in each state at the expense of his opponent, he would win in the Electoral College an additional 13 percent of the time. (Why 13 percent and not 26 percent? Because among the close elections, the candidate is already on the winning side half the time, in which case the bonus votes would be superfluous.)

Now, I don’t mean to suggest that Mr. Obama’s odds of winning re-election have improved by 13 percent. A formal model would need to be far more sophisticated than this. More importantly, the notion that Mr. Obama’s approval ratings will enjoy a permanent one percentage point improvement is just a hypothetical.

But if the killing of Bin Laden produces any lasting impact on Mr. Obama’s approval rating at all — 2 percentage points, 1 point, even half a point — that translates into a relatively material improvement in his re-election odds, considerably more than the mere decimal-point increase that bettors at Intrade have posited. Unless those bettors are quite certain that the news about Bin Laden will have almost literally no long-term effect, they were either overvaluing Mr. Obama’s stock before or are undervaluing it now.