When is it rational to take a big risk?

When the status quo isn’t proceeding in a way that you feel is favorable. When you have less to lose. When you need — pardon the cliché, but it’s appropriate here — a “game change.”

When a prudent candidate like Mitt Romney picks someone like Representative Paul D. Ryan of Wisconsin as his running mate, it suggests that he felt he held a losing position against President Obama. The theme that Mr. Romney’s campaign has emphasized for months and months — that the president has failed as an economic leader — may have persuaded 47 or 48 or 49 percent of voters to back him, he seems to have concluded. But not 50.1 percent of them, and not enough for Mr. Romney to secure 270 electoral votes.

That reading may be correct. National polls tell different stories about the state of the race — but most have Mr. Obama ahead. Polls of swing states have been a bit more consistent. In states like Ohio, Mr. Obama’s lead has been small — but it has been steady and stubborn.



The economy? Well, it isn’t very good. But it also doesn’t appear to be getting much worse, and some recent signs — like the July jobs report — suggest a slight brightening of the outlook. It’s not quite the case that incumbent presidents are favored to win unless there is an outright recession, but that also isn’t that far from the truth. Incumbent presidents tend to get the benefit of the doubt from voters, especially when, as in Mr. Obama’s case, they are regarded as likable, their party is in its first elected term, they are perceived as competent on foreign affairs and they have avoided major scandals.

The forecast model I developed for FiveThirtyEight, which accounts for state and national polls and the condition of the economy but not other factors, estimated as of Friday that Mr. Obama was about a 70 percent favorite to win re-election. Betting markets and bookmakers have been slightly more equivocal, but have also had Mr. Obama ahead, generally giving him between a 60 and a 65 percent chance of winning a second term.

Either prediction allows for plenty of winning scenarios for Mr. Romney. Even three months out, the economy is very difficult to forecast. With a growth rate of only 1.5 percent in the second quarter, a blowup in Europe, or in the Middle East, could send it back into recession.

Even without that, there are still some undecided voters left: not many, but a few. It is not the case, as a general rule, that undecided voters tend to break against the incumbent. (You can safely ignore someone on your television set who says the opposite: they haven’t done the research.) But it’s also not necessarily the case that the undecideds will split evenly. In some elections, one candidate (either the incumbent or the challenger) wins most of them. It could be Mr. Romney, especially since his campaign figures to have more money to spend on advertisements in the remaining months.

And as for the voters who had seemed to have made up their minds — well, we think we know what they are going to do, but we are not sure. Polls are imperfect instruments, especially at a time when even the best pollsters struggle to get more than 10 percent of Americans to return their calls. And no pollster is perfect at forecasting exactly who will turn out to vote.

That ambiguity, however, also presents the opportunity to read the evidence in jaded or biased ways. Mr. Romney’s campaign could have cherry-picked the polls that showed him ahead, the worst economic statistics, the most favorable historical precedents, and concluded that it was a favorite.

Evidently, it did not do that. The ability to perform an honest self-assessment is rare for all of us. Mr. Romney, in making this outlook, may have been aided by his background in seeking to turn around distressed companies.

Why am I concluding that Mr. Romney would have chosen Mr. Ryan only if he felt he was losing? Because from a Politics 101 point of view, this isn’t the most natural choice.

Vice-presidential choices are inherently risky to a degree, but the risks are asymmetric, and weighted toward the downside: It’s far easier to name choices who undermined campaigns than those who helped them. The best way to mitigate that downside risk is to select someone who has been tested on a national stage before, ideally by having run for president themselves — or failing that, by having been elected multiple times from a large and diverse state.

Mr. Ryan is a national figure of some repute — before Saturday morning, his national name recognition was about 50 percent — but he has never been elected to anything larger than his Congressional district of about 700,000 people. Members of the House of Representatives have only occasionally been selected as running mates. The last one on a winning ticket was John Nance Garner, the speaker of the House, in 1932. The last time an ordinary member of the House was elected vice president, and the last Republican, was more than 100 years ago: in 1908, when William Howard Taft and James S. Sherman, a New York congressman, were chosen by voters. (Coincidentally, that fall was also the last time that the Chicago Cubs won the World Series.)

Politics 101 suggests that you play toward the center of the electorate. Although this rule has more frequently been violated when it comes to vice-presidential picks, there is evidence that presidential candidates who have more “extreme” ideologies (closer to the left wing or the right wing than the electoral center) underperform relative to the economic fundamentals.

Various statistical measures of Mr. Ryan peg him as being quite conservative. Based on his Congressional voting record, for instance, the statistical system DW-Nominate evaluates him as being roughly as conservative as Representative Michele Bachmann of Minnesota.

By this measure, in fact, which rates members of the House and Senate throughout different time periods on a common ideology scale, Mr. Ryan is the most conservative Republican member of Congress to be picked for the vice-presidential slot since at least 1900. He is also more conservative than any Democratic nominee was liberal, meaning that he is the furthest from the center. (The statistic does not provide scores for governors and other vice-presidential nominees who never served in Congress.)

Can Mr. Ryan help Mr. Romney to carry his home state, Wisconsin? Possibly, but Mr. Romney is quite far behind in the polls there. And although Mr. Ryan has won by impressive margins in his home district, his popularity statewide is mixed, with 38 percent of voters having a favorable impression and 33 percent an unfavorable one throughout Wisconsin. Because of these factors, a recent analysis I performed placed Mr. Ryan 10th from among 14 potential vice-presidential picks in terms of his immediate impact on the Electoral College. If Mr. Romney wanted to make the best pick by this criterion, he would have been better off to choose an alternative like Senator Rob Portman of Ohio, or Gov. Bob McDonnell of Virginia.

Instead, however, Mr. Romney decided to change his strategy rather than to make a tactical choice. He wants to shake up the race, and I expect Mr. Ryan to do that.

Young, attractive and outspoken, Mr. Ryan will be loved by conservatives — and just as assuredly, detested by liberals. In a race that lacks compelling story lines and fresh faces, he may become the focal point. It seems entirely plausible that his rallies will draw larger crowds than either of the presidential candidates themselves, and that stories about him will draw more Internet traffic, especially in the early days of his candidacy. He should also be a fund-raising magnet — for Mr. Romney, and probably also for Mr. Obama.

Mr. Ryan’s controversial budget, which polls poorly, will obviously get much more attention than it had previously. The fate of the presidential race and the fate of Congressional races may become more closely tied together. Mr. Obama will no longer have to stretch to evoke the specter of Congress and its 15 percent approval rating. With Mr. Ryan on the opposing ticket, he will be running against a flesh-and-blood embodiment of it.

Taking risks like these is not what you do if you think you have a winning hand already. But Mr. Romney, the turnaround artist, decided that he needed to turn around his own campaign.

It’s going to take some time before we can reliably measure the impact of Mr. Romney’s choice. Vice-presidential picks sometimes produce “bounces” in the polls, especially when they are as newsworthy as this one, but they often fade after a few days or a few weeks. And the party conventions, which almost always produce polling bounces, are coming up soon.

I think there are other “bold” picks that Mr. Romney could have made — Senator Marco Rubio of Florida, for instance, or Gov. Chris Christie of New Jersey or Gov. Brian Sandoval of Nevada — where the balance of risk and reward would have been a little better. Some of these candidates, especially Mr. Rubio and Mr. Christie, would also have excited the Republican base. But they might also have had a more natural appeal to independent voters, and to demographic groups that Mr. Romney is struggling to win over.

Mr. Christie or Mr. Sandoval, also, or Mr. McDonnell of Virginia, would not have carried Mr. Ryan’s burden of being a symbol of a deeply unpopular Congress.

But at least Mr. Romney is taking a risk, something his cautious campaign had not been doing much of previously.