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What Are Paul Ryan’s Chances of Becoming President?

On Saturday when introducing his new running mate, Mitt Romney initially referred to Paul D. Ryan as the “next president of the United States.”

Mr. Romney quickly apologized for the slip-up, saying that he hoped that Mr. Ryan would become the next vice president instead. (Apparently, the stress of a vice presidential rollout can take its toll even on relatively unflappable candidates like Mr. Romney; Barack Obama made a similar slip when introducing Joe Biden four years ago.)

Of course, it’s not literally impossible that Mr. Ryan could turn out to be the 45th American president precisely (Mr. Obama is the 44th). It just couldn’t be through a sequence of events that Mr. Romney would be rooting for. Either the Republican ticket would have to win this year’s election — but with Mr. Ryan, not Mr. Romney, at the top of the ticket. Or, the more likely case: Mr. Obama would need to win the election and serve out his remaining four years, and Mr. Ryan would have to run for and win the presidency in 2016.

What, exactly, are the odds of one of these scenarios transpiring?

For that matter, what are Mr. Ryan’s odds of someday becoming president — whether he’s the 45th, 46th, 47th, or some later number in the sequence of people to hold the office?

Even more broadly, what does the future hold for running mates on winning tickets? And what about those on losing ones?

There are too many variables to compute these chances exactly, but we can make some reasonable guesses based on the historical record.

First, let’s consider the case that Mr. Romney would be most pleased with: that he and Mr. Ryan are the winning ticket in November, and Republicans re-capture the White House.

Twenty-eight men have been elected vice president since 1900, double-counting those (like George Herbert Walker Bush in 1980 and 1984) who were elected twice. Let’s give Mr. Biden a mulligan, since he hasn’t yet had a chance to seek an open nomination. That leaves us with 27 cases.

In the chart that follows, I’ve sorted the 27 winning vice presidents by the margin by which their ticket won the popular vote. Then I documented whether they sought the presidency in some subsequent election, whether they won a party nomination, and whether they were actually elected to the Oval Office.

The clear majority of winning vice presidential nominees — 21 of 27, again counting cases like Mr. Bush twice — ran for president themselves at some point. One qualification: the definition of what counts as “running” for president is a little fuzzy, especially in the era before presidential primaries were common. But I’ve applied a relatively liberal standard. For instance, the winning vice president under Franklin D. Roosevelt in 1940, Henry A. Wallace, gets credit for both running for and winning a party nomination in 1948 — although it was with the Progressive Party, and not the Democrats.

The elected vice presidents who failed to eventually seek the presidency had pretty good reasons for it. James S. Sherman, elected vice president to William Howard Taft in 1908, died during the course of the 1912 election when he and Mr. Taft were seeking another term. Spiro T. Agnew, the winning vice president in 1968 and 1972, resigned from office before his second term was completed. Charles Curtis, who was Herbert Hoover’s vice president in 1928, saw his ticket lose disastrously in the landslide of 1932. And Dick Cheney was exceptionally unpopular by the time that Republicans were planning for the 2008 election cycle.

Of the winning vice presidents who did run for the presidency, 13 eventually won their party’s nomination. This includes cases, like Lyndon Baines Johnson, of men who had ascended to the presidency before doing so, and ran for re-election as incumbents.

Even if you exclude those instances, however, you wind up with a batting average of close to 50 percent when former vice presidents sought their party nomination. That’s pretty impressive, considering that there might typically be a half-dozen viable candidates seeking an open nomination. Sitting vice presidents are, literally and figuratively, the “next in line” in their parties, and they can sometimes clear their fields of competition.

Finally, there were eight cases (counting Richard Nixon and the elder Mr. Bush twice each) in which the winning vice-presidential nominee was later a winning presidential candidate — or about 30 percent of the total.

Incidentally, there have been no cases since 1900 in which someone was elected vice president, and then ascended to the presidency after a death or resignation, without later being elected to another presidential term themselves. What about Gerald Ford? He succeeded Mr. Nixon in 1974, but then lost his bid for re-election in 1976. But Mr. Ford had also never been elected vice president; instead, he succeeded Mr. Agnew. So he’s excused on a technicality.

Put these bits of trivia aside. A very obvious (and intuitive) fact emerges from this data. Mr. Ryan is much more likely to eventually become president if he and Mr. Romney win this year’s election.

In fact, the track record of losing vice-presidential candidates is quite underwhelming. There are 28 of these cases since 1900. (We will count Sarah Palin even though we didn’t count Mr. Biden, since she had an open nomination this year but declined to seek it.)

Of these 28 men and women who lost their vice-presidential bids, only nine later ran for president. Only three of them later won their party’s nomination, and just one — Franklin D. Roosevelt — later won the presidency.

The losing candidates who later ran for president generally had one of two things in common. First, if their loss was very close, it did not seem to harm their reputations nearly as much. Of the eight vice presidential candidates whose tickets lost the election by 5 or fewer percentage points, seven actually did run for president at some later point. (The exception was Charles W. Fairbanks, who unsuccessfully sought the Republican presidential nomination in 1916, but did not seek the office again after his vice presidential bid also failed that November.)

The other circumstance is when a vice president on a losing ticket had previously been on a winning one. Walter Mondale and Dan Quayle, who later sought the presidency (although Mr. Quayle’s bid in 2000 was a flop), had won the vice presidency in 1976 and 1988, respectively, before losing it four years later.

The exceptional case is Mr. Roosevelt. He and the Democratic nominee for president, James M. Cox of Ohio, were decimated in the 1920 election, losing to Warren G. Harding and Calvin Coolidge by more than 26 perc
entage points.

But Mr. Roosevelt later came back to be elected president four times. So nothing can be ruled out.

Still, if Mr. Ryan fails to win the vice presidency this year, his political future should be aided substantially if he and Mr. Romney at least keep the margin respectable. If the Republicans lose the election by about 3 points — around what their deficit to Mr. Obama appears to be now — then Mr. Ryan will be able to claim that he at least did not do the ticket any harm.

A narrow defeat for Mr. Romney and Mr. Ryan, also, would still leave Republicans with decent-to-good chances to retain the House of Representatives. And it’s not impossible that they could take over the Senate, since there are quite a lot of seats in play, and since a good half-dozen of them are idiosyncratic cases that may come down more to local factors than the overall partisan tide.

If Republicans do reasonably well in these Congressional races but fail to win the presidency, some in the party may even claim — and it’s a logical enough case — that the problem was with the top of the ticket and not with Mr. Ryan.

A decisive loss, however — if Mr. Obama wins re-election by 5 percentage points more, potentially coming close to his margin of victory in 2008 — could substantially tarnish Mr. Ryan’s reputation. At that point, Mr. Romney will have gotten a worse result than his standing in the polls before he selected Mr. Ryan.

Furthermore, such a loss would be suggestive that there was something fundamentally wrong with the Republican candidates. Somewhat contrary to the conventional wisdom, most of the forecasting models put together by economists and political scientists predict either an essentially tied election, or a narrow win for Mr. Obama. (Why? Incumbents have historically gotten a lot of credit from voters. And voters have historically had short economic memories. If a case can be made that the economy is improving, the incumbent’s odds are decent, even if it is clearly not firing on all cylinders.)

But few of these models call for a decisive win for Mr. Obama. If he wins by 7 points or so with this economy, and with only break-even approval ratings, that will be more than getting the benefit of the doubt from voters. Instead, it would suggest that many voters felt they had no other choice, given an uncharacteristically poor Republican alternative.

With a margin in the mid-to-high single digits, also, Democrats would be clear favorites to retain the Senate, and the House of Representatives would be in play. Mr. Ryan would undoubtedly retain pockets of support within his party, but unless there were some other excuse for the loss (an unexpectedly good series of jobs reports, or an unexpected scandal involving Mr. Romney), he would be remembered as being part of a hugely disappointing election.

We can systematize this knowledge by performing a regression analysis on the historical data. For our technically-inclined readers: what I’ll be using here is a type of regression called ordered logit, which is appropriate when there is a hierarchy of categorical outcomes (running for president; winning the nomination; becoming president). The independent variables are the ticket’s margin of victory or defeat in the popular vote, a variable indicating whether they won the Electoral College and ascended to the White House, an interaction term between the two, and a time trend.

The interaction term serves to capture the asymmetry in the data. If you are elected vice president, it doesn’t seem to matter much what your ticket’s margin of victory was. Once you’re in office, you’re in, and it’s hard to predict what will transpire from there other than that your chances of someday becoming president have gone way up.

But if you lost the election as the vice-presidential candidate, keeping it close seems to make quite a bit of difference to your fortunes. That way, you can make a more credible claim that the problems with the campaign were isolated to a few issues or bouts of misfortune — none of them implicating your role in it, of course — rather than the whole thing having been a debacle and everyone associated with it being inherently suspect.

The inclusion of the time trend is more debatable. Over the past century or so, there has been a very modest tendency toward vice presidents remaining more active in presidential politics after they ran for the office. The variable isn’t statistically significant, but it coincides with a general increase in stature for the vice-presidential slot, so I think there is a theoretical basis for including it. But it only has an impact around the margin, raising Mr. Ryan’s odds just slightly.

The figure below reflects the actuarial odds of Mr. Ryan running for president, winning his nomination, and winning the election in some future November, conditional upon different margins of victory or defeat for him and Mr. Romney this year. You will notice that there is a kink in the graph. This is when Mr. Ryan and Mr. Romney go from losing this year’s election to winning it, and Mr. Ryan’s odds of becoming president some day increase sharply.

If Mr. Ryan and Mr. Romney lose the election by a single point, the equation estimates that Mr. Ryan still has better-than-even odds — 63 percent — of someday running for president. His chances of winning the nomination are 28 percent under this analysis, and he has a 14 percent chance of winning a general election as the presidential candidate.

But what if they lose in a 7-point blowout, and Mr. Obama matches his winning margin from 2008? Then Mr. Ryan’s chances of running for president are down to 44 percent. And his probability of actually becoming president are cut in half, to 7 percent.

The best case, of course, is if Mr. Ryan and Mr. Romney win. Suppose, for instance, that they do win, but by a single point (and also win the Electoral College).

Then, Mr. Ryan’s chances of running for president are calculated at 84 percent. His probability of winning a future party nomination is 53 percent, and of becoming president, 33 percent — about one in three.

When I average these results across the entire range of scenarios that our forecast model articulates — substantial losses for Mr. Romney and Mr. Ryan, narrow losses, and wins by various plausible margins — I come up with about a 15 percent chance of Mr. Ryan someday becoming president.

His odds of becoming the 45th president are slimmer, however. For that to happen, he first needs Mr. Obama to win re-election. Unfortunately for Mr. Ryan, that’s the “easy” part. Our forecast now gives Mr. Obama about a 72 percent chance of winning another term.

Next, he needs Mr. Obama to finish out his entire second term. If Mr. Obama resigns sometime in mid-2014 after a major scandal, Republican odds of re-claiming the White House will look very good in 2016 — but someone (probably Mr. Biden) will have become the 45th president first, before Mr. Ryan or another Republican could become the 46th. Without considering any factors
specific to Mr. Obama, historically 83 percent of presidents have completed their four-year term.

Then Mr. Ryan needs to win the general election in 2016. Conditional upon he and Mr. Romney having lost this year’s election, the model does not evaluate his chances of this as being all that good. Specifically, the model gives Mr. Ryan a 9 percent chance of eventually becoming president conditional upon losing this year’s election. Moreover, some of those cases involve instances where Mr. Ryan would become president in 2020 (or 2024 or 2028, and so on) after someone else — Hillary Rodham Clinton or Marco Rubio, for instance — succeeds Mr. Obama as the 45th president. If you correct for that, it lowers Mr. Ryan’s odds to about 7 percent of becoming president after the 2016 election specifically, after having lost this one.

Finally, we consider the entire parlay of events: that Mr. Obama wins in 2012, that he serves out all four years, and that Mr. Ryan runs and wins in 2016. The chances of this are only about 4 percent.

We can also account for the alternate means by which Mr. Ryan could become the 45th president: if, for some reason, Mr. Romney is unable to complete his bid this year — and then Mr. Ryan replaces him, and wins the election. Historically, of the roughly 100 major-party tickets in the history of the nation, only one presidential nominee (Horace Greeley in 1872) died, or resigned the nomination, between the party conventions and Inauguration Day. Accounting for this oddball case, Mr. Ryan’s probability of becoming the 45th president increases only to about 4.5 percent.

So Mr. Romney’s misstatement will probably not turn out to be ironically prescient: the odds that Paul Ryan literally becomes the next president of the United States are about 20-to-1 against. But his odds of someday becoming president are much higher than that, and they’ll increase to about 1-in-3 if he and Mr. Romney win this November.

Of course, this is a one-size-fits all calculation, which doesn’t consider anything about Mr. Ryan specifically. The fact that he is quite young, that the Republican Party lacks an obvious successor other than him, and that he commands the respect of both the party base and the party establishment, all work in his favor in terms of running for and winning future nominations. Whatever happens this year, he is likely to be a major part of the American political landscape for a long time to come.

This post has been revised to reflect the following correction:

Correction: October 23, 2012

A previous version of this post misstated the year in which Dan Quayle won the vice-presidency. Mr. Quayle was elected vice-president in 1988, not 1992.

Nate Silver founded and was the editor in chief of FiveThirtyEight.