We published this article on The Conversation. Shortly thereafter, Newsweek picked it up. The authors: Mark Payton, Oklahoma State University and Ole J. Forsberg, Oklahoma State University

[Flag of the United States]And so, Super Tuesday as well as Saturday’s caucuses and primaries are behind us. If the rest of the primary season holds to this trend, it appears the battle for the presidency will be between Donald Trump and Hillary Clinton. Each leads in both state wins and delegate counts. Clinton has won 12 of 19 contests, garnering 1,121 of the 2,383 needed delegates. Trump has also won 12 of 19 states and 382 of the 1,237 delegates needed to win the nomination.

A common argument made by candidates is that they – and not their opponents – are electable. Examples of this rhetoric can be seen in both political parties. Bernie Sanders, expecting a Trump victory on the Republican side, has stated that Hillary Clinton cannot defeat Trump in the general election. On the Republican side, Marco Rubio has clearly stated the he is the “best chance” to beat Hillary Clinton.

However, how valid are these claims of exclusive electability?

Why most headlines about electability are misleading

[Donald Trump]

Republican contender, Donald Trump

Many pundits and political experts rely on national head-to-head polls to arrive at a conclusion about electability. If we rely only on such polls, then we get some interesting conclusions.

The following table provides estimated national support for each match-up as of March 3, 2016:

Estimates of National Level Support
with estimated 95% margins of error (March 3, 2016)
Matchup Republican Wins Democrat Wins Margin of Error
Cruz vs Clinton 50.6 49.4 1.4
Cruz vs Sanders 42.7 57.3 1.6
Rubio vs Clinton 52.1 47.9 1.4
Rubio vs Sanders 46.8 53.2 1.6
Trump vs Clinton 46.9 53.1 1.4
Trump vs Sanders 44.5 55.5 1.6

What conclusions could you draw from this table? First, Democratic candidate Bernie Sanders wins in all match-ups. Second, Trump loses in all match-ups. Third, the outcome of the Cruz versus Clinton election is unclear, as the estimates are both within the margin of error for the estimates.

If we rely on these polls, then we also need to ignore a few things. First, the general election of November 8 is many months away. The true level of uncertainty nine months away from election day is much greater than any reported “margin of error.”

Second, these polls ignore the value of the vice president. Were Cruz to win the nomination and select Rubio as his running mate, he would have a different probability of winning the election than would be reported in such polls. Conventional wisdom suggests that the vice president has a negligible positive effect on the presidential race, but Cruz may select Rubio as his running mate simply to remove him from competition.

Finally, the U.S. presidential election is not decided based on the nationwide popular vote. It is really a collection of 51 separate elections aggregated and weighted through the Electoral College.

In other words, national estimates, though enlightening about the mood of the country as a whole, are mostly irrelevant in regard to the result of a national election. What’s more important is how these head-to-head match-ups play out in the battleground states.

In a recently published paper, we introduced a multilevel model that combined state- and national-level polls into a single estimate for each individual state. The model appears to be effective, as it successfully predicted 50 of the 51 elections held in the states, plus D.C., in each of the last three presidential elections.

What does the model have to say about the six possible face-to-face matchups? Did Super Tuesday help the Republicans or the Democrats in the race to the White House?

Cruz versus Clinton or Sanders

According to the national match-ups: Cruz wins neither of these matches outright. He is handily beaten by Sanders by more than 14 percent and is within the margin of error against Clinton.

Following our multilevel model: the expected number of electoral votes won by Cruz against Clinton is only 256. As this is 14 shy of the 270 needed to win the election, the probability that Cruz wins in a contest against Clinton is less than 50 percent.

Against Sanders, Cruz does even more poorly. He only receives 197, falling 73 electoral votes short of a majority and the presidency.

It is interesting that in a match-up against Cruz, Sanders wins all of the states Clinton does, plus three others: Florida, Missouri and North Carolina. In the map below, the dark red states are won by Cruz in both match-ups. The dark blue states are won by both Clinton and Sanders. The light blue states are won only by Sanders.

Electoral map of Cruz (red) versus Clinton (dark blue) and versus Sanders (all blues)
Ole J. Forsberg

The difference in the two contests goes beyond the electoral maps. The states considered battlegrounds change, as well.

If we define battleground states as those where the probability of the Republican candidate winning is between 25 percent and 75 percent, the Cruz-Clinton contest has four battleground states: Colorado, Nevada, New Mexico and Virginia. The Cruz-Sanders match-up has two of those four states safely in the Sanders column, with Colorado, Missouri, Nevada and North Carolina being the battleground states.

Rubio versus Clinton or Sanders

The multilevel model suggests Rubio could win the race, but only if his opponent is Clinton. In that match-up, Rubio receives an expected 318 electoral votes to Clinton’s 220. In a Rubio-Sanders race, Rubio receives an expected 247 votes, with Sanders receiving the remaining 291.

Again, Sanders wins all of the same states Clinton does, and adds a few of his own. Here, those Sanders-only states are Colorado, Iowa, Michigan, New Hampshire, New Mexico, Nevada and Virginia.

Electoral map of Rubio (red) versus Clinton (dark blue) and versus Sanders (all blues).
Ole J. Forsberg

Also, as with the Cruz contests, Sanders takes most of the Clinton battleground states and makes them safely Democratic. The battleground states in the Rubio-Clinton race are the usual Florida, Michigan, Nevada, New Mexico, Pennsylvania and Wisconsin, plus the typically blue states of Maine and Oregon. With Sanders the battleground states are just Colorado, Florida, Iowa, Missouri and Nevada. Maine and Oregon return to the safely Democratic column.

Trump versus Clinton or Sanders

Without question, Donald Trump is the current Republican front-runner. He has been such essentially since entering the race in 2015. This is despite the best efforts of the Republican leadership to dethrone him. In the Wake of Super Tuesday, Trump led the field with 319 delegates. Cruz, his closest rival, has only 226 delegates. Rubio, who may be the Republicans' best chance to win the White House, has 110.

So, how does Trump do in head-to-head match-ups for the general election? According to the model, the expected number of electoral votes won by Trump against Clinton is 236, which is 34 fewer than the 270 needed to win the election. Against Sanders, Trump only receives 203.

As in the other match-ups, Sanders does better than Clinton, with Sanders taking all Clinton states plus Missouri and North Carolina.

Electoral map of Trump (red) versus Clinton (dark blue) and versus Sanders (all blues).
Ole J. Forsberg

Additionally, the rule that Sanders makes the Clinton battleground states safer for Democrats holds here, as well. With Sanders, only Missouri and Arizona are battleground states.

But … the election isn’t today

A few conclusions can be drawn from these maps. First, as usual, the large majority of states are either safely Republican or safely Democratic. Those states that are not, the battleground states, depend on the particular match-up.

Second, paying attention only to the national polls suggests that a Cruz-Clinton contest would most likely end in a Cruz presidency. Paying attention at the state level, this conclusion is not supported. The most likely outcome would be a Clinton win. In fact, the only path to a Republican White House is Rubio versus Clinton.

On the Democratic side, it appears as though Super Tuesday made Clinton inevitable once again. On the Republican side, a knockout blow was not delivered, but Trump became more likely to win the nomination. If the actual presidential election is between Trump and Clinton, and if nothing else happens on the political scene, Clinton will most likely receive 304 electoral votes, 34 more than she needs to win. This is 28 fewer than Obama won in 2012. The difference is Florida.

Finally, all of these estimates, like political polls, are based on some rather untenable assumptions. Namely, they assume either that the election is today or that there will not be a significant political event between now and election day.

The ConversationMark Payton, Head of the Department of Statistics, Oklahoma State University and Ole J. Forsberg, Visiting Assistant Professor of Statistics, Oklahoma State University

This article was originally published on The Conversation. Read the original article.