Our research relies on a new approach to measure the vice-presidential home state advantage, known as “synthetic controls.” For each running mate, we use a combination of similar states to construct a “synthetic” version of their home state, which mirrors the electoral results of the home state over a series of past elections.

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For example, to estimate how much Vice President-elect Mike Pence helped the Republican ticket in Indiana, we constructed a “synthetic Indiana” that combines Nebraska, Montana, Pennsylvania, Hawaii, Utah and Alabama. None of these states, on their own, perfectly match Indiana in the last several elections. But once combined, the Republican vote share in “synthetic Indiana” looks quite similar to that of Indiana from 1984 to 2012.

The difference between Indiana and “synthetic Indiana” is that “synthetic Indiana” does not have a home state running mate on the ticket in 2016. The gap that emerges between the two versions of Indiana, in 2016, is our estimate of Pence’s home-state advantage: 2.53 points.

Given the GOP’s strength there, Pence’s presence on the ticket did not flip the state. Indeed, as we noted after Pence’s selection, Indiana is a reliably Republican state. Trump would have received nearly 58 percent of the vote there even without Pence’s support.

Kaine’s influence in Virginia is a different story. Our estimate is that Kaine added 2.81 points to Clinton’s vote share. Given that she received only 52.78 percent of the two-party vote in Virginia, this means she could have lost Virginia if not for Kaine — although it would have been quite a nail-biter.

Of course, Kaine’s presence on the ticket didn’t change the overall outcome. At most, it might have prevented Trump from winning an even larger electoral college majority.

Nevertheless, Kaine’s potential impact on the outcome shows the value in selecting a running mate from a major swing state. If Clinton had performed slightly better in other swing states, while still needing Virginia to hit 270 electoral votes, Kaine could have been a true game-changer. Future presidential nominees should use this knowledge to their advantage.