Although the Democratic and Republican primaries aren’t over, the question of who the presidential nominees will select as running mates is already receiving considerable attention.

One key question is whether vice presidential nominees actually help the ticket win voters in the nominees’ home states. And if so, is this advantage large enough to actually make a difference in the election outcomes?

Existing studies have found that the vice presidential home state advantage is small to non-existent — less than 1 additional percentage point. These studies have also found that the advantage is larger only in small states, which are less likely to have enough electoral votes to swing the outcome.

Campaign advisers and political observers have taken notice. In 2012, Karl Rove advised Mitt Romney to ignore campaign considerations in his vice presidential selection process. Recently, William Galston provided similar advice to the 2016 candidates.

However, in a new study published in American Politics Research, we come to a different conclusion. We find that the average vice presidential home state advantage is considerably higher: nearly three percentage points, on average.

We also find that this advantage exists in battleground states with enough electoral votes. This means that a vice presidential candidate from an important swing state could very well make the difference between winning or losing that state.

Why do our results differ so much from the traditional findings?

Typically, people measure the home state advantage by taking account of both the national vote in that year’s presidential election and the average presidential election performance of the party over several previous elections. The logic is to estimate how well the party did in the vice presidential nominee’s home state relative to how it should do. The difference between the actual vote and the expected vote is the home state advantage.

This strategy has several problems, however. One particular problem is that running mates tend to be selected from states in which the party has seen a decline in popularity in the run-up to the election year. As a result, averaging the party’s performance over previous elections generally overestimates the strength of the party there, and thus underestimates the VP’s home state advantage.

For example, according to the standard measure, Lyndon Johnson’s home state advantage in Texas in 1960 was actually a huge disadvantage: -15 percentage points. This implies that John F. Kennedy would have improved his performance in Texas by nearly 15 points if he had not selected Johnson. This is highly unlikely given that Johnson outperformed the Kennedy-Johnson ticket in his own senate race in that same election.

A much better explanation is that the formula radically overestimates the expected result for 1960 because Texas does not match the national vote well and because the Democrats used to routinely win 80 percent or more of the vote there in the 1940s. As a result, Johnson is erroneously assigned a negative home state advantage.

Our method relies on “synthetic controls” to create a new measure of the home state advantage for vice presidential candidates from 1884-2012. We focus on historical elections returns in states that are similar to the vice presidential nominee’s home state. These similar states together constitute the “synthetic” version of the home state that is similar the actual home state except in terms of the vice presidential candidate’s identification with the home state.

For example, to estimate how much Joe Biden helped the 2008 Democratic ticket in Delaware we construct a “synthetic Delaware” by combining Florida, Maryland, Rhode Island, Maine, and New Jersey. Although these states differ in key ways from each other and from Delaware, once combined the Democratic vote in “synthetic Delaware” looks very similar to the actual results in Delaware between 1976 and 2004.

However, in 2008, Delaware has a home state vice presidential candidate on the ticket in 2008, “synthetic Delaware” does not. The gap between the two is Biden’s home state advantage: an estimated 4.3 points.

Overall, we find that vice presidential candidates add an average of 2.7 points in their home states. In crucial swing states, they added 2.2 points.

This average effect could have changed the outcome of four presidential elections since 1960. Assuming that a vice presidential candidate from a key swing state could have been on the ticket, Republicans might have won the 1960 and 1976 elections, while Democrats could have won in 2000 and 2004.

What do these findings mean for the 2016 presidential election?

Certainly, there can be good reasons for selecting vice-presidential candidates from states that are safely Democratic or Republican. Presidential candidates obviously want someone qualified, in case of presidential death or incapacitation.

Even from the perspective of campaign strategy, presidential nominees may think beyond swing states. For example, the choice of a running mate may target certain demographics — defined by race, ethnicity, gender, ideology, and so on — rather than a certain state.

But our research suggests that the home state advantage is real and can affect the outcome of close presidential elections. Thus, presidential candidates should consider home state in their selection process, especially if qualified vice-presidential candidates from states like Florida or Ohio are available.

Boris Heersink is a PhD candidate in the Woodrow Wilson Department of Politics at the University of Virginia and a National Fellow at the Miller Center. Brenton D. Peterson is a PhD candidate in the Woodrow Wilson Department of Politics at the University of Virginia and a Research Affiliate at Strathmore University.