Donald Trump has selected Mike Pence as his vice-presidential candidate — a move in line with a recent tradition by nominees of selecting running mates from “safe” states.

Since 2000, only one vice-presidential candidate (John Edwards in 2004) was from a state that could have been competitive in November. Pence, the incumbent governor of Indiana, doesn’t break that pattern: Recent polls have Trump comfortably ahead in his state.

Could Trump have made a different strategic choice by selecting a running mate from a swing state instead? Is there any evidence that vice-presidential nominees actually help the ticket win voters in their home states? The answer is yes, and this is why Trump has probably left votes on the table.

Existing studies have found that the vice-presidential home-state advantage is small to nonexistent — representing 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 overall 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 3 percentage points, on average.

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

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 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 candidate’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: minus 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. That 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 to 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 to 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 constructed a “synthetic Delaware” by combining Florida, Maryland, Rhode Island, Maine and New Jersey. Although these states differ in key ways from one another 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, while “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.

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.

Pence, however, is unlikely to do so. While he may very well add points to the Republican ticket in Indiana, Trump is likely to win there regardless. By playing it safe, Trump is missing out on a bump that could have helped him win a crucial swing state and, in the case of a very close election, maybe even the White House.

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.

This is an updated version of a post that originally ran on April 26, 2016.