Democrats are not fond of the Electoral College these days, for obvious reasons. Two Republicans, George W. Bush and Donald Trump, have won the presidency in the past 20 years, and both of them galumphed into the Oval Office after losing the popular vote. In this era of tight national races, the system has clearly given Republicans a built-in advantage that allows them to govern with a minority of the public’s support.

And now, a new working paper by researchers at the University of Texas at Austin has quantified just how big that edge might have been in recent decades.

In their baseline results, the authors find that during the past 30 years, a hypothetical Republican who earned 49 percent of the two-party popular vote—that is, the vote total won by Democrats and Republicans, excluding third parties—could expect to win the Electoral College about 27 percent of the time. A Democrat with that share of the vote would have just an 11 percent chance of winning. At 49.5 percent of the popular vote, a Republican would have enjoyed a 46 percent probability of walking away with the presidency, versus a 21 percent chance for a Democrat. In a photo finish where the two parties split the vote about 50-50, a Republican would have had a 65 percent chance of spending the next four years in office.

Before Bush and Trump, only two American presidents had ever won the Electoral College while losing the popular vote: Rutherford B. Hayes and Benjamin Harrison, both of whom pulled it off in the 19th century. Academics call these sorts of results “electoral inversions,” and economists Michael Geruso and Dean Spears wanted to know how likely they were to actually occur, and which parties were most likely to benefit from them. Were the 2000 and 2016 races statistical flukes, low probability bad breaks for the Democrats? Or were they the kind of finishes Americans should regularly expect to see in tight White House races?

“If you want to make an argument for or against the Electoral College, you should at least have a sense of how often you’re going to have these politically contentious outcomes,” Geruso told me.

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To find out, Geruso, Spears, and research assistant Ishaana Talesara essentially took the sorts of election modeling tools that data journalists like FiveThirtyEight’s Nate Silver and the Upshot’s Nate Cohn have popularized for forecasting future elections and pointed them backward into history, building on actual state-by-state voting results to simulate millions of hypothetical races. They focused on three specific periods: the antebellum era, Reconstruction, and the years 1988 through 2016, which they call the “modern era.” (In the paper, they explain that they picked those timespans because the political parties in the United States were relatively stable during them.)

Their results showed that the Electoral College has always made inversions fairly likely in close contests. Across all three periods, when the candidates finished within 2 percentage points of each other in the two-party popular vote, there was a roughly 30 percent chance that an inversion would occur. In races decided by 1 percent of the popular vote, there was a roughly 40 percent chance of an inversion.

In other words, the Electoral College has always made it pretty likely that, in a nail-biter election, the popular vote would get overturned. “I think it’s easy for people to look at the current political cycle and think the inversion in 2016 or potentially 2020 is a sign of extraordinary political times,” Geruso told me. “And it’s not.”

Meanwhile, the study’s results also confirmed the conventional wisdom that Republicans get a serious advantage from picking presidents this way. During the modern era, they have been much, much more likely to win the Electoral College even if they lose the popular vote than the Democrats. Full stop.

What makes the Texas team’s study convincing on this point is that they don’t just simulate election results and reach their conclusions using a single model, or even a handful of different models. If they had, their results might have been baked into a few assumptions about how voting patterns correlate between different states or whatnot. But instead, they test hundreds of different models to see whether any change the basic finding of their paper. They don’t. In this graph below focusing on the 1988 to 2016 period, the authors show that 92 different models deliver basically the same result, where the Electoral College is much more likely to bail out Republicans than Democrats.

Why does the Electoral College give the GOP such an advantage? In large part, it’s what you’d expect. Because every state gets two Electoral College votes for each of its senators, the system gives more weight to lightly populated states where Republicans excel. The winner-take-all system that most states use to award Electoral College delegates also leads Democrats to waste a lot of votes running up the score in big states like California, while losing in small states.

This is just an early working paper, and other experts in the field may have criticisms. But so far, I haven’t heard any damning takedowns. Jonathan Katz, a professor of social sciences and statistics at Cal Tech, told me that based on a quick review, the study “actually looks solid” and he only had “some minor quibbles with it.” Nicholas R. Miller, a political scientist at the University of Maryland Baltimore County,* has previously found that the Electoral College is not systematically biased in favor of either the GOP or the Democrats. But he told me his own recent modeling work was “less sophisticated” than what the Texas team has produced, and that he’s still looking into why their results differ from his.

The Texas paper is, technically, about past elections, not future ones. Its authors were trying to weigh the probability that a candidate would have won the White House while losing the popular vote through history, not forecast the next race. But Geruso told me he sees no reasons why the Electoral College should favor the GOP any less going into 2020. The Democrats aren’t imagining that, as long as the vote is close, the odds are stacked against them.

Correction, Sept. 18, 2019: An earlier version of this post incorrectly referred to the University of Maryland Baltimore County as the University of Maryland Baltimore College.