Some defeats never lose their sting. In Washington this week, Hillary Clinton summed up her bid for the White House in 2016.

“You can run the best campaign. You can have the best plans. You can get the nomination. You can win the popular vote. And you can lose the electoral college and therefore the election.”

Clinton beat Donald Trump in the popular vote by nearly 3 million ballots yet lost the electoral college – the body of people who represent states and actually get to choose the president – by 304 votes to 227. A black swan event never to be repeated? No. In 2020, it could easily happen again.

A study from the University of Texas at Austin found that the electoral college is much more likely than previously thought to elect the candidate who loses the popular vote. In close elections, researchers argues, such “inversions” are normal, not exceptional.

In a race decided by less than 2% (2.6m votes), the study found, the probability of an inversion is 32%. In a race decided by less than 1% (1.3m votes), the probability is 45%.

“It’s almost a coin flip,” said Michael Geruso, an assistant economics professor.

Some critics of Trump have never quite accepted him as the legitimate president, pointing out that he does not represent the will of the majority. After his uniquely divisive first term, a repeat could trigger a furious backlash.

The Republicans do a really determined job of winning power with fewer voters Senator Sheldon Whitehouse

In 48 presidential elections since 1824 there have been four inversions: in 1876, 1888, 2000 and 2016. All four favoured Republicans, although the researchers argue there have been periods when it was more likely a Democrat would win by inversion.

“We wanted to understand, were these statistically likely events or were they flukes?” Geruso said. “And in some sense it was just shocking to us that no one had asked and answered that question yet.”

Geruso and his colleagues found that all the most common election models used by political scientists led to a very similar result for the probability of inversion.

“There’s lots of questions where different models would give different answers but, on the question of how likely is an electoral inversion in a close race, we don’t need to agree or decide on what the perfect model of elections is. They all give the same answer.”

Clinton ran up huge margins in states such as California, Illinois and New York. Agonisingly, her loss of Michigan, Pennsylvania and Wisconsin by a combined 77,000 votes cost her the electoral college.

Some analysts doubt Trump could get so lucky again. But Geruso said he has a decent chance of catching lightning in a bottle once more.

“It’s really easy to look at the 2016 election and for people to feel like that was an extraordinary election, an extraordinary political moment, it was unusual in a lot of ways. And that may all be true but it turns out that’s not why the 2016 election ended in a mismatch between the electoral college and national popular vote. It ended in an inversion because that election was close and close elections, we show, just have a relatively high probability of ending in an inversion.”

It is less about Trump’s appeal to certain constituencies than simple geography and maths.

“Don’t be tempted into thinking that the reason that 2020 might be an inversion is because Donald Trump is running in that race. Inversions are going to keep happening in close races for as long as we have the electoral college because they have been happening.”

According to Geruso, two major reasons are often cited for inversions. When Clinton won New York and California she did so by big margins, but when she lost states such as Florida or Ohio she did so narrowly. Thus there was an imbalance in the aggregate vote tallies.

Second, since a state’s number of electoral college votes is determined by how many senators and representatives it has, and every state has two senators, small states have greater representation in the college relative to population size. Each senator in California represents nearly 20 million people. Each senator in Wyoming represents 290,000. The current alignment favours Republicans, although there are exceptions such as the District of Columbia.

The researchers found a 77% probability that, if an inversion occurs, it will be a Democratic popular vote majority and a Republican electoral college win.

‘Second-grade soccer’

Several Democratic candidates for president, including Senator Elizabeth Warren and Mayor Pete Buttigieg, have called for the college to be abolished. The party, however, is wrestling with how to exploit it as ruthlessly as Republicans do.

Senator Sheldon Whitehouse of Rhode Island, appearing on Real Time with Bill Maher, said: “The Republicans do a really determined job of winning power with fewer voters and we don’t take on that infrastructure and we don’t take on that strategy. We’re too happy fighting the fight of the minute. It’s second-grade soccer, chasing the ball, and they are planning ahead.”

The electoral college actually undermines democracy LaTosha Brown

Some observers fear the electoral college encourages voter suppression. Republican efforts to use voter ID laws to limit registration in Michigan, Pennsylvania and Wisconsin will be closely scrutinised.

Stanley Greenberg, a Democratic pollster and strategist and author of the new book RIP GOP, said: “If there is a close national election, Republicans will resort to things they have done demonstrably well over the last decade of trying to suppress the vote.

“There’s no doubt that the Wisconsin case in 2016 was produced not by low turnout among African Americans but pushing them off the voter rolls with new voter ID laws, and so there was a sharp drop in eligible voters and people were prevented legally from voting. So obviously the most important thing is to make sure we did not have a close election.”

While southern states such as Mississippi, Louisiana and Georgia have the highest proportions of African Americans in the country, those who vote for the Democrat are effectively ignored by the electoral college.

Hillary Clinton delivers her concession speech, in the New Yorker hotel. Photograph: Rex/Shutterstock

LaTosha Brown, co-founder of Black Voters Matter, said: “They never have any influence on picking the president because of winner takes all. It gives the impression everyone in the south is conservative.

“In these states it’s based on a systemic history of racism. What I’m seeing is people of colour don’t fundamentally believe they’re living in a democracy. Why don’t you have proportional representation? What possible justification is there for winner takes all? The electoral college actually undermines democracy.”

Few expect Trump to win the popular vote. But in a chilling warning for Democrats, the New York Times suggested he could win the electoral college again, because mostly white working-class rust belt states remain at the centre of the electoral map.

“A strategy rooted in racial polarization could at once energize parts of the president’s base and rebuild support among wavering white working-class voters,” Nate Cohn wrote. “Many of these voters backed Mr Trump in the first place in part because of his views on hot-button issues, including on immigration and race.”

Bill Whalen, a research fellow at the Hoover Institution thinktank at Stanford University in Palo Alto, California, noted that George W Bush lost the popular vote in 2000 but won it in 2004 after improving in Texas and post-9/11 New York.

For Trump, he said, “it’s a tight squeeze. There’s not much margin for error. But he could do it again, like he did in 2016, without the popular vote.

“So expect Trump derangement syndrome to get even worse.”