Donald Trump won the presidential election despite polls that indicated Hillary Clinton was favored. One popular explanation for this is that some people were afraid to admit to pollsters that they supported Trump — what’s being called the “shy Trump” phenomenon. A review of the evidence, however, suggests that probably isn’t why the polls got Trump wrong.

The “shy Trump” theory is the latest twist on an idea that dates back to at least the 1980s, when California gubernatorial candidate Tom Bradley and other black candidates did worse in elections than the polls had predicted. That led some experts to conclude that voters were hiding their true preferences from pollsters to avoid being seen as prejudiced. The idea resurfaced during this year’s presidential primaries, when Trump won the Republican nomination even though most experts said he wouldn’t. There wasn’t much evidence to support the theory in the primaries — the polls turned out to be fairly accurate — but that didn’t stop speculation that in the general election, Trump supporters would be reluctant to admit they were voting for a candidate with a history of making racist and sexist comments.

It will probably be weeks or months before we fully understand why the polls underestimated Trump in many states in the general election. But there are several reasons to doubt that shyness on the part of his supporters was a major part of the explanation.

First, the “shy Trump” theory relies on the notion of social desirability bias — the idea that people are reluctant to reveal unpopular opinions. So if the theory is right, we would have expected to see Trump outperform his polls the most in places where he is least popular — and where the stigma against admitting support for Trump would presumably be greatest. (That stigma wouldn’t carry over to the voting booth itself, however, so it would suppress Trump’s polling numbers but not his actual results.) But actual election results indicate that the opposite happened: Trump outperformed his polls by the greatest margin in red states, where he was quite popular. The two states that had the largest polling error for Trump were Tennessee and South Dakota, where Trump won more than 60 percent of the vote. Meanwhile, Trump underperformed his polls in states where the stigma against him would seem to be strongest: deep-blue states like California, Hawaii, Massachusetts, New York and Washington. Overall, as my colleague Carl Bialik and I (as well as Andrew Gelman) have pointed out, there’s a very strong correlation between how Republican a state is and how much better Trump did than polling averages indicated he would.

The second reason to be skeptical of the “shy” theory is that Republican Senate candidates outperformed their polls too. The theory behind the “shy” phenomenon is that voters are reluctant to admit support for particularly controversial or politically incorrect candidates. Yet mainstream Republican Senate candidates such as Ron Johnson, Marco Rubio and Pat Toomey — hardly examples of bomb-throwers like Trump — all did better than the polls indicated they would. They weren’t alone. A look across Senate races reveals that most Republican Senate candidates bested their polls.

REPUBLICAN MARGIN STATE POLLS ELECTION RESULT DIFFERENCE South Dakota +30.0 +43.7 +13.7 Vermont -40.3 -28.3 +12.1 Idaho +27.2 +38.4 +11.2 North Dakota +52.9 +61.5 +8.6 Indiana +1.8 +9.7 +7.9 Wisconsin -3.2 +3.4 +6.6 Utah +35.3 +40.9 +5.7 Arkansas +17.7 +23.1 +5.4 Alaska +27.8 +33.1 +5.2 Kentucky +9.3 +14.5 +5.2 Ohio +16.2 +21.4 +5.2 Maryland -29.0 -24.0 +5.0 Iowa +19.7 +24.5 +4.8 North Carolina +2.2 +5.8 +3.6 Pennsylvania -1.5 +1.6 +3.1 Georgia +11.2 +13.8 +2.6 Arizona +10.5 +13.1 +2.6 Missouri +0.8 +3.1 +2.3 Colorado -7.6 -5.5 +2.1 Louisiana +23.4 +25.2 +1.8 Florida +6.0 +7.7 +1.7 Oregon -24.8 -23.3 +1.5 Alabama +28.0 +28.4 +0.4 South Carolina +23.6 +23.6 +0.0 Kansas +30.5 +30.3 -0.2 New Hampshire +0.3 -0.1 -0.4 New York -41.9 -43.0 -1.1 Illinois -12.4 -14.2 -1.7 Nevada -0.6 -2.4 -1.8 Connecticut -26.0 -28.4 -2.4 Washington -15.8 -18.5 -2.8 Hawaii -40.9 -51.4 -10.5 Average +3.0 Republican Senate candidates outperformed their polls “Polls” refers to the final margin in the FiveThirtyEight polls-only adjusted polling average. Oklahoma is excluded because there was no FiveThirtyEight polls-only adjusted polling average for this contest. Sources: Connecticut Secretary of State, New York Times, Dave Leip’s U.S. Election Atlas

Third, Trump didn’t outperform his polls with the specific group of voters who research showed were most likely to hide their support for his candidacy. A Morning Consult study conducted in October found that there were some “shy” Trump voters, enough to suppress his support in polls by a statistically insignificant 2 percentage points. But the study found that the voters most likely to lie to pollsters were those with college degrees. So under the “shy Trump” theory, we’d expect to see Trump outperform his polls on Election Day in states such as Massachusetts and New York with high numbers of people with college degrees. But instead, Trump did better than his polls in states with the highest concentration of white voters without a college degree, including pivotal states such as Michigan, Pennsylvania and Wisconsin.

Finally, Trump’s own pollsters told us that there weren’t many shy Trump voters by Election Day. A few months before the election, internal polling showed Trump getting about 3 percentage points more support in polls conducted online or by automated voice recording than in live calls, according to David Wilkinson, data scientist for Cambridge Analytica, a data-analytics firm that conducted polling for the campaign. That suggests some Trump supporters were reluctant to reveal their true preference to a telephone interviewer. But in polls conducted just before Election Day, that 3-point gap had narrowed to just 1 or 2 points. “Shy Trump voters started to come out of the woodwork during the course of the election,” said Matthew Oczkowski, director of product for Cambridge Analytica.

The bottom line is that Trump did better than the polls predicted, but he didn’t do so in a pattern consistent with a “shy Trump” effect. It’s more likely that polls underestimated Trump for more conventional reasons, such as underestimating the size of the Republican base or failing to capture how that base coalesced at the end of the campaign.

Carl Bialik contributed to this article.