Saying this, that there’s no evidence, is a hedge. We say it just in case somehow there emerges evidence that, indeed, hundreds of people registered to vote illegally and went to cast ballots. If we say it didn’t happen and then some evidence emerges, we are stuck. So we say “there’s no evidence” instead of “it didn’t happen.”

That’s on the scale of hundreds of votes. On the scale of millions of alleged fraudulent votes, though? It didn’t happen. There’s not only no evidence that it did, it defies logic and it defies statistical analysis to insist that millions of votes were cast illegally in the 2016 election.

Some, like Rep. Steve King (R-Iowa), roll sketchy rumors down snowy hills to come up with fantastical snowballs of numbers that are unlinked to reality. To NBC on Tuesday, King said that he had extrapolated outward from one report of illegal voting in Virginia to assume that perhaps 2.4 million people had voted illegally nationally. He appears to be referring to a report covered by the conservative media that looked at voting from 2005 to 2015 — not 2016.

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If there was rampant fraud in most counties in 2016, no one has detected it. That includes the Republicans who are running the elections in most states. (It’s generally Democrats who are assumed to be the fraudsters.) It also includes statisticians, who have looked for mathematical markers of unusual vote surges and found nothing.

King’s not alone in such elaborate mathematics. Often operating from the assumption that voter fraud exists, any number of people have woven elaborate tapestries to present a gauzy case for the presence of fraud in our elections. Were it just the Steve Kings of the world who were embracing this idea, that would be problematic. But on Tuesday, King was responding to a question driven by no less a figure than the new president of the United States, Donald Trump.

The day before, Trump met with congressional leaders and reiterated a claim that millions of people had voted illegally for his opponent. In fact, he upped his estimate from 3 million to as many as 5 million — 3.6 percent of all votes cast in the election.

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There are various levels at which this is total unsubstantiated nonsense — a claim even more nonsensical than his assertion that 1.5 million people attended his inauguration. The idea that millions of people voted illegally stems most immediately from one tweet from one guy in Texas that was picked up by the conspiracy-hawking site InfoWars. Repeatedly asked for proof of his claim that millions had voted illegally, that guy, Gregg Phillips (who is associated with a group called True the Vote), repeatedly declined to do so. There’s simply no available evidence that Phillips’s claim was true. (True the Vote also declined to substantiate his claims.)

What’s more, Phillips himself admits that the 3-million-vote number he threw out doesn’t necessarily mean that all of these alleged illegal voters backed Hillary Clinton. So Trump took that number, added a possible 2 million more and asserted that all of those ballots were cast in opposition to him. Why? Probably for the same reason that he lied about the turnout at his inauguration: to make himself look better. If 3 million people voted illegally for Clinton, that would mean that he won the popular vote after all. They didn’t; he didn’t. But that clearly stings.

Another likely reason, raised by Sen. Bernie Sanders (I-Vt.) in a statement, is that Trump was “sending a message to every Republican governor in this country to go forward with voter suppression.” In other words, by making the case for rampant fraud, the case for anti-fraud measures is bolstered. Those measures often disproportionately filter Democrats and people of color out of the voting pool, to Republicans’ advantage.

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On Tuesday, the situation got worse. Press secretary Sean Spicer, asked to defend Trump’s illegal-vote comments, tried to claim that the claims were rooted in evidence.

There are no studies and no evidence that there is widespread voter fraud in general, much less from the 2016 election. (An election, we will remind you, in which a great deal of attention was paid to the possibility of fraud, given Trump’s having raised it before Election Day — probably because he expected to lose.)

Trump has, in the past, cited a study that looked at errors on the voter rolls that was compiled in 2012. That report, from Pew Trusts, aimed to highlight antiquated voter registration systems by noting that dead people were often not removed from voter rolls quickly. It looked only at data from 2012 and made no assertions about the extent to which those registrations might have been used to cast ballots. But Trump, and others, have highlighted the possibility of 2 million-odd dead voters on the rolls as somehow suggesting that 2 million illegal votes had been cast.

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During the campaign, Trump also claimed that the illegal voting was being done by immigrants here illegally. At one point, he focused on a statement from a Border Patrol official that conflated illegal entry with illegal voting. The official later clarified that he had misspoken, but the idea that undocumented immigrants have flooded into the country — particularly into California, where Clinton won overwhelmingly — has caught hold.

Paul Mitchell of California voter-data firm Political Data provided The Post with data on the California electorate. About 1.4 million registered California voters were born in Latin American countries. Just over a million such voters cast ballots in November. If all million of those voters were registered illegally, Trump still needs to find 4 million people elsewhere. But there’s no evidence that any significant number of those million voters were registered illegally.

In fact, when Trump’s general election opponents sought a recount in Michigan, his own attorneys said in a court filing that the election was “not tainted by fraud or mistake.”

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There’s a deep strain of partisanship involved here. A survey conducted shortly before Election Day found that Republicans agreed with the idea that noncitizens were voting illegally in significant numbers. There’s no evidence that this is the case, but it’s an argument that was being made by the most high-profile Republican in the country. That clearly had an effect. (A study from Dartmouth: “[T]he voter fraud fears fomented and espoused by the Trump campaign are not grounded in any observable features of the election.”)

It’s frankly stunning that the president of the United States would make such an assertion, much less make it repeatedly and at ever-increasing levels of error. It’s stunning, too, that his press secretary would claim that there was evidence that the president was correct — or, it would be stunning had Spicer’s tenure not begun the way it did.

The most telling demonstration that Trump’s numbers and Spicer’s defense are nonsensical, though, came from a follow-up question posed to the press secretary. If millions of people voted illegally, Spicer was asked, wouldn’t that demand an investigation into the integrity of the election? (Such an investigation, of course, might put at risk Trump’s narrow margin of victory.)

“He won fairly,” Spicer said of his boss.