In the wake of the UK’s vote Thursday to leave the EU, comparisons of Brexit's success to the rise of Donald Trump have been flying far and wide. This is only natural, since anti-immigrant, anti-elite, and nationalist sentiments played major roles in both shocking phenomena.

Of course, many of these analogies are too facile. The US faces no comparable controversy over regulations from a transnational economic bureaucracy. The US electorate is much more diverse than Britain’s. Trump himself has massive weaknesses in personality, popularity, and campaign mechanics that an issue-oriented campaign doesn’t. And where "Leave" and "Remain" were essentially tied in polling averages, Trump is clearly trailing Hillary Clinton at this point.

Despite all these differences, though, the Brexit result should jolt American liberals out of any complacence they may feel about Trump’s candidacy. While prediction markets currently give him about a 25 percent chance of winning the presidency four and a half months out, they gave Brexit less than 20 percent chance of winning just this week. And potential economic turmoil, the possibility that the polls can move, and even basic probability are all strong reasons nobody should take Trump’s defeat for granted.

1) Economic turmoil is usually a big risk for the incumbent party

When I asked political scientist Norm Ornstein last month about what could make Trump more likely to win the presidency, he mused, "What if Brexit happens and you get turmoil in the global economy? And it affects the US?"

Well, er, about that. ... Global markets did not respond well to the Brexit news, with stocks plummeting in the Europe, the UK, Japan, and (as of midday Friday) the United States. It remains to be seen whether this is a passing shock or the first sign of more serious problems.

But lots of research has made it clear that voters take the state of the economy into account in their presidential decisions and that when things aren’t going well, they tend to take it out on the incumbent party. And as Dylan Matthews has written, the economic fundamentals are already pretty mediocre for Clinton — to the point where some well-respected models indicate Republicans should have the advantage this year. So if things take a turn for the worse on the economic front, she could be in trouble.

Of course, it’s possible that an economic crisis environment could lead voters to flock to the "safe" choice of Clinton rather than the erratic, unpopular Trump. The billionaire is pro-Brexit after all, so if economic turmoil ensues as a result, voters could blame him.

Still, the electorate’s desire for change could be powerful and lead voters to see what they want to see in Trump. "Elections that occur after eight years of a two-term president focus around how much change you want," Ornstein told me. "And if events occur that create more of a desire for change, then people might roll the dice with Trump."

2) Take the polls seriously — while also keeping in mind that they can change

Both in the US presidential primaries and in the Brexit vote, polling has for the most part been pretty good overall. Trump led polls of Republicans since July, and the final polling average for Britain’s referendum was essentially a tie.

But both outcomes were viewed as shocking because elites in both countries simply refused to believe either thing would happen again, and constructed convincing-sounding stories to explain why the polls were wrong.

Now, the comforting lesson American liberals can take away from this is that the polls currently show Trump losing to Clinton by 6 to 7 points on average. Nothing to worry about, then, right?

Not so fast. This is actually a recent change from where the polls were just one month ago, when Trump and Clinton were tied. So, first of all, if the polls changed this much in a month, they could certainly change again. And second, the last time Clinton was ahead by 6 points, liberals were already acting like the election was wrapped up, only to see her lead vanish in just days. There’s a long time between now and November.

3) Take the possibility of unlikely events seriously

David Byler of RealClearPolitics had a good tweetstorm on Friday in which he pointed out some shortcomings in how many people understand probability. For months, he observes, prediction markets had given Brexit a 20 to 30 percent chance of happening — and that tends to be the same back-of-the-envelope estimate of Trump’s chances of winning that election wonks give. (It’s also where the prediction markets are now.)

"When I say [that Trump has a 20 to 30 percent chance of winning]," Byler writes, "whoever I’m talking to typically responds w/ a big sigh of relief. And whatever they say after that usually indicates that they rounded that 30ish percent chance down to zero or something close to it."

"But if you’re worried about a Trump presidency," he continues, "that shouldn’t be your response. A 30% probability should be really scary." After all, things with a 30 percent chance of happening end up happening one in three times!

Byler’s right on here. If you agree with most liberals and American elites that a Trump presidency is likely to be uniquely norm-breaking and terrible in a way a normal Republican presidency wouldn’t, it’s really quite terrifying that he’s gotten this far at all.