Even at the end of a presidential campaign, polls don’t perfectly predict the final margin in the election. Sometimes the final polls are quite accurate. An average of national polls in the week before the 2008 election had Barack Obama winning by 7.6 percentage points. He won by 7.3 points. Sometimes, however, the polls miss by more. Four years ago, an average of survey results the week before the election had Obama winning by 1.2 percentage points. He actually beat Mitt Romney by 3.9 points.

If that 2.7-point error doesn’t sound like very much to you, well, it’s very close to what Donald Trump needs to overtake Hillary Clinton in the popular vote. She leads by 3.3 points in our polls-only forecast.

And 2012 isn’t an outlier. For presidential contests since 1968, here’s the average of national polls taken a week before the election compared with the final result.

DEMOCRATIC ADVANTAGE YEAR NATIONAL POLLING AVERAGE ELECTION RESULT ABSOLUTE ERROR 1968 -1.2 -0.7 0.5 1972 -25.0 -23.2 1.9 1976 +1.3 +2.1 0.8 1980 -2.5 -9.7 7.2 1984 -17.2 -18.2 1.0 1988 -9.1 -7.7 1.4 1992 +5.7 +5.6 0.1 1996 +11.8 +8.5 3.3 2000 -2.9 +0.5 3.4 2004 -1.6 -2.5 0.9 2008 +7.6 +7.3 0.3 2012 +1.2 +3.9 2.7 Average 2.0 Polls a week before the election aren’t perfect predictors

On average, the polls have been off by 2 percentage points, whether because the race moved in the final days or because the polls were simply wrong. In many elections, the race isn’t so close, the leader in the polls goes on to win and few people notice the difference between the final polling and election margin. But when the election is close, a few percentage points can matter.

In 2000, George W. Bush led Al Gore in national polls by 3 percentage points, on average. Before the election, much of the talk was that Bush might win the national popular vote but lose the Electoral College. Of course, the opposite happened: Bush won the Electoral College but lost the popular vote. When races are so close, errors like that are possible. State polls can have errors as large as national polls can, and they can benefit different candidates.

All of this is to say that even if Clinton’s lead over Trump doesn’t shrink anymore, Trump might still win. He would need only a normal-sized polling error. Of course, that error would need to be in his favor, and there’s nothing inherent about polling errors that says they must aid the trailing candidate. Ronald Reagan’s defeat of Jimmy Carter in 1980, for instance, is often described as an upset. But that’s not the case — the polls had Reagan winning. They did, however, vastly underestimate how much he would win by. The same thing could happen this year; Clinton could win and do even better than the pre-election polls are saying she will. That’s why our model assigns a higher chance to a Clinton landslide than other models do (ours also shows Trump with a better chance of winning).

And to be clear, we shouldn’t expect a polling error just because national polls struggled in the 2012 presidential election and in some international votes since then. The polling in the 2004 and 2008 presidential elections was quite good (after two elections in which the national polls were well off the mark). Also, in half of the contests since 1968, the final polls missed by a percentage point or less.

Still, Clinton’s lead is small enough that it wouldn’t take more than a normal amount of polling error to wipe the lead out and leave Trump the winner of the national popular vote. If Clinton wins by 3 percentage points, she’s very likely to win the White House. But that’s still a medium-sized “if.”