Did we lull voters and the news media into a sense of complacency about the election? In hindsight, it would have been better to express Mrs. Clinton’s polling margin as equivalent to a 2.2 percentage point lead — and that the true margin could be higher or lower by several points. That would have better conveyed the race’s uncertainty.

Poll aggregation is built on the idea that pollsters are more accurate as a group than they are individually. During the primaries, I used state polls to argue that Mr. Trump was the strong favorite to win the nomination. However, general-election polls did less well, and so did I. State polls underestimated the Republican-versus-Democrat margin by four percentage points, the largest error in decades. This presidential-level polling error was echoed in the national House popular vote and Senate polls, which were also both off by a median of four percentage points. As Nate Silver of FiveThirtyEight has pointed out, errors are often correlated. A warped ruler is flawed no matter how many measurements are averaged.

The pattern of polling errors provides a clue to why Mr. Trump’s victory came as a surprise. In states that Mr. Trump won, his actual margins against Mrs. Clinton were a median of six percentage points better than the last available polls. In contrast, in states won by Mrs. Clinton, the gap between polls and outcomes was 0.2 of a percentage point. Mr. Trump’s hidden strength in the states he won suggests that some fraction of Republican voters were struggling between party loyalty and difficulty with accepting Mr. Trump. In the end, their loyalty won out…

As a scientist, I am committed to learning from my mistakes. Despite this year’s failure, data is still our best resource for predicting events, but it is important to get good data in the first place. This will be on my mind in the spring, when I am teaching a seminar on the application of statistics to public affairs. A key topic will be partisan gerrymandering, which lends itself much better to hard facts like final vote totals, and not prediction. This year’s election will remind me to add a heavy dose of humility to the proceedings.