Donald Trump’s slimming chances of victory

By THE DATA TEAM

A NEW axis of evil—comprising an unholy alliance of the mainstream media, pollsters and traitors within the Republican party—threatens Donald Trump’s electoral chances. So says the beleaguered candidate, who today vented on Twitter that “we are winning and the press is refusing to report it”. He also contributed a free tip to journalists, saying the “major story” of the election was Democrats rigging polls against him.

Mr Trump may simply be hedging his bets. Assuming no cabal of conspiring pollsters is uncovered, the outlook for his presidential hopes appears grim. An average of professional polls with statistically sound methodologies—the kind the Republican nominee scorns—puts him roughly six percentage points behind his opponent, Hillary Clinton. This close to the election, presidential polls have historically missed the final tally by only 1.8 points, dispiriting news for still-hopeful Trumpistas.

Using polls’ record of accuracy in past American presidential contests, it is possible to construct rough probabilities of victory for Mr Trump and Mrs Clinton. Surveys taken months before the November election, when primary races are still being contested, are of course more prone to error than ones conducted just a few days before the vote. Even a seemingly commanding lead of eight percentage points 200 days ahead of the election, when polls historically miss the mark by four points, could conceivably evaporate. As a result, the confidence intervals (a range of likeliest outcomes) surrounding polling averages are wide early in the campaign, when there is more uncertainty, and narrow steadily as it nears its end.

In the increasingly vibrant discipline of statistical election forecasting, the single most important number is the probability of victory. Applying a quick, back-of-the-envelope method (see below) based on polls’ historical performance yields a 96% chance of a win for Mrs Clinton. That figure is in the same ballpark as more sophisticated projections, but slightly higher: the New York Times gives her 92%, FiveThirtyEight 87% and PredictWise 90%, not that any of those marks should provide much solace to Mr Trump. The Republican nominee will probably reject this reality and insist that the polls are tainted. But the last major effort to “unskew” the polls—when the author Dean Chambers claimed in 2012 that they systematically under-represented supporters of Mitt Romney—concluded in heartbreak for the GOP.

Methodological appendix: To derive the probability of a victory for Hillary Clinton, we first calculated the historical error rate for polls using a data set of presidential-election polling going back to 1952 compiled by Robert Erikson and Christopher Wlezien, two political scientists. For each day in the sample, we computed the average error from the final tallies, and how much those errors varied from one election to another. We used this mean and standard deviation to fit a t-distribution with 15 degrees of freedom (since our data set consists of 16 elections), yielding a probability for every possible magnitude and direction of error. Based on this distribution and the current polling average as reported by RealClearPolitics, presidential polls two weeks before the vote should understate the trailing candidate’s support by a margin greater than the favourite’s lead just 4% of the time. All analysis was conducted on two-party vote share.