It’s taken me a few days to write this because I’ve been basically unconscious for the last 3 days.  To recap, Hillary Clinton, certainly a weak candidate, but also clearly the most qualified candidate to ever run for president, got hundred of thousands (and when it’s all said and done likely millions) more votes than Donald J. Trump, a racist, sexist, xenophobe, who doesn’t understand the Constitution, but the latter will be the president because we choose presidents based on a system that was created in a time when England had a king, some people owned other people, and before scientific evidence of germs.

The silent majority isn’t a majority, it’s just an arbitrarily, geographically well located minority.  I know this makes you want to scream into a pillow or punch a wall, but if you want to do something productive instead, here are some suggestions.

Anyway, the point of this post is to review the six poll aggregators that made numeric predictions for each state and were compiled on the New York Times The Upshot: New York Times (NYT), FiveThirtyEight (538), Huffington Post (HuffPost), PredictWise (PW), Princeton Election Consortium (PEC), and Daily Kos (DK) (The raw data can be found on my GitHub Page in the repo Statsinthewild).

Below is a sweet plot that I made comparing the predictions of these six aggregators.  I’ve ordered the states from most red to most blue based on the average of the six predictions from November 5 three days before the election.  Then for each state I plotted a boxplot for the distribution of the 6 predictions and overlaid the individual predictions on top.  The colors of the boxplots are blue if the state (or district) went to Clinton and red if they went to Trump.

What immediately stands out for me on this plot is how much lower the Clinton win probabilities were for 538 compared to the other five sets of predictions for states starting and Nevada and moving right on the plot towards bluer states.  Other notable outlying predictions include Huffington Post’s predictions for Florida and North Carolina, which were 97% and 89%, respectively. The New York Times had some outlying probabilities that were high for Clinton in states like Mississippi and Missouri as well as Utah and Georgia.  FiveThirtyEight had many outlying probabilities for the “blue” states, but their most notable outlier for the red states was Alaska, which they gave Clinton a 26% chance of winning.  The next highest probability for Clinton in Alaska was 10%.

So now let’s analyze who was the best.  I’m going to do this in two ways: Brier Score and Logarithmic Loss.  I computed results based only on the 50 states and Washington, D.C. ignoring the weird districts in Maine and Nebraska.  Results are below: 

The worst of the poll aggregators was the Huffington Post.  This looks to be because of their overconfidence in Clinton in several states that Trump won. For example they had Pennsylvania and Wisconsin at >99% and 98% for Clinton, both of which she lost.  Daily Kos comes in 5th with a similar Brier score as Princeton Election Consortium and New York Times, but a much worse Log Loss.  Log loss punishes you heavily for being over confident and wrong, and with predictions like Michigan and Wisconsin at >99% and 99%, respectively, the Daily Kos got crushed by Log Loss.  New up we have Princeton Election Consortium and the New York Times who finished 3rd and 4th, respectively, using Brier score.  However, they flip flop rankings when using Log Loss.  Next up, and claiming the Silver medal is the market site PredictWise with a Brier score of 0.074 and a Log Loss of 0.259.

So who was the big “winner” of this Election?  Nate Silver.  A few days before the election I said that for him to look good in this election he needed it to be close or have Trump actually win.  Well Trump won and he was the only person who really gave Trump any chance of winning.  On top of that, his state by state predictions outperformed all of the other poll aggregators, and I’m crowning Nate Silver the champion of poll aggregators for the 2016 presidential election.  What Silver did better than any of the other models was when a state was truly a toss up, his model reflected it.  He had North Carolina, for instance, at 50% and Florida at 51% FOR the Republicans on November 5.  The only other set of predictions to get close to those numbers was PredictWise, which had North Carolina at 63% and Florida at 53% for Democrats.

Finally, here is a plot of the six poll aggregators with their Log Loss score on the x-axis and their Brier score on the y-axis.  Scores that are on the lower left are best and scores on the upper right are the worst.  

P.S. Here is a list of articles critical of Nate Silver before the election from the Huffington Post, Fortune, Vox, the Washington Post, Huffington Post again, Mashable and Wired.  Whoops.

Cheers.