As of the time of my writing this post, we are 276 days into Donald Trump’s first term as President of the United States. That means the 2020 presidential election is still 1,107 days away. Is it too early to start speculating about whether Trump will be elected to a second term? Yes, absolutely. Nonetheless, I’m going to throw caution to the wind and try anyway.

As anyone who follows politics most surely knows, President Trump’s job approval ratings have been pretty dismal since taking office back on January 20th.

According to my poll aggregator, the percentage of Americans who approve of Trump’s job performance is a mere 38%, whereas the percentage who disapprove is 56%. These numbers have held fairly steady since February 14^{th}, when Trump’s approval peaked at an average of 47% and his disapproval sat at an average of 49%.

For some reference, Barack Obama’s approval rating was 51% at this point in his first term, and George W. Bush’s approval rate was 88% (a result of the 9/11 terrorist attacks).

Interestingly, aside from Trump, only one president in recent history has had an approval rate below 50% at this point in his first term, and that was Bill Clinton, with an approval rate of about 48%.

The graphic below shows all the recent presidents’ approval ratings 1,107 days prior to Election Day, excluding Gerald Ford and Lyndon Johnson because, for them, no polling data are available for this date.

Job approval numbers are useful because, obviously, they provide a good window into what the American public thinks about the president’s priorities, agenda, and job performance. Additionally though, job approval ratings are useful because they actually do a pretty good job of predicting whether or not a president will be re-elected to a second term.

Take a look, for instance, at the graphic below, which shows real and estimated job approval numbers heading into re-election for all the former presidents for which we have a reasonable amount of job approval data. Some of the approval numbers had to be estimated using Loess Regression, because polling was relatively sparse during most prior administrations (more on that below). Presidents who went on to be re-elected are represented in blue, whereas presidents who failed to be re-elected are represented in red.

If the graphic above looks messy, it’s because it most certainly is. But what’s clear is that by the time Election Day rolls around (see the graphic below), approval ratings correctly differentiate winners from losers in 10 out of 11 instances, yielding an overall accuracy of 91%.

The only exception is Gerald Ford, who failed to be re-elected even though I estimate he had an approval rating of about 51-52% on the day of the 1976 election.

Of course, none of this is to say that approval ratings are an exceptionally good predictor of re-election.

As the messiness of the graphic above illustrates, job approval ratings can be incredibly variable, and this is particularly true early in a president’s term and far in advance of an election. Some pollsters and political scientists argue that approval ratings aren’t very predictive of subsequent re-election until about 6-8 months ahead of Election Day.

But – and although we should be hesitant to place too much stock in any sort of re-election prediction this early on in Trump’s presidency – perhaps we can still glean some useful insights into Trump’s re-elections chances by closely tracking his approval numbers over the next three years.

Toward that end, I’ve developed a model to track Trump’s chances at re-election based entirely on job approval numbers.

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## The Geek Psychologist Job Approval-Based Re-election Model

My re-election model estimates the chance that Donald Trump will be elected to a second term using current and historical job approval ratings from Gallup’s telephone-based daily tracking poll. I obtained all Gallup polling data from the American Presidency Project.

The Gallup tracking poll is particularly useful because it’s been around for a long time, and there’s a good amount of historical data to draw upon for the purpose of comparing Trump’s current job approval numbers with the job approval numbers for previous presidents.

In fact, George Gallup was the first to conduct presidential job approval ratings in the U.S. in the late 1930’s. As such, the Gallup organization possesses job approval ratings for the last 13 administrations, stretching all the way back to July 1941, during Franklin Roosevelt’s third consecutive term in office and before his re-election in 1944 to a fourth term. Unfortunately though, Gallup’s approval numbers for Roosevelt are of limited use because, due to World War II, no polling was conducted in 1944.

## How the Model Works

To estimate Trump’s chances of being re-elected in 2020, my model takes Trump’s current approval ratings and looks for approval ratings that roughly match these numbers within a comparable window of time in the historical data for each of the previous 11 administrations. I’ve excluded Kennedy because he was assassinated prior to re-election, and Roosevelt because, as mentioned above, Gallup did not poll for job approval in 1944 due to World War II.

If the model finds a set of poll numbers that roughly match the latest numbers for Trump, it next computes the probability of re-election based on a determination as to whether Trump’s latest approval numbers seem more characteristic of a president who later went on to be re-elected or whether they seem more characteristic of one who later went on *not* to be re-elected.

For instance, say the model is looking to compute the probability of Trump being re-elected as of October 20, 2017, which was 1,110 days prior to Election Day on November 3, 2020. To do this, it will scour the approval ratings for each of the previous 11 administrations (again, excluding Kennedy and FDR) and look for any past presidents with similar approval ratings at around 1,110 days prior to Election Day.

So, if Trump’s approval rating, according to Gallup, was 36% at 1,110 days out from Election Day, the model will look for past presidents with approval numbers between 26-46% at around 777-1,381 days prior to Election Day (more in a minute on how these ranges are determined). Then, it will estimate the probability of Trump being re-elected using *Bayes’ Theorem*, which is a mathematical formula describing of the probability of some event based on prior knowledge and conditions that might be related to that event.

Since the model looks to calculate the probability that Trump will be re-elected *given* a particular range of job approval numbers, the final calculation is based on four pieces of information:

- The baseline probability of being
*re-elected regardless of approval ratings.* - The probability of a particular range of approval ratings for incumbents who later went on
*to be re-elected.* - The baseline probability of
*not being re-elected* - The probability of a particular range of approval ratings for incumbents who later went on
*not to be re-elected*.

## Model Predictions as of October 23, 2017

For comparison purposes, I’ve developed three different prediction models – one that uses Bayesian inference, as described above, to provide estimates based solely on job approval numbers from the Gallup tracking poll (referred to as the “Gallup-Only Model”); a second that also uses Bayesian inference, but which relies on aggregated polling data from many polls in addition to Gallup (referred to as the “Aggregate Polling Model); and a third that does not rely on Bayesian inference at all, but instead uses a logistic regression model with two predictor variables, specifically approval ratings from Gallup tracking polls and the number of days prior to Election Day each poll was conducted.

The predictions for each model, as of October 23, 2017, are shown below:

## Major Take-Away

As of October 23, 2017, my job approval-based models estimate that Trump has anywhere between a 74-85% of being re-elected. The Gallup-only model puts his current chances at 74%, and the Aggregate Polling Model puts his chances somewhat higher at 79%. The logistic regression model, which is considerably less variable and more optimistic about Trump’s prospects at this point, estimates his chances for re-election at 85%.

If these percentages seem high, particularly in light of Trump’s underwater job approval numbers, it’s partly because, in recent political history, incumbent presidents generally have an extraordinary advantage over their political challengers when it comes time for re-election.

Since 1941 (the earliest year for which we have job approval numbers from Gallup), only three out of 12 incumbents, excluding Kennedy, failed to be re-elected – Gerald Ford in 1976, Jimmy Carter in 1980, and George H.W. Bush in 1992. That means the baseline probability of being re-elected, regardless of approval ratings, is an impressive 75% (or slightly lower at 73% if we exclude FDR, as we did in the present analyses).

So, even though Trump’s job approval numbers are presently low, the advantage for incumbents is so great that even these dismal poll numbers aren’t quite bad enough to do major damage to his chances for re-election – at least not yet, anyway. Indeed, there’s still a lot of time before the 2020 Election for things to either turn around for Trump, stay the same, or potentially get even worse.

Indeed, if we plug some numbers into my logistic regression model, we see that, if Trump’s approval ratings remain at around 40% six months prior to Election Day, his chances at re-election will sink to 47%. And if he fails to bring his approval numbers up by Election Day, he will have just a 39% chance at being re-elected.

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## Some Important Caveats

Finally, just a few brief points about some of the potential limitations to these model predictions.

Given everyone’s difficulty forecasting the 2016 presidential election, and the fact that Election Day is still quite far off, I certainly don’t expect these models to offer perfect forecasts at this point in time. So, take these predictions with a grain of salt for the time being, and keep in mind a few important caveats.

First, because we only have job approval data going back to 1945, my model’s predictions are necessarily based on an extremely small sample size of only 11 presidents. Moreover, and as already mentioned above, the sample size of recent presidents who failed to be re-elected is even smaller, at only three. The degree to which we can extract meaningful generalizations from such a small data set is presently unclear.

Second, polling for presidential job approval ratings is much more popular today than in years past. The graphic below shows the number of job approval polls Gallup conducted for each incumbent president prior to each respective Election Day.

Gallup conducted 863% more job approval polls during the Obama administration (1,321 polls) than during the next most polled administration, which was that of George H.W. Bush (153 polls).

Because polling is far more commonplace today than during the time of previous administrations, it’s not always possible to find, within a given window of time, historical approval ratings that roughly match the latest numbers for Trump. This is especially true when scouring data from older administrations, when polling was especially infrequent, and when both the range of approval ratings and the window of time being considered are narrowly defined.

I’ve tried to get around this problem by doing two things.

First, my Bayesian model casts a wide net when scouring the historical database for job approval numbers that roughly match those of Trump’s. For instance, the model is currently set to look for approval ratings that come within 10 percentage points of Trump’s latest numbers, and to scoop up polls from past administrations as long as they were conducted within about 333 days of the sought-after date. Importantly though, these windows will narrow over time as we get closer to Election Day.

The second way I’ve tried to combat the problem of infrequent polling during prior administrations is by using Loess Regression to estimate approval ratings for those days for which no polling data exist. Although this strategy has the advantage of increasing the size of the historical database of presidential approval ratings, it carries the disadvantage of introducing yet another source of error into the models’ predictions.

All of this is to say, then, that these model predictions should be viewed, at best, as mere estimates of Trump’s chances at re-election. Nonetheless, these estimates should stabilize and increase in predictive value as we get closer to Election Day 2020.

So, check back often, as I’ll be updating the model’s predictions over the course of the next 1,107 days. I may tweak the inner workings of models a bit here and there, too, as we go.

# Author

*Brian Kurilla is a psychological scientist with a Ph.D. in cognitive psychology. You can follow Brian on Twitter @briankurilla** *