## NEW

Explore scenarios and track each candidate’s chances of claiming the presidency, depending on which states they win—and by how much.

# The electoral map

Hover over a state to see the chances each candidate has of winning it, and click on a state to see more detailed forecasts.

has a chance of winning, but what does that really mean? There is a wide range of possible outcomes, at the state level and nationally. Click the button above to randomly simulate a possible election outcome.

### All the possible outcomes

The histogram above shows the distribution of electoral votes that the model is currently predicting. The wide range of possible outcomes reflects the inherent uncertainty in predicting elections. The fact that small numbers of votes can flip a state from one candidate to another, along with all of that state’s electoral votes, means that this distribution is very spiky, unlike a normal bell curve.

# How the odds have changed

The model works by first building a structural forecast for the national race and the race in each state, based on economic indicators, the president’s approval rating, past election results, the home states of each of the candidates, and incumbency and regional effects.

The model then uses state and national polls to estimate public opinion in every state and nationally, and makes a forecast for Election Day by simulating thousands of possible elections, taking into account the structural forecast based on the non-poll factors.

Of course, there is a lot of uncertainty in elections and polling. The model takes this into account, combining uncertainty across all of these factors to arrive at an overall distribution of the number of electoral votes that each candidate will win. From this distribution, we can figure out the chances that Biden and Trump will win at least 270 seats and claim the White House.

The model is updated regularly as new economic and polling data come in. The charts below show how the forecast has evolved over time.

This chart shows how the model’s estimate of the overall probability of winning the presidency has changed over time. Because the model is based on random simulations, these probabilities will naturally jump around a bit, so a shift of a few percentage points in either direction doesn’t usually reflect a change in the state of the race.

This char shows the estimated range of electoral votes that Biden will win, and how it has changed over time.

The range will narrow as we approach the election, because we will have more information, and there will be less time for the race to be upended by an economic or political development.

The outer band above is an 90% credible interval, meaning that based on the information available at the time the forecast was made, there was an 90% chance that Biden would win a number of electoral votes somewhere in that interval. The inner band shows a 50% credible interval.

This chart shows the estimated popular vote margin (excluding write-ins and third party candidates), and how it has changed over time. Right now, the model estimates that Biden has a chance of winning the popular vote.

The range will narrow as we approach the election, because we will have more information, and there will be less time for the race to be upended by an economic or political development.

The outer band above is an 90% credible interval, meaning that based on the information available at the time the forecast was made, there was an 90% chance that Biden would earn a popular vote total somewhere in that interval. The inner band shows a 50% credible interval.

# State forecasts

The table below summarizes the race in every state, including the forecasted vote share (excluding write-ins and third parties), probability of winning, and some measurements of how important each state is to the overall race. You can click on the column headers in order to sort the table, or click on a state to see more details.

What does it mean to say that a state decided an election? If we think about listing states in order of their support for the winning candidate, and then going down the list, counting up the cumulative number of electoral votes, the deciding state is the first state on the list where the cumulative votes are above 270. In 2016, the deciding state was Wisconsin; in 2012, it was Colorado. (These states are also called “tipping-point states”.)

If we divide the chance that a state decides the election by the number of voters in that state, we get the chance that a single voter will decide the election. If we compare this chance to the average chance across the country, we get a measure of how much relative power voters in every state have to determine the election. Small states where the election is close have the most powerful voters, whereas large states or states where the election isn’t very close have the least powerful voters.

State Chances of winning Estimated vote share
Bands show 50% and 90% credible intervals
Margin Chance of deciding election Relative voter power

Select a state to see detailed forecasts and how they’ve changed over time.

has electoral votes and voted for and .

# Possible scenarios

Usually, whichever candidate wins the popular vote wins the presidency, but as the 2016 election showed, that’s not always the case—the electoral vote winner could have less than a majority of the popular vote. And there might not even be a clear winner of the Electoral College on election night:

• There is a chance of an exact tie in the Electoral College, in which case the election would be thrown to Congress.
• There is a chance that the deciding state will have a vote margin less than half a percentage point that will trigger a recount, which could take weeks. Think Florida in 2000.

As for the other scenarios, it’s much more likely that Biden will win the popular vote but lose the election, like Clinton in 2016, than that the same will happen to Trump.

### What happens if… ?

There are many paths to 270 electoral votes. No one state is critical for a candidate to win. But states’ outcomes are highly correlated with one another, and winning one state can be a sign of strength elsewhere.

The buttons below are for the fifteen states most likely to decide the election. Click them to cycle through hypothetical winners and play out different scenarios. What if Trump wins Florida but Biden wins Pennsylvania? What if Biden sweeps the Rust Belt? You could even use these buttons on election night to provide live estimates of the race as each state is called.

Reset all

# Model components

The model works by combining various structural, non-polling factors with state and national polls to arrive at an overall forecast for the election. The sections below provide more detail on each of these components.

### Prior model

The first component of the model is a so-called “prior” guess about what the national popular vote will be. This is based on a simple but accurate model by political scientist Alan Abramowitz, which has correctly called the winner of the popular vote in every post-World War II election except 2016, where it predicted Trump would win the popular vote. The model takes three inputs:

• The average of second- and third-quarter annualized GDP growth is estimated by the New York branch of the Federal Reserve at .
• The president’s current approval rating (among those stating an opinion) is .
• Trump is a first-term incumbent.

These give us a prior expectation of the national popular (excluding write-ins and third parties) vote of for Biden.

The second part of the model is a prior guess about how the vote in each state will differ from the national vote. The best predictor of this differential is the results in the last two elections, but the model also adjusts for year and region variation, incumbency effects, and home state effects—the tendency of presidential (and to some extent vice-presidential) candidates to over-perform in their home states.

### National polling

With the initial prior guesses in hand, the model then combines them with polling data to arrive at an election-day forecast.

Support for Biden or Trump in polls now is obviously not necessarily the same as their vote share on Election Day. The model adjusts and averages polls to estimate public opinion for each 3-day period of the race up to the present day, and then forecasts how it will change toward November.

Since Super Tuesday, polls have been conducted. Polls conducted early on in the race (especially national polls) don’t have much impact on the overall forecast, since voters’ opinions will change a lot before November. But as we get closer to Election Day, the polls become more informative about the final result.

The chart below shows the model’s estimates of voters’ margin of support for the candidates for each point in the race. The rightmost values on this chart are the election-day popular vote forecast.

In estimating the popular vote from polling data, the model also takes into account the tendency of certain kinds of polls to over- or under-estimate the support for each party. For example, polls of likely voters are generally more accurate than polls of all registered voters, and the latter tend to lean more Democratic.

In addition, certain polling firms have a pattern of producing polls that lean toward one party or another. These “house effects” are estimated by the model and used to make adjustments in estimating overall public opinion. Negative house effects (red) mean that the firm’s polls overestimate Republican support; positive effects (blue) mean that the firm overestimates Democratic support.

FirmPollsHouse Effect

### Methodology

The above components section lays out the general overview of the model. All submodels operate on the logit scale. The prior models for the national vote and state differentials are linear models (with random effects for the state model); Cauchy(0, 2.5) priors on scaled and centered predictors were used. The random effects in the state prior model give the predicted state outcomes a pairwise correlation of around 0.5; this correlation is rather sensitive to the model specification but does have an impact on final inferences. More robust estimation of the state result covariances is an area in which the model could be improved.

The polling model is similar to a 2016 election model by Pierre-Antoine Kremp, which in turn is built on Drew Linzer’s dynamic Bayesian forecasting model. In contrast to those models, this one incorporates a critical adjustment for the bias of registered-voter and all-adult polls, uses past election data to estimate polling errors, and uses more informative priors on national and state outcomes, built from the linear models described above.

Essentially, there is a latent national voter intent, and latent state differentials (how much more or less Democratic the state is than the national vote), which evolve as a random walk with Gaussian increments in 3-day and 3-week steps (the states’ walk has larger steps for computational reasons). The national and state priors become priors on the final step of the random walk, so prior information is percolated backwards in time. Student-t-distributed increments were also explored but the data were not very informative for the degrees of freedom parameter, and the model predictions changed very little.

Each poll is considered to be a binomial draw whose probability depends on the latent national and state (if a state poll) voter intent, adjusted for the polling firm’s house effects, the type of respondents (registered voters, likely voters, or all adults), poll-specific error, and state, regional, and national polling error.

Each of these adjustments is a parameter that the model estimates. Polling error cannot be estimated from polling data, and essentially just adds noise to the model. The distribution of these polling errors is estimated from past elections’ polling errors. For computational reasons, states’ polling errors after accounting for national and regional error are assumed to be i.i.d. This yields pairwise correlations of state polling errors of around 0.7. In reality, polling errors (and final outcomes; see above) are likely to be more correlated in geographically close and demographically similar states; this remains an area of potential improvement.

Election outcomes are simulated by looking at the Monte Carlo draws of the latent state and national intent parameters on Election Day. The congressional-district based electoral vote allocation rules in Nebraska and Maine are not modelled; elections in which one of the states’ votes go to a candidate other than the statewide winner are unlikely to be elections in which the outcome is decided by a single electoral vote.

Fit to data from the 1972 to 2012 elections and run on 2016 polling and economic data, the model identified the Rust Belt as an area of weakness for Clinton and consistently gave her a less-than-50% chance of winning the election, in contrast to all other major polling aggregators in 2016. Of course, hindsight is 20/20, and some knowledge about the final result inevitably crept into model development and testing. But in contrast to most aggregators, the model is fully Bayesian and therefore optimally blends structural forecasts like Abramowitz’s time-for-change model with polling data, rather than making ad-hoc weighting adjustments or ignoring the latter entirely.

Models were fit using Stan. Model code and data are available online. Email me with any questions.