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## The Details

Almost since its founding, FiveThirtyEight has published comprehensive averages of polls for a wide variety of questions related to U.S. politics. In June 2023, we debuted a new set of models for these averages that aims to improve the models’ accuracy and how the results are visually conveyed to our readers.

The most important differences from our old polling-average model are:

**We now use separate models for each type of polling average.**Polling averages need to process information differently in different contexts: For example, presidential approval ratings and horse-race polls can change faster than favorability ratings and generic ballot polls. To account for these variations, we now derive separate sets of parameters to control the aggressiveness of each of our polling averages for presidential and vice-presidential approval, politician favorability and different types of horse-race averages (presidential elections, presidential primaries, senate and gubernatorial general and primary elections, and the generic congressional ballot), using our historical database of polls.**House effects can change over time, and have more uncertainty.**We don’t want to make unnecessarily large adjustments to a pollster’s house effect as a result of a poll conducted when one candidate happened to be surging, so our house effects are now calculated using the value of the polling average on each day of the time series, rather than the average over the entire time period. Our house effects are also now formally Bayesian, which means the value we end up using in our final average is higher when (a) we have more polls for that pollster and (b) the individual differences from the average for each poll are more narrowly distributed.**We dynamically adjust our average based on two different aggregation models.**We want to avoid scenarios where there aren’t many polls for a while, then a deluge of new data creates a whiplash in the average. To help with that, when we have more data in a recent time period, we rely less on our slow-to-update exponentially weighted moving average and more on our more aggressive polynomial regression trendline. This also has the benefit of giving us averages that are more responsive to quick movement in the data when multiple polls reflect that movement, without reacting too aggressively to any one individual survey showing a big change.**We calculate uncertainty for every average.**Previously, we only displayed uncertainty intervals for our presidential approval average. Now, to visualize the noisiness and estimated error across each of our models, we show uncertainty intervals for all the various types of averages we run.

Here are all the steps we take to calculate our averages:

**Which polls we include**

FiveThirtyEight’s philosophy is to collect as many polls as possible for every topic or race we’re actively tracking — so long as they are publicly available and meet our basic criteria for inclusion. After determining that a poll meets our standards, we have to answer a few more questions about it before sending it off to the various computer programs that power our models.

**Which version should we use?**If a pollster releases multiple versions of a survey — say, an estimate of President Biden’s approval rating among all adults and registered voters — we choose the survey that best matches either the breakdown of polls in our historical database or the preferred target population for that type of poll. In practice, that means if historical polls on a particular topic (for example, presidential approval or favorability ratings) were mostly published among all adults, we will prefer polls of all adults to polls of registered voters and polls of registered voters to polls of likely voters. But for polls of a primary or general election, where we are mainly interested in the subpopulation of Americans who are likely to (or at least able to) vote, we prefer polls of likely voters to polls of registered voters and polls of registered voters to polls of all adults.**Is it an especially large survey?**When polls are fed into the model, we decrease the effective sample sizes of large surveys. Leaving these large numbers as they are would give those polls too much weight in our average. As a default, we cap sample sizes at 5,000. Then, for all polls conducted for a given context (say, approval ratings), we use a method called winsorizing to limit extreme values.**Do we know the sample size?**Some pollsters do not report sample sizes with their surveys, especially for polls released a long time ago. While we can usually obtain this number for recent surveys by calling up the firm, we have to make informed guesses for past data. First we assume that a missing sample size is equal to the median sample size of other polls from that same pollster on the same topic (i.e., favorability, approval or horse race). If there are no other polls conducted by that firm in our database, we use the median sample size of*all*other polls for that poll type.**Does this matchup reflect something that could happen in reality?**For horse-race polls, we exclude polls that ask people how they would vote in hypothetical matchups*if*those matchups have already been ruled an impossibility, such as after each party has chosen its nominee. We also exclude polls that survey head-to-head matchups in races with more than two major candidates.**Is this a tracking poll?**Some pollsters release daily results of surveys that may overlap with each other. We account for this potential overlap in these “tracking” polls by running through our database every day and dynamically removing polls that have field dates that overlap with each other until none are overlapping and we have retained the greatest number of polls possible for that series and firm, paying special attention to include the most recent poll.**Is there any other problem with this survey?**In addition to excluding all polls for all pollsters that don’t meet our standards, individual surveys may also be excluded for other methodological reasons, which we explain in detail on our polls policy page.

**How we weight and adjust polls**

After all this data is in our database, we compute two weights for each survey that control how much influence it has in our average, based on the following factors:

**Sample size.**We weight polls using a function that involves the square root of its sample size. We want to account for the fact that additional interviews have diminishing returns after a certain point. The statistical formula for a poll’s margin of error — a number that pollsters (usually) release that tells us how much their poll could be off due to random sampling error alone — uses a square-root function, so our weighting does, too.**Multiple polls in a short window.**We want to avoid a situation where a single pollster “floods” a race with its data, overwhelming the signal from other pollsters. To do that, we decrease the weight of individual surveys from pollsters that release multiple polls in a short time period. If a pollster releases multiple polls within a 14-day window, those polls together receive the weight of one normal poll. That means if a pollster releases two polls in two weeks, each would receive a weight of 0.5. If it releases three polls, each would receive a weight of 0.33.

Once we have these weights, we calculate a cumulative weight by multiplying the two weights. We then test and adjust for any factors that could be systematically shifting groups of polls in one direction. We consider three main adjustments here.

**Population adjustments.**For each type of survey, we have a preferred sample universe — for example, likely voters for horse-race polling or all adults for presidential approval. Not every poll will use that preferred sample universe, though, so we adjust to minimize variation between different population groups. These adjustments come from a generalized additive model that predicts poll results using variables for the population of each survey, its methodology (whether people were reached online, by phone via a live interviewer, by phone via automated dialer, etc.) and the end date, which the model transforms using a spline (you may also have heard this referred to as a “piecewise polynomial”). The result is an estimate of how much polls from each population category differ from each other on each of the possible candidates or responses. We use those values to adjust polls from populations we are not interested in to look more like the one we are targeting.**House-effect adjustments**. Second, we adjust polls for “house effects,” or the tendency for certain polling firms to produce polls that consistently lean one way or another relative to the average poll conducted around the same time. We estimate house effects using a similar formula to the population adjustment explained above, but we use a statistical technique called Bayesian updating to make sure the adjustments for a given pollster are not sensitive to noise in the data. That’s because what looks like a house effect in an individual poll could just be abnormal amounts of random sampling or other error. This added step shrinks our model’s initial estimate of a pollster’s house effect back toward zero. Our assumption here is that house effects may look large at the beginning of a series but will diminish over time in the absence of other data. Specifically, the regression we run in the adjustment model gives us both an estimated mean and standard deviation for the house effect for each pollster, which we use to update a normal distribution with a mean of 0 and a standard deviation of 3. For national averages, we estimate house effects using only national polls. For state-level averages, we estimate house effects from both national polls and state-level polls, since there typically aren’t enough state-level surveys from an individual pollster to reliably calculate a state-level house effect.**Trendline adjustments.**Finally, for averages of state polls, we apply a trendline adjustment to control for movement in the national political environment between the time the poll was taken and whatever day the aggregation model is run on. This adjustment gives us a better estimate of public opinion in states with sparse polling data. Imagine it’s the 2016 election and you only had polls from Pennsylvania up to Oct. 15, but national polls released up until Election Day. An average of national polls would have shown significant tightening in the race over the last three weeks of the campaign, but an unadjusted average of the Pennsylvania polls would have been stuck at the value of polls taken in mid-October. This simple average would thus have been highly misleading if taken at face value.

**How we average polls together**

Once we have collected our polls and adjusted them, we can finally calculate a polling average. Our final polling average is actually an average of two different methods for calculating a trend over time.

The first is an exponentially weighted moving average, or EWMA (a popular tool in financial analysis). The EWMA calculates an average for any given day by calculating a weight for each poll based on how old it is, multiplying the poll result by that weight, then adding the values together. We select the value for a parameter called decay, which determines the rate at which older data points are phased out of the average according to an exponential function.

The second is a trend through points, calculated using a methodology similar to that of the now-defunct Huffington Post Pollster website and the forecasting methodology used by The Economist. We fit this trend using our custom implementation of a kernel-weighted local polynomial regression, which is just a fancy way to calculate a line through points. The trendline and weight on any given poll in this regression depend on two parameters that we also have to set: the bandwidth of the kernel and the degree of the polynomial.

Once these two trendlines are calculated, we calculate a mixing parameter to determine how much weight to give each trendline in our final average. This weight depends on the number of polls conducted over the last month. We put more weight on the polynomial regression when there is more data available to estimate it. That has the benefit of giving us less noisy averages, because the local polynomial regression detects movement quicker than the EWMA, which is useful when we have news events that move public opinion and coincide with a big dump of new data.

Finally, we use a technique called optimization to test the calibration of our model by calculating thousands of different averages for each politician and race in our historical database using different values for each of our four hyperparameters (the parameters that govern the behavior of a model): decay, bandwidth, degree and the mixing parameter. For each type of polling average, our model picks the set of parameters that generate the optimal values for two measures of accuracy:

- The
**mean absolute error**our polling average has in predicting future real poll results. For every time series in our historical database, we calculate an average on every day in the series and then take the average difference between every poll result and the calculated polling average 28 days earlier. **Error autocorrelation**, which captures how well we can predict the differences between polls and the average on a given day based on*previous*differences between the polls and the average. This ensures that the model strikes the right balance between predicting future poll results and describing past data; a polling average shouldn’t bounce around to match the value of every poll on every day, and neither should it be a straight line on a graph. When autocorrelation is too high, a model is not reacting enough to movement in the underlying data. Too low, and it’s reacting too much.

In 2023, we started calculating these hyperparameters values separately for each type of polling average (that is, presidential approval ratings, favorability ratings and horse-race polling averages). That means that we are always specifying the type of aggregation model that minimizes these two measures of error *for that type* of polling average. This results in averages that are more reactive to changes in the horse race, which tend to happen as a result of real campaign events, and less reactive to changes in favorability rating polls, which are due more often to noise.

And that’s basically it! FiveThirtyEight’s polling averages can really be thought of as two different models: one that measures any biases resulting from the polls’ underlying data-generating process, and another to aggregate polls after adjusting for those biases.

There is one last feature of note. As with any model we run, polling averages contain uncertainty. There is error in the individual polls, error in our adjustments and error in selecting the hyperparameters that produce the optimal trendlines. Starting in 2023, all our polling averages convey this uncertainty by calculating and displaying the 95th-percentile difference between the polling average on every day and the polls published those days. This “error band” represents the uncertainty in that average.

Finally, while we have tried to squish all of the obvious bugs in our programs, we are always on the lookout for anything we might’ve missed. If you spot something that you think is a bug, drop us a line.

## Version History

**1.0** Favorability, approval and horse-race averages.

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