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Sharpening the 2016 Presidential Forecast

August 21st, 2016, 2:47am by Sam Wang

Today I present a beta version of the sharpened forecast. In May, I said that I would update the model after the dynamics of this year’s race became clear. Back then, I wondered whether the 2016 campaign would be more like 1952-1992 (high variability), or like 1996-2012 (low variability). This year’s data indicate that it is the latter – opinion is relatively stable. That stability affects the November forecast.

This is an open comment period. Technical feedback is welcome. (The comments section is rather good this time.)

The Princeton Election Consortium’s prediction of November outcomes is based on the assumption that the race, as measured by the Meta-Margin, can drift in either direction between now and Election Day. The Meta-Margin, which is calculated entirely from state polls, is measured in units of margin between the two major candidates. Today it is Clinton +5.5%, which means that Hillary Clinton would defeat Donald Trump in the Electoral College, and polling margins would have to move across the board by 5.5% toward Trump in order to create a toss-up. If the change is larger, then Trump would be favored to win.

To understand how likely such a change would be, we have to have a measure of volatility during the general election season. That measure is the standard deviation. Since 1952, it has looked like this:

From 1952 to 2012, the two-candidate polling margin has had a typical standard deviation of 6% during the general election campaign. In other words, if you compare any two moments in time during the campaign, national polling margins at those two moments will usually be within 6% of each other – about two-thirds of the time, to be precise. If the two moments are close in time – for instance October 1 and Election Eve – the difference would be even smaller. This allows us to make a prediction about the future.

However, something changed starting in 1996. As I have written before, national politics in the United States became dramatically more polarized starting around 1994, when Newt Gingrich led Republicans to take over the House and Senate. Since then, as the graph shows, Presidential campaign dynamics have gotten much more stable. National polling margins have varied by only 3% on average. The Meta-Margin is even more steady, with a standard deviation of 1-3%.

The same point is obvious when examining the original time series plots of Wlezien and Erikson, whose data I used to make the graph above.

It is now apparent that 2016 is more like 1996-2012 than it is like 1952-1992. Data points for 2016 are included in the graph above. Even though the breakdown of the Republican Party and the advent of Donald Trump have made 2016 a crazy political year, public opinion is more stable than ever.

The Princeton Election Consortium’s initial assumption was that 2016 would be as volatile as typical campaigns since 1952 (SD=6%). This was a conservative assumption with lots of uncertainty. It was consistent with claims by pundits – and by Republican candidate Donald Trump – that the electoral map was scrambled. However, that scrambling has not materialized. Obama blue states are still Clinton blue states, and with a few exceptions, Romney red states are still Trump red states. This again shows that voters are highly entrenched in their views.

Here is what a “high variability” assumption (SD=6%) gives:

And here is what a “low variability” assumption (SD=3%) gives:

Starting today, we will use a lower-variability assumption. This makes the November win probabilities higher for the leading candidate, Hillary Clinton. The random-drift win probability goes from 78% to 92%, and the Bayesian win probability goes from 86% to 95%.


Finally, there is another step, which is converting the somewhat obscure Meta-Margin back into electoral votes, which is far better known. This has also been updated. Previously, the conversion was done using June polling data and 2012 election results, which led to a hard ceiling for Hillary Clinton because Romney’s wins were fairly large. Now that we have polls in more states, it has emerged that both Clinton and Trump have some fairly weak leads. That means that a small swing of opinion in either direction now leads to corresponding changes in EV. The “electoral strike zone” now reflects that possibility.

Going forward to Election Day, the electoral strike zone will be based on the latest polling data.

High-variability, with old Meta-Margin to EV interpolation:

Low-variability, with new Meta-Margin to EV interpolation:

The change not only makes a Trump win less likely. It also makes an electoral blowout by Clinton less likely. It might also make a switch in House control less likely.

By the way, originally I was going to wait until after Labor Day to make this modification. It would have been a logical time. However, the variability in national poll margin and in Meta-Margin is not going to change in the coming two weeks. Plus I am impatient.

Also…Labor Day is in only two weeks. Summer is nearly over, everyone!

Update, August 22, 3:00pm: The best counterargument in the comments section is the issue of undecided/third-party voters. This year, that fraction is at 20.5% of voters; in 2012, the corresponding number was 9.5%. This raises the issue of whether this year is going to be like 1968/1980/1992/1996, years where the third-party candidate got 7-19% of the popular vote. In those years, the SD ranged from 4% to 14%.

Graph credits: Thanks to Prof. Christopher Wlezien of the University of Texas for the national polling data, which forms a major foundation for his book with Robert Erikson, The Timeline of Presidential Elections. The Meta-Margin data come from past calculations here at the Princeton Election Consortium.

Tags: 2004 Election · 2008 Election · 2012 Election · 2016 Election · President

101 Comments so far ↓

  • Shawn Huckaby

    Great to see things coming into sharper relief. Do you see this greater stability model reducing the likelihood of the Senate and House flipping as well?

  • Richard

    I find the 1992-1996 anomaly in standard deviation very disturbing. You point to Newt Gingrich as an element, but it looks like there was a huge change in US politics. Is there more going on here?

    • Greg

      The fairness doctrine was abolished in the late 80s and Fox News was founded in 96. I suspect that is part of the explanation for the change.

    • Heavenly Blue

      Likely related to the rise of the internet, social media, and alternative media. Instead of getting information from relatively neutral sources like cable news, people isolate themselves into echo chambers with personalities saying exactly what they want to here. Consideration of different viewpoints doesn’t extend beyond hurling 140 character insults at the opposition.

    • Sam Wang

      1990: Rush Limbaugh show reaches five million listeners.

      1994: Newt Gingrich multiyear campaign in House leads Republicans to gain control.

      1996: Fox News Channel founded.

    • Richard

      The changes in law/media must be part of the answer, but would seem to predict a gradual and progressive change, instead of the observed step-function (?)

    • AWC

      The period 1986-1994 is when the GOP completed its takeover of the South at the state level.

      For instance, Alabama elected its first GOP governor since Reconstruction in 1986. Mississippi elected its first GOP governor since Reconstruction in 1992.

      This gave the parties a much greater ideological, ethnic, religious, and geographic cohesiveness.

    • Kalil

      I think partly, ’92’s instability was dramatically exacerbated by the closest thing we’ve actually had to a ‘black swan’ even in the last half century or so – the Perot exit and return. Without that, the transition to post-post-partisan politics might have appeared more gradual.

    • Scott J. Tepper

      Although it occurred in 1986, William Rehnquist’s elevation to Chief Justice and Antonin Scalia’s appointment as an Associate Justice began to be felt in the early 1990s when the Court began to dismantle much of the social safety net. The Court’s actions in doing this should not be discounted on their affects on our society and politics.

  • George

    As a Clinton supporter I like the new numbers, but as a person who finds this year very unsettlingly different from previous campaigns, I would have waited until Labor Day and the effects of the latest “pivot” came into better focus. Time will tell.

    • Sam Wang

      Yes, that was the original plan. However, I was fixing a small problem (the Meta-Margin to electoral vote imputation for November) and I got impatient to fix everything at once.

      Anyway, the metrics I was using – standard deviation of national polls and Meta-Margin – will not be affected by anything that is likely to happen in the coming two weeks. There is little to be gained by waiting…other than decorum.

    • Rachel Findley

      Remember 2004? It seemed so reasonable to project…. What was it…. Undecideds breaking against the incumbent? Instead of sticking to the half baked tossup. Beware the seemingly reasonable thumb on the scale. I’m leaving the cake in the oven until after Labor Day.

    • Sam Wang

      Note that I am not doing anything untoward with the polls! No assignment of undecideds. nope, definitely done with that.

      Now, it could be argued that I have moved on from erroneous assumptions about the first moment, and I have graduated to being wrong about the second moment. Rachel, is that what you think? ;-)

      Seriously, are you saying it is better to just put up with the Eisenhower-era assumption? Comment please.

    • NHM

      It seems to me that the safest thing to do would be to use the election with the highest MM SD. Each election is different, and I would prefer to know the worst case scenario now so as to temper expectations. As election day approaches, this ends up mattering less with respect to your “prediction”

    • Alan Cobo-Lewis

      Sam Wang wrote:
      Now, it could be argued that I have moved on from erroneous assumptions about the first moment, and I have graduated to being wrong about the second moment. Rachel, is that what you think? ;-)

      Move on to third moment. Then you could say the polls are–ahem–unskewed.

      Thank you, I’ll be here till Nov 8

    • Sam Wang

      Don’t forget to tip your server. Try the chicken – it’s excellent.

  • Marco

    Foreign born, arrived in the states in ’85. I observed, somewhat with detachment, Bush senior election and subsequent loss to Bill Clinton. That loss so riled the Republican party (even though it was all Ross Perot’s fault) that their initiated their strategy of de-legitimizing (they are not honest, not like me and you, they are evil, they are stupid etc) anything the Democrats did. Add Hate Radio, Gingrich and Fox, and this lead us to Trump. The country is divided in two, and not one side believe the other side at all. The fluctuation of opinions are now ONLY due to a few that have not made their mind yet. Sam is right. Changes will be minimal, if any.

  • Greg Gross

    Sam, the cake! It’s baked! It is out of the oven and on the cooling rack. I am impatient to have a slice. But until I taste it in November, I will just enjoy the aroma…. Thanks for interpreting this stuff in a manner that even statistics morons (like me) can find understandable.

  • bks

    I track all the regularly updated, serious, electoral vote projections that I am aware of (currently 11). One peculiarity is that the most (D) site, Daily Kos, has Trump with the most EV (226) and the most (R) site, RealClearPolitics, has Trump with the least EV (154)

    • Andrew

      Daily Kos is very conservative (not in the political sense) in its election ratings across the board. Charlie Cook and Larry Sabato, for example, estimate somewhat better Democratic prospects in the Senate this year than does the Daily Kos official rankings.

    • Jim Higgins

      It’s all about setting expectations, when “setting” is part of the equation. That’s what I love about Sam’s work. He just looks at the numbers. I love his personal bias, but love even more his dispassionate analysis of data.

  • Brandon Steele

    Something changed? Counterpunch launched in 1994. Drudge Report in 1995. Fox News and MSNBC in 1996. Smoking Gun and WND in 1997. And since then we have Huffington Post, Politico, Breitbart, Right News, Democracy for America, and legion other news boards, discussion threads and other self reinforcing bubbles.

    • Chris

      The Internet also hit critical mass in terms of diffusion between 1993 and 1995, which means 1996 would have been the first election that the Internet played a large role. The cold nature of the Internet as a medium of information creates an incentive for echo chambers. Selective biases have become the norm and probably leads to higher level of polarization and lower likelihood of changing your mind.

  • E L

    Well, Sam, that’s a relief. I can’t help but get caught up in the pundits attempt to turn the election into a close election for viewing $$$. I think my small panics are caused by my Trumpophobia. And now that he’s put Steve Bannon into a position to set his election strategy, my Trumpophobia intensity meter has gone to 9+. Fortunately, in Sam I trust.

  • Paul LeVine

    Remember too that Bill Clinton’s first election was a pretty seismic shock to the right, really marking the beginning of the hyper-partisan period in which Democrats were really identified as “the other” and the Republicans’ : was to oppose him at all cost.

  • Bruce Sands

    Bks mentioned black swans – I would guess those type of events increase volatility? A major terrorist attack, or a major negative revelation about either candidate? Is there a way to model a negative event?

    • Sam Wang

      Use a t-distribution, which has long tails of unexpectedness, instead of a Gaussian.

    • BrianTH

      Here is a super crude model, but I find it useful to clarify my thinking.

      Take the probability of an event that is so dramatic if renders the polling before it truly irrelevant. In a way this probability is just going to be a guess because there is no real way of estimating this from historic data.

      But one caveat to that–it has to be a REALLY dramatic event. We’ve seen lots of events over time people thought would really shake up a contest, and often the lasting effects end up being minor. So we are talking here about a candidate dying, a truly epic scandal that forces a withdrawal, something like that. And something like that happening should get a low probability–something like 5%, say.

      OK, now divide it in half, because such a thing could benefit either candidate. Using 5%, that’s 2.5%.

      OK, so each candidate gets a fixed, unremovable, 2.5% chance of winning. And let models like Sam’s (or another if you prefer) handle the other 95% (or whatever is left if you don’t use 5%).

    • Some Body

      The thing about black swan events is that they are very rare, almost by definition (BrianTH proposed a 5% probability, but it does tell you something that not one such event as described happened in all the presidential elections from 1788 to 2012, which is n=57, so a probability much more than 2% seems a bit overly-cautious). An argument along the lines of “but a black swan event may happen” has no more bite against a 95% probability prediction than it has against an 80% probability. It’s only good against claims for absolute certainty (100% probability), or something very close to that.

  • shma

    Hi Sam, two questions

    1)Are the degrees of freedom in your t-distribution for the near-term drift chosen based on empirical data (i.e. do you tune it based on the historical frequency of upsets)?

    2) Should you keep M2016SD=6 in the prior now that’s you’ve settled on the low-variability assumption? I would think 3, or the actual variability year-to-date would be more in line with that assumption.

    • Sam Wang

      I chose d.f.=3 to give a bit of a tail. The small number of elections does not constrain this parameter well. I just wanted to allow for a small likelihood of a black-swan event.

      I purposely set the prior to be weak. This time around, I did think about making it narrower, but I held back simply because I started it so weak. Anyway, with a narrow SD to limit the maximum diffusion, the prior does not seem to make a huge difference.

  • Scott J. Tepper

    Your data assume Trump will run a typical campaign. So far he hasn’t. While GOTV may only be good for 1%-3%, sicne Trump doesn’t have any, that could make this a blow out election notwithstanding the steadiness.

    • Jay Sheckley

      Scott, you write,”Your data assume Trump will run a typical campaign. So far he hasn’t. ”
      But, PEC’s data assumes Trump has THIS campaign, as is, and tracked here.
      We may see Trump’s stock rise due to the coming debates, as debates are too often judged as entertainment, with an unfortunate emphasis on the blathering of voters still undecided by Fall.
      But PEC’s forecast is based on the variability seen to date.
      “While GOTV may only be good for 1%-3%, sicne Trump doesn’t have any”
      Well there’s that, though GOP underticket candidates and RNC may Get Out The Vote.
      “… that could make this a blow out election notwithstanding the steadiness.”
      Or _because_ of the steadiness, right?

    • Kevin King

      I have a feeling this might happen. IIRC, while the race was still seen as competitive Cruz, who had an advanced campaign operation, consistently overperformed Trump to the extent that I think Sam took account of it. The persistent underperforming eventually went away, but I think there might be a chance that the effect will come back.

      I was listening to a podcast interview of Jeff Rowe by Glenn Thrush of Politico, and Mr. Rowe said that he thinks the difference in the campaigns could lead to a 2%-5% Clinton advantage in the swing states. He’s a numbers guy, but I don’t know what he based that on.

  • Dan Albert

    “Meta” Technical Question of sorts: The Forecast Certainty Principle?

    How does measuring the state of and projecting the election influence the course and result of the campaign?

    Politicians, donors, operatives and the public read polls, and that changes behavior.

    Trump’s sustained miserable polling since the convention has changed behavior. Just one salient example, Republicans openly talking about ‘breaking the glass’ — abandoning Trump and focusing on the down-ballot.

    Thought and data welcome.

  • mbw

    That first figure is fascinating. And thanks for the very transparent description of the switch.

  • Richard

    It’s ironic that Fox News and the ’90s-2000s rise of Right Wing radio has not really helped the Republican as intended. Yes, combined with Gerrymandering, it’s done wonders for the GOP in the House, state legislatures, and, to an extent, the Senate. But what these media phenomena have •also• done has been to (1) solidify a ceiling of Hard Right voters in around the mid-to-high 30 percent range of the US electorate; and, (2) repulse or otherwise frighten off around 50% of the rest of the electorate.

    On top of this is the fact that the several million loyal listeners to Limbaugh and his brethren, and who devotedly watch Fox News, means a revenue stream continues for such media, so they’re not going away anytime soon. But they’ve hit their respective ceilings, AND their demographic (older white men) is shrinking in both real terms and as a percentage of the total US population.

    Interesting times…

  • Mark F.

    My feeling is that a Trump win is very unlikely, but the Democrats will take back the Senate with 51 or 52 seats. I expect the Democrats to gain about 15 House seats, not enough for a majority. Many Republicans will vote for Clinton or Johnson , but will not vote for Democrats for Congress.

    Policy implications? The Dems will try to pull a few Republicans over to their side on some issues. The Senate filibuster will prevent any radical changes, and will force President Clinton to make more “moderate” Supreme Court choices.

    • Scott J. Tepper

      If Schumer is smart (and I don’t believe anyone thinks otherwise), he’ll try to modify the filibuster rules again. Ideally they should prohibit filibusters on any judicial or executive appointments, and allow delays but only delays in legislation. There may be a few old line Democrats who will be reluctant to go along, but you can’t get there unless you try. Gridlock is bad for democracy, notwithstanding what Republicans think (and what Justice Scalia used to write to the contrary).

    • Josh

      This seems like compelling logic at first blush, but then how do you explain the fact that the Generic Congressional Ballot (D +7) and Hillary’s lead over Trump (D+7.5) are almost identical? Do you think poll respondents are asserting that they’d vote for D’s up and down the ballot but will bail on down-ticket Democrats once in the booth?

    • Sam Wang

      An alternative explanation for the close match between Presidential and Congressional preference is that disaffected Republicans respond to the presence of Trump on the ballot by becoming less likely to vote. This would alter Presidential and Congressional preference by the same amount.

    • Mark F.

      I don’t think most people lie to pollsters. The evidence argues against my theory right now, you are correct. But things could change.

  • Jeffrey Henning

    Given the small sample size of Presidential elections, I fear you are overfitting. I liked the model better before this change.

  • Jim Higgins

    I have the statistics training of a Wharton MBA and many years as a stock analyst, and the logic makes perfect sense to me. Black swans are, by definition, unpredictable, but it’s hard to envision any event that would want to put Trump closer to the nuclear codes by a meaningful amount.

  • Bill Herschel

    Upon reflection it is not at all surprising that as the electorate has become more extreme and fixed in its views electoral variability has declined. I guess you’ve said that.

    What seemed unusual for a brief time was Trump’s lack of adherence to the extreme belief playbook of his party, in particular, his accommodation with Russia and his sympathy for LGBT people.

    But Trump has now shown his true colors (and I don’t mean orange). He is the opportunist’s opportunist. In the words of a friend of mine, he bullshits the bullshitters.

    It’s over.

  • George

    Sam, in response to your question back to Rachel about whether to keep the “Eisenhower Era” assumption – here is my non-math answer:
    When I look at the spikes in variability, I see 1964 (Goldwater Extremism), 1980 (Iranian Crisis in context of crappy economy) and 1992 (plain speaking Ross Perot in the mix). Then I look at this year’s candidates and situations and see similarities, e.g., the extremism of the Goldwater year, the scandals or pseudo scandals of emails and Benghazi along with a less than robust economy looking a bit like the 1980 situation, and the non-orthodox campaign of Trump, along with a potential spoiler roll for Johnson. So my non-math approach would have been to stick with the high variance model, OR incrementally crank it down week by week (or not), as you/we saw whether or not things were baking or shaking. But time will tell….

    • Daddyoyo

      The economy today is in far better shape than the stagflation of 1980 and there is nothing comparable to the hostage crisis. Perot got into the debates. Johnson won’t.

  • A New Jersey Farmer

    Many of us thought that the first debate in 2012 was a Black Swan for Obama, and it looked pretty ominous as the Meta-Margin took a dive, but it only turned out to be that Romney showed he was not the rapacious capitalist monster that Obama’s ads made him out to be.

    This year, only an arrest would swing the election to Trump. The first debate will be entertaining, but it won’t move the needle much.

  • Amitabh Lath

    I think going to a smaller SD is the right move. I looked up the original post from May 1 where you first showed the Wlezien and Erikson plots. The lack of jitter in the more recent (high-polarization era) plots is unmistakable.

    Here is the link:

  • Ketan

    I think the 3% red range is too tight because there are 2.6 months left, and there was a 3% shift in the MM since mid-July.

    The ~1% green dot for the MM in 2016 also seems too low. If the MM didn’t change for the rest of year at all (which would most justify the tightened range,) then half the time it is around 3% and the other half around 5.5%. Despite being bimodal, I don’t see how that ends up being a 1% SD.

    With respect to black swans, it feels like there is a minimum level of uncertainty in the polling data that doesn’t cancel out with more data. All the polls can, in hindsight, be wrong about turnout or make a bad choice on demographics, for example.

    Thanks Sam for keeping this site going. It’s truly refreshing.

    • Amitabh Lath

      Ketan , I’m missing your point. The SD is taken from the Wlezien and Erikson data which plots deviation from the final election results, not the value of the MM. The deviations for all elections had a larger SD than post-1996 elections.

      So, if the MM did not change at all going forward (and that was the election result also) then you get 3 months of zero deviation (now -> Nov).

    • Sam Wang

      I agree that the shift in MM since mid-July is an interesting event. However, the SD of the Meta-Margin so far is 0.74%, considerably smaller than the 3% that I am assuming.

      (If you do not feel like munging through this website to figure out that the MM is stored in column 14 of this CSV file, recall a useful rule of thumb: SD is approximately 4* the range of the data. The maximum Meta-Margin is +5.7% so far, and the minimum is +2.5%, giving an estimated SD of (5.7-2.5)/4=0.8%.)

      If the MM stayed at 5.7% until Election Day, the overall SD would end up as 1.2%. If it suddenly went to zero and stayed there until Election Day, the overall SD would be 1.9%.

    • Ketan

      @Amitabh – There are tiny green dots in the bottom right of the first graph in this post. It shows an SD of ~3, 1.5 and 1 for 2008, 12, 16 respectively for MM.

      My point about the SD (which I made poorly..) is that the current MM average (~3.5?) is less than recent values. As the average catches up, the variance of the whole set will rise. In other words, the variance is currently low because we don’t have many data points where it is outside (3, 4).

      I agree that variance over campaigns is low and has been falling, per W+E data. (However, take a look at the congressional D-R graph. It’s much swingier; so less entrenchment or something else?)

    • Sam Wang

      I calculated the House preference statistics for May 1st to now, and got an average=D+3.1%, with an SD=3.0%…which isn’t that bad. Obviously there is a big discontinuity toward the end of June. However, for all January-May, there were only 6 polls.

      Calculating from the original polling data points (as opposed to the filtered time series plot), for 2016 I get average=D+5.8%, SD=3.6%. This SD includes pollster-to-pollster variation, which tends to be larger for this question than for named-candidate polls. So the true SD is probably 2.5-3%.

    • Ketan

      @Sam. Makes sense; 3% is a good compromise between 1 and 6. Thanks for the reply!

    • Jeremiah


      “(However, take a look at the congressional D-R graph. It’s much swingier; so less entrenchment or something else?)”

      We really cannot compare the variation of the House Congressional Preference to the meta-margin (say) because it should be much more susceptible to swings in the polls. The Electoral Vote is the aggregate of the median of 50 state polls and the House poll is the median of 3 of the latest polls.

  • Matt McIrvin

    I can’t help but compare this chart to your earlier analysis of regional realignments, which implies that really big year-to-year swings in regional voting differences yielded to a more gradual motion around 1976-1980.

    In both cases, there was an abrupt drop in variability, but it happened at different times. Maybe this is essentially the same shift, but masked for a while by the effect of Reaganism?

    • Sam Wang

      Could be, though it depends on what you think caused the residual change from 1980 to 1992. Correlations mask first-order effects like Reagan’s big electoral wins by effectively subtracting the average. I see your point though – in particular, based on this post, which contains the following graph.
      If you inspect these graphs closely, it still seems that electoral alignments froze into place around 1996.

      In fact…this frozen configuration is what allows to talk about “red states” and “blue states” – the D and R states stay stable from election to election, so TV and cable have a motivation to keep the visual display the same. Apparently this uniformity started in 2000.

  • Steve Scarborough

    I think you are right on target in moving to the lower SD assumption based on 1996 and later. I have made my livelihood as a statistician since the early 1970s. Did not start presidential election modeling until 1992. I started noticing the same thing you are addressing but in 2000. So, I say keep up the good work! FYI, I switched to using medians back in 2012 after studying your work for my own election modeling. I use a shortened version of the polynomial; but I also deploy a 100k monte carlo simulation using win probabilities. FYI, for the data as of this past Friday, the state by state medians show Clinton with 347 ECVs. My 100k simulation shows 85% chance of Clinton winning. I characterize this as just for if the election were held now. As of now, I have not tried to project to November 8th. Thanks for your great work and willingness to share!

    • josh f

      Sam, always great articles and this year particularly the insight of consistently taking a big picture view has been refreshing. I think making your change 2 weeks earlier than planned gives you a nice window to take in feedback and refine if needed- interesting approach.

      re: shrinking bayesian lookback, i respect your decision but i wonder how years with 3-party vote variance compares to more typical two-party variance? i believe since 50s there’s at least 4 data points there (1968, 1980, 1992, 1996), so maybe doesn’t tell you much but overall i think 3rd party vote is greatest risk to your forecast.


  • Joel

    Is in-sample variance predictive of future variance? In other words, if there are large swings in public opinion in June-July, does that predict larger swings in public opinion (for the same election) in August-September?

    • Sam Wang

      That is an excellent question. To answer both Ketan and Amit, here is a comparison of the last 90 days before the election with 91-180 days before the election. Today we are at 77 days.

      The correlation is r=+0.38 for 1952-2012 overall, +0.34 for 1952-1992, and +0.64 for 1996-2012). Significance values (p<0.1) are insufficient for peer review but then again see my blogging credo. ;-)

      For 2016 national polls, the SD for 91-180 days was 1.4%, solidly in the 1996-2012 range.

      Finally, for parameter estimation: the early/late ratio is 1.7 +/- 0.8 (median +/- est. SD) for 1952-1992, 1.0 +/- 0.2 for 1996-2012. A ratio of 1.0 means that if we accept the polarization argument, we now have a good estimate of volatility in the coming months.

    • Jeremiah

      I think of all the discussions this is the critical chart to consider. I didn’t really look at this chart closely yesterday but it is very instructive. I think the way to look at this chart is to ask oneself what scenarios would point to upsetting the prediction? Even with all of the data the maximum SD for 1-90 days before the election is 4 percent and the average is much less than this. A SD assumption of 3 percent would therefore seem conservative. Also, there are no data points in the upper left quadrant of the chart and there is only one data point where the SD got much larger closer to the election and that was still less than 3 percent.

  • Matt McIrvin

    538 is talking about how they see a very mild tightening in national polls but not, yet, in state polls. That’s not really a surprise: I’d expect at least a little bit of regression to the mean after the DNC and Trump’s subsequent disasters.

    I was a bit baffled when Sam’s last re-analysis of the strike zone made it more symmetrical in EV, since, while Trump is weaker than past Republicans in deep-red states, I still didn’t think most of them would flip linearly with a rise in Meta-Margin.

    I see that the asymmetry has returned to a milder degree, and that a result above 380 EV for Clinton is about as improbable as Trump winning. That strikes me as about right.

  • Amitabh Lath

    Ketan’s question about the recent shift in the MM made me look at the historical data.

    There is a clear feature in the polls at day = -90ish. You can see in the E&W data for most years. For instance look at the 2000 data, it seems bimodal.

    Even in years with a lot of scatter (1952, 1980, 1988, 1992) the last 90 days or so seem remarkable stable.

    Maybe worth looking at a tightening of the SD post-Labor-day?

  • Matt McIrvin

    A good way of describing the current red zone is that it’s more or less bracketed on the bottom by Obama-2012-without-Florida (which was Sam’s call on election eve, if I recall correctly: Florida was polling really close) and on the top by Obama 2008.

    • Josh

      That sounds right to me. Hillary would probably have to win the popular vote by less than 3% to lose Florida, and would have to win the popular vote by more than 7-8% to go above 350 EV (Obama got to 364 by winning Indiana which is probably out of Hillary’s reach).

    • Matt McIrvin

      Hillary’s path to the 2008-level numbers is slightly different from Obama’s: it might involve winning Arizona, Georgia or Missouri instead of Indiana, for instance.

  • JAW

    How much of the reduction in SD is due simply to polling density increasing? I wonder if old polling was done at swingier points and was more infrequent inflating the SD.

  • NHM

    I completely disagree with doing this. You’re essentially using a sample size of three to come to this conclusion. There is still a lot that could happen between now and the election date to drastically alter the meta margin. For instance: What if Johnson ekes out another 5-8% more support in the polls and gets into the debates? If it happened, then who knows how this might shift the meta-margin (increase Clinton’s advantage substantially? Decrease her advantage?)? You could potentially be looking at a 1992 scenario. I’m in no way saying this scenario is “likely”, but it is “possible”… and considering it’s still a possibility, such a scenario should be incorporated into the uncertainty of the model.

    What if Johnson doesn’t get into the debates? Well… these debates are without a doubt still going to be THE most watched debates since perhaps the Reagan/Carter debate of 1980. What if there is a major gaffe? I won’t even speculate what sort of gaffe that might be, but the 1980 debate is often cited as a primary reason that Reagan had a “come-from-behind” victory (arguably not an accurate assessment – see your figure above… but what IF that happened?). What if one of the FOUR debates now could produce a sizable shift (in who knows which direction) in voter sentiment outside your SD = 3%? You could be looking at a 1992 scenario.

    What if Trump successfully moderates his message from now on? I’m not suggesting this is “likely”, but it is a “possibility”. What if there is a major “international incident” with political ramifications? China tested its first nuke in 1964 and this greatly affected the campaign discussion. Goldwater managed to moderate his extremist right-wing views after the primary? You get something like this happening, you’ve got an election potentially similar to 1964. Again, I’m not saying it’s “likely”. I’m saying it’s “possible”, and as such should be incorporated into the model.

    I don’t think any of the scenarios that I describe above are “likely”, and I do believe that Clinton is “likely” to win. However, I believe it’s quite “possible” that she will lose, and you will pardon me if I take your own advice:

    “[I] take no interest in specific scenarios; we want the median outcome that takes into account all possibilities. This gives the most precise possible answer, but it lends itself poorly to color commentary.”
    – In the current situation, you have limited your scenario to a very specific “lower-variability” assumption rather than taking into account all “possibilities” (not “likelihoods”… “possibilities”).

    As a result, your “prediction” / calculation (“while it lends itself [well] to color commentary”) has resulted in it being VERY close to a significant outlier (Grubbs test) relative to other statistically-based prediction sites. Therefore, as a “consumer” of such sites, I think that on any other day you would suggest that I look at the median calculation as giving “the most precise possible answer”… and that is about 10 points lower than your current “prediction”.

    While I’m an avid Clinton supporter and I WANT your 95% calculation to be true (especially this far out), I frankly don’t believe it … and if it wasn’t your calculation I don’t think you’d believe it either.

    (Further, if Clinton ends up winning within your new predicted margin (with lower variability), you don’t get to say “I told you so”… Because you would have gotten to say “I told you so” with your “old” high-variability predicted margin anyway! I think you’re taking a risk, and you’re positioning yourself well to “call” the election earlier than other sites, and if Clinton wins [which is admittedly likely, but it’s “possible” she’ll lose], you’ll get lots of accolades… accolades from people who haven’t been reading your site for multiple elections [even when you made similarly bad assumptions before]).

    • Sam Wang

      I see your point, though I guess my counter-question is: what is the appropriate range of elections over which we should estimate this parameter?

      Your point about the range of projections by other sites is well taken. Does this mean that probability=90% today is okay, while 95% is “too much”? I agree that it is kosher to ask whether the outputs satisfy my intuitions – and other sites are a source of intuition. But when does that become following the crowd?

      Finally, a note on what difference any of this makes. As of today, with MM=Clinton +5.7%:

      drift = 3% –> random drift probability 92%, Bayesian 95%
      drift = 4% –> random drift probability 88%, Bayesian 92%
      drift = 5% –> random drift probability 83%, Bayesian 89%
      drift = 6% –> random drift probability 79%, Bayesian 86%

    • G Washington

      Bro, do you even read this site?

      The whole of the meta-margin and all of the analysis is that it is completely based on polls. All of your hypotheses are for the land of pundits, not here.

      While you can argue about the choice of standard deviation (did Trump “scramble” the map???), the data support the current choice. Regardless, this part is the prediction, which always requires some choice. Even in your scenarios, you would make a choice, but one that is not based on data.

    • Matt McIrvin

      (Further, if Clinton ends up winning within your new predicted margin (with lower variability), you don’t get to say “I told you so”… Because you would have gotten to say “I told you so” with your “old” high-variability predicted margin anyway!

      This is a defect of the political media, though. I’ve always thought Nate Silver’s predictions were over-hedged, even on Election Day. It ought to be more impressive if you call a result with narrower error bars. The performance of prediction sites in the past few cycles does suggest that if you’re broadly agreeing with 538, you’re probably overhedged too.

      Sticking your neck out is good, if the distribution we see in reality turns out to be commensurate with the claimed values. Sharper hypotheses are more interesting than vaguer ones.

    • Amitabh Lath

      NHM, the issues you are raising that could affect the election are all eminently possible. But in terms of writing down a probability density function (PDF) these sorts of cataclysms are accounted for by making the tail heavy, not necessarily by fattening the core of the PDF with a larger SD.

      As to the tail, I believe Sam already uses a non-gaussian PDF (t-distribution?). You could argue he should use a Pareto or log-gamma distribution maybe.

    • Lorem

      NHM, this sounds like an argument from loss aversion. What if the things you list happen and they change nothing? That feels very likely to me (and I don’t mean the “happen” part).

      My preference is to try to estimate the “true” probability, and using updated numbers seems like a reasonable way to do that. I don’t see a reason to prefer assumptions that seem less accurate to those that seem more so, particularly when the gap in accuracy seems significant.

      If you feel reluctant to believe 95% because you anticipate that you would feel really bad if the 5% comes to pass, I believe it is much more appropriate to brace yourself and check your expectations of how you would feel, rather than altering the probability estimate.

      I should mention that my personal bias is that from the beginning, I have had a strong suspicion that the election would have low variance due to both candidates being very well known (as well as polarization). So, I am happy that assumptions are being shifted in that direction.

  • Mike

    Sam – I think a lot of people share an intuition that there is something about this race that should discourage us from grouping it with the other post-1996 elections in terms of volatility. It seems like it would be worthy to look for numerical support for that intuition, if only to see what the strongest argument is against the low-variability assumption.

    • Sam Wang

      I agree with you, and I welcome the argument.

      I offer this synthesis of data (2016’s SD of national polls and Meta-Margin so far) and events (crazy Trump): the U.S. is suffering from a near-fatal case of polarization. Think of it as the culmination of the partisanship and gridlock of 1996-2012.

      The best counterargument I can think of is a general version of NHM’s comment. We currently have 20% undecided-plus-Gary-Johnson votes. The Clinton+Trump total is 79.5%, compared with 91.0% Obama+Romney on the same date in 2012. Because third-party votes are especially fluid in the home stretch, that leads to more uncertainty in 2016 than in 2012. This is especially important because many of those voters are Republicans who might break toward Trump.

    • alurin

      I don’t see why we should weight intuition more highly than data. Despite all the pontificating about how crazy this race is, the polls have not been very volatile, the red states are the red states and the blue states are the blue states. It’s an entertaining/frightening race if you read the papers, but a pretty boring one if you look at the numbers. So far, the difference between The Donald and Mitt Romney is that Romney did better overall, not that anything is qualitatively different about this year.

    • Olav Grinde

      Seems to me there is yet another important contrast to past presidential elections (be they pre- or post-1996: An election victory by Donald J. Trump is actually far more likely than him giving a concession speech in the event of a loss.

      Such a questioning of our democratic institutions – and the viability of American elections – is truly historic! And it may have some very ugly repercussions.

    • Sam Wang

      The concern about undecided/third-party voters can be quantified as follows. (tl;dr – scenarios involving third-party voters coming “home” seem to fit within the SD=3% assumption).

      Compared with 2012, the additional uncertainty this year is Gary Johnson voters, who are currently at about 8%. The maximum plausible range of what they will do ranges from all going for Trump (i.e. 8% toward him) to maybe a 5%-3% split toward Clinton (i.e. net movement of 2% toward her). The approximate SD of such a range of possibilities is one-fourth of the total span. So SD_3rd_party =10%/4 = 2.5%.

      Now, let us further assume that this is a source of uncertainty that is totally independent of what we’ve seen so far in polls. The empirical SD so far this season is 1.4% so far. Independent errors sum using a rule that amounts to SD_overall = sqrt(SD1*SD1 + SD2*SD2) = sqrt(2.5*2.5 + 1.4*1.4) = 2.7%. That is pretty close to the sigma=3% in my new assumption.

      A two-sigma event would occur if three-fourths of Johnson voters all went to Trump, and none went to Clinton. I think it is reasonable to classify that occurrence as a two-sigma event, i.e. “unusual but possible.”

    • Some Body

      @alurin: There *is* something qualitatively different this year, even if it were the case that the polls show no evidence for it (though they do, indirectly). Horeserace numbers are not all that counts, and not all that matters in life is quantifiable.

    • Mike

      Sam – If I understand your update, the argument is that taking undecideds into account for 2016 pushes the SD up to 2.7%. But in years with similar number of undecideds (1968/1980/1992/1996), SD was 4%-14%. Would your analysis applied to those years have also predicted SD < 3%?

      Also are the Wlezien and Erikson data available?

  • RoF

    Awesome as always, Dr. Wang. Question: how soon have you seen a poll change after the debates? Does it usually take a 3 day cycle as most other polls do after something significant in the media is touted? Or is it more of a snap poll? Thanks again.

  • Ketan

    I claim that half of the other/undecided voters will not vote. I offer as (weak) evidence the difference between polls on registered voters (RV) versus likely voters (LV).

    FL. last three RV polls put 18-20% as other/undecided
    FL. last six LV polls puts 8-13% as other/undecided.

    Looking at 2012, looks like the LVs had about half as many undecided as the RVs at the end (5% vs 9%).

    So, the 20% undecided will shrink going forward as the polls switch (mostly) to using LV vs RV.

    Still 10% is a lot, and it would be interesting to see the demographics of undecideds who plan to vote.

  • John Handy Bosma

    Relaying a question from my nine- and 11-year-old daughters. What do the colors in the Meta-Margin and Median EV Estimator mean? They’ve taken a keen interest in the election and asked me why I was reading your page … I explained, but they’d rather see a legend than take my word for it. I see their point.

    • Sam Wang

      That is terrific. I think the election is a great way to learn about math and statistics, because it has an outcome we care about, especially with the historic nature of Hillary Clinton’s candidacy. Math helps us understand it without all the shouting and opinionating that happens in the news.

      The red and yellow bands are similar to what we see on hurricane maps. They show where the Presidential race is most likely to end up.

      The red band is the range where the Meta-Margin (or the final Electoral Vote count) is most likely to end up. Approximately two-thirds of the time, polls that are like today’s should end up somewhere in the red band. This band is sometimes called the “one sigma range,” because sigma (a Greek letter that is like S) is a measuring stick that describes how much the Meta-Margin (or Electoral Vote count) will go up or down.

      The yellow band is the “two sigma range.” About 95% of the time, conditions like today’s will end up in the yellow band.

      This has been a great discussion. Thank you all.

  • Letteredwolf

    Sam, a question about the electoral college map you have on the right side. There doesn’t appear to be a comments section on that page so posting here.

    Currently, as I type this, the legend on the bottom left says:
    Trump safe 139 EV
    Clinton safe 256 EV

    The Trump number of the EVs of the states shaded the darkest red is correct. But the Number for Clinton appears off. Taking the EV of all the dark blue states, so not including the medium and light blue states of NC, OR, NC, and OH, nets a total of 296 EVs.

    So a couple possible reasons I can see, the number of safe EVs is not updating, the color isnt updating, I am being blind or being tricked by an optical illusion, or something else.

    On a note about the colors, for me at least, the difference between the 95% color and the 80-95% color for both red and blue is close enough that if a state in any of those colors wasn’t bordering a state of the same faction for comparison purposes I would find it hard to figure out if a state was in the safe or the likely category. As an example Florida in the current map. I am pretty sure it is showing 95% blue, mainly thanks to it being so close to the legend. But even then I have a slight error bar in my mind of that.

  • Alan Cobo-Lewis

    There seems to be a big step function in the earlier era around 100 d before election. Im guessing this is the used-to-be-big convention bounce. What does SDresid look like if this conventionbounce*year interaction is removed?

  • Ketan

    Sam mentioned that the low-variance facet of this campaign “might also make a switch in House control less likely.”

    But 20% of even LV are undecided (and no Johnson element to factor); so maybe still time for some variance?

  • H

    Could you pls, explain what the widths of the yellow and orange zone projections actually mean — in your figures for EV and vote percentages etc.? How many SD or …?

    Even a little documentation — just following the most basic scientific standards– would be really helpful here … Thanks!

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