Princeton Election Consortium

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Sound bites and bug bites

November 4th, 2016, 9:19am by Sam Wang


We’re entering a period when all the math and data gets converted to short quotes. The above quote is pre-Comey, but I will live with it.

I have some interviews this weekend. I doubt that I will be asked about median-based probability estimation. With luck I will get to the question where there’s real suspense: who will control the Senate?

Here are the weekend’s planned TV hits. I’ll update this as things develop.

All times are Eastern.

Friday: 6:00pm, CNN Money cancelled!. 10:00pm, MSNBC with Lawrence O’Donnell. 11:00pm , CNN w/Don Lemon to talk about this.

Saturday: 9:00am, CNN with Mike Smerconish (possible rebroadcast at 6:00pm).

Tags: 2016 Election · President · Senate

227 Comments so far ↓

  • NeverNeverTrump

    Sam
    Love your blog. Thanks for helping me sleep better these last couple of weeks.

  • kelly m

    Just wanted to say thank you! This site helps me sleep at night.

  • Not gonna be year 109

    I’m new to this website, and I really love the analysis. I think what I like even more is the lack of trolls that I see on every other site. Dr. Wang, do you actively purge trolling statements or is it just a matter that this is a bit more of a pedantic site and that discourages the trolls? I apologize if this has been asked often, I tried looking through the comments and didn’t see it posted elsewhere. Regardless, great stuff–keep up the good work!

  • Brian MacDougall

    You didn’t specify exactly how you would eat a bug, did you? Just, “I’ll eat a bug?” Voila, chocolate chip cookies made with cricket flour:

    https://bittyfoods.com/products/chocolate-chip

    They won’t, however, get the taste of President Trump out of your mouth… that will be likely to linger longer.

    • ErnestoDelMundo

      Maybe Pootie can make Trump the prez of the Ukraine as a consolation prize. Manafort is already keeping the seat warm for him.

    • Corey

      Remember, he also has to eat a bug if Hillary wins Texas. If Dr. Wang keeps up this bug talk he’s going to have a bug riding on an awful lot of outcomes.

  • Eli

    Dr. Wang (or regulars who know), what was the meta-margin computed from the actual 2012 state returns, versus the final poll MM? And is this available for earlier elections as well?

    I’m interested in what the observed difference is between polling — even if you had infinite amounts of polling — and voting. This might come from the challenge of likely-voter modeling, and the effects of GOTV and vote suppression.

    • Josh

      Final national polling median ’12: Obama +1
      Final MM ’12: Obama +2.78
      Final actual MoV: Obama +3.9

  • Jeffrey Weiss

    This is the best comment string related to this election today. High culture, incomprehensible math and bug recipes…

    (I will ask this: Given the shifts in many of the recent polls, shouldn’t there be *some* shift in the forecasts here?)

  • afleitch

    Sam,

    There seems to be a flood of unknown firms flooding the average by having ties in MI and PA, Clinton +1 in Colorado and only +3 in NM (the internals are…intersesting) How does the model deal with these? We have less polls this year (and 2012 had less than 2008) because ‘who needs polls, we have the models’, which in turn leads to less polls going into the model and perhaps, though only perhaps, polls designed to impact upon the model. There needs to be something like the British Polling Council; if you’re not signed up and you’re not transparent, then it’s not counted as a poll.

    What are your thoughts?

  • Anthony

    BREAKING: Shots fired between Nate and Sam on Twitter.

    • Kevin King

      Yeah, I heard Nate fire a shot at Sam on his podcast! He said don’t follow Sam, basically.

    • anonymous

      The fox is going all out for clicks this election. It seems to be a high pressure time. Just curious, what is the origin of this conflict?

    • Tim L

      Sam’s comeback killed it. i can’t believe the headlines on his site today – “Trump is within a polling error of the lead” (or something like that). Isn’t everyone? All the time?

      I know what they meant, but the headline is total click bait.

    • 538 Refugee

      Danged. You guys made me go look at that site. SHAME ON YOU! Let Nate do his own click bait. ;) I wonder if Silver would take bets at the odds he’s pitching? He has New Hampshire as the state that decides the election? According to his tipping point point chart whoever wins New Hampshire wins the election. Currently he gives the nod to Clinton. A few more bad polls for Clinton there and he’ll be picking Trump to win the election.

      After missing Trump in the primary he has a lot riding on this outcome I guess. Is he over compensating the Trump appeal because HE missed it first time around? Now only HE sees it for what it is? We shall see on Tuesday I guess.

  • Kevin B.

    H’m. The current snapshot histogram seems to allow for a tiny number of Trump wins within the 95% confidence interval. The random walk prediction (which doesn’t use a Bayesian prior?)is at 98% confidence in a Clinton win, however. I follow this site pretty closely, but I guess I don’t understand these predictions as well as I think?

    • Tony Asdourian

      Right. I left a comment above asking the exact same question. Since half of the remaining 5% is on the right side of the curve, that would make 97.5 % confidence if the red line was exactly on the left edge of the blue. But since the red line is inside the blue, it would seem like the Clinton win snapshot is at 97% or 96% today. I too don’t understand how that becomes 98% in 4 days without the Bayesian prior.

  • Bill

    Another thing to consider before we become too sure of the presidential race: the mass-transit strike in Philadelphia. We NEED those votes in Philly and its suburbs to ensure victory in PA.

    I thought I’d read the union was willing to provide service on Election Day if the strike was still on, but now I read the city will have to FORCE them to (if the strike has not been resolved) and that the union president is saying they may refuse to provide service even if ordered to by a court.

    That union–in its short-sighted FOLLY–is holding the nation–and the world–hostage. They may get Trump elected if, because of their strike, we lose PA.

    • ErnestoDelMundo

      PA has not gone Republican in a presidential election since 1988. It isn’t nearly close enough this year for a transit strike to flip it to the likes of Donald Trump. This election has set so many all-time records for bedwetting and handwringing and there are still four full days to go!

    • Ruth Rothschild

      Bill,
      Sam addressed this in another thread at this site the other day when someone asked the same question. His response was that alot of people (apparently ones living in the downtown Philly area) walk to the polls rather than use public transportation. Hopefully, their union won’t refuse to provide service for those who rely on it to get to the polls. I would hope that, in case the union president follows through with his refusal to provide transportation for the public, there are both contingency plans being put in place by city officials and also that the courts have an order all set to go with a warrant for the union president’s arrest and immediate incarceration so that mass transit can temporarily resume for Tuesday. This is just another form of voter suppression if the union president does this and he should be arrested for this blatant suppression.

  • Kuriakose

    Amitabh, i like the reference to Godel with reference to the constitution. Our intentions cannot be completely specified in a finite document.

  • TeddyVienna

    I think for most of us, this election is like a colonoscopy. We have every reason to think it’ll turn out OK, but we’re not exhaling until it’s over, and the prep for the procedure is dreadful.

  • M. Leo Cooper

    The developing story is FBIgate. A cabal of former FBI agents, in collusion with Rudy Giuliani and possibly a few others, conspiring to try to influence the outcome of the election by carefully timed leaks. Now that the details are becoming clearer, will a backlash develop that helps Clinton?

    https://www.washingtonpost.com/news/post-nation/wp/2016/11/04/rudy-giuliani-is-claiming-to-have-insider-fbi-knowledge-does-he-really/

  • Michael Bol

    Thailand imports 800 tons of bugs to eat every year. You’ll be in plenty of company.

  • AAF

    The median outcome, currently 311, has moved pretty far away from the mode, which looks like it’s at 323 and dwarfs every other individual EV outcome probability. If this were a competition among prognosticators, would you be betting on 311 or on 323?

    I think Upshot doesn’t even disclose the median, just a histogram and the mode. It’s hard to tell what 538 does but I think it might be the mean, which seems kind of weird.

  • fred flint

    Just an opinion but I think Sam is being overly cautious by suggesting Trump can get to 240EV.

    I think, with Hillarys massive ground game and media money buys, compared to Trumps unusual lack of either this cycle, it will be a bigger win than todays numbers suggest.

    Last week I would have said that it could be a bigger win than Romneys 206EV’s in 2012, I’m a little less sure about that this week.

    • Mark F.

      I would not be SHOCKED if we either had a very narrow Trump victory or a +8 Clinton blowout. Smart money is that she does about as well as Obama in 2012.

  • fred flint

    Turn off and tune out. The only poll that matters is the election day result. Media always always always wants to portray a horserace. It’s mostly all noise.

    This site is such a nice no drama respite from all that.

    • Johnny

      Damn right. I cannot listen to any more of the hyperventilating cable news coverage. If the race was “tightening” as much as their continual loop graphics have had it for the last week, it would implode like a neutron star. We really need to repeal and replace the TV media.

  • Alejandro

    Long time lurker, first time poster Dr. Wang. I’ve found your website to be an island of sanity in this sea of clickbait-narrative driven uncertainty. That being said, you have to work on your threats. Cricket tacos are delicious and if you’re ever in Jalisco, MX I’ll tell you where to get the best in town!

    Regards,
    Alejandro

  • Mark F.

    Will you live stream the bug eating? I think Clinton will win, but I think Trump gets over 240. ;-)

    • Froggy

      It’s a little early for final predictions, but if I had to make one today it would be Clinton 323, Trump 215.

  • Drew

    How does one go about getting the time series history for each state? I see one CSV for the final EV with no dates..but no state level data

  • Ezra

    The tipping point for Sam eating a bug is Florida. If Hillary wins Florida, there is no way Trump can make 240 even if he wins every swing state “less Democratic” than Colorado. If Trump wins Florida, it’s likely a 272-256 election (Hillary wins with VA+CO, but I’m giving Maine’s 2nd district to Trump).

    • Sam Wang

      The bug tipping point…that is a new one on me.

    • TeddyVienna

      We used to go bug tipping in college all the time.

    • Matt McIrvin

      It actually seems kind of odd to me that the red strike zone is now smaller than Florida. I guess the several days of post-Comey snap polls there have been pretty consistent with about a Clinton +2, which bodes well.

    • ErnestoDelMundo

      Republican women might be the demographic that crushes Trump in Florida.

    • BrianTH

      You can also replace Florida with OH/NC or AZ/NC, but obviously Florida is the most likely path to a bug-free meal (well, detectable-bug-free . . . ).

  • Justin

    But Dr. Wang, as a Princeton alum, I must inform you: some bugs are delicious.

    Crickets from Mexico? Tarantulas from Cambodia?

    It better be a nasty, uncooked bug, or else this promise doesn’t hold enough weight!

    • Kevin B.

      I think that if Clinton wins but Trump gets over 240, Sam gets to eat a delicious bug. If Trump wins, it will need to be a gross one.

      More seriously, can Sam put a probability on Trump >240? Or would that require the use of a model involving Monte Carlo simulations?

    • JohninDenver

      Years ago, I was introduced to fried baby bees in honey ….

    • Josh

      Is eating bugs a thing that only people who went to Princeton have experience with?

  • Porkadiah

    Sam, bugs are nutritious and delicious. The practice of entomophagy is growing by leaps and bounds in the West (it’s always been practiced in the rest of the world). Being a man of reason, I hope I can appeal to you when I say there is no compelling or rational reason not to eat them, other than, “Ewww, yyyuck, grosss!” which is nothing other than cultural conditioning, and the logic of which can be easily challenged. On the other hand, there are many compelling and rational reasons to eat bugs. Might I suggest if Trump passes 240 EVs you consume something truly horrifying, such as Trump Water (TM)?

    • Arun

      Bugs (some) are healthier for you than beef. I’ve heard crickets are delicious as well.

    • Dharma

      I love reading this site. Statistics polls and bugs all at the same time..

    • Matt Sharp

      A rational reason might be that bugs can feel pain. Obviously much less likely than vertebrates, but still a possibility.

  • Gelatinous_Cube

    Looking at national trends for popular vote estimates at FiveThirtyEight and RCP (HuffPo is harder to read) it looks like most of the narrowing comes from undecideds and Johnson voters moving Trumpwards. But is this effect distributed across the states in a manner that alters the expectation drawn purely from the MM?

    Also, might the “break moment” for undecideds and 3rd party leaners be different depending on whom they eventually break for? In other words, could the crypto-Trump vote just be showing its hand early, and the Clinton holdouts will come around when they start to think their votes really matter?

  • Harry

    Technical question, since I’m doing some optimisations at the moment – how long do the PEC calculations take to crunch? Is there a strong argument against doing more simulations? The EV estimator seems kind of spikey

    • Sam Wang

      There are no simulations done at all. It is a closed-form calculation of all possible outcomes. Time is not a factor. The histograms are exactly as intended.

    • Bill Ricker

      The EV histogram spikiness is artifact of EV being bucketed in un-even numbers. Only ME and NE divide their award. So as with NFL, some total scores are more or less easy to reach, particularly with the total of Red Wall and Blue Wall states’ EVs as starting points. (If one presumed a stronger correlation in state swings than Sam uses, it might be even spikier; without the ME, NE three +-1 districts there might even be impossible totals and thus gaps, if Wall states are assumed fixed.)

    • anonymous

      To reduce spikiness, one could fit a smoother histogram to the spikier one, but what would be the point? There is a certain probability for every EV value, which is what is being shown.

    • Sankalp Sharma

      Quick question for Sam: (and I’m sure you’ve already answered this numerous times on this page!): How are you incorporating early voting results from Florida and NC in the projection?

      I’m using a Monte-Carlo simulation to calculate Clinton’s probability of winning (median/std dev) and as of 3.15 pm I get a 71% chance of a Clinton win there. However, I’m hearing that there is a Trump lean in the early votes, I don’t know how to incorporate the early voting results in my model. Have you done that in your model?

    • Sam Wang

      No, state polls only.

  • Emigre

    If everything gets converted to short quotes pre Election Day then mine is this one from Verdi’s Falstaff:
    “Tutto nel mondo è burla ” :-)

    • Jon

      Let’s hope it ends up as in the conclusion of Don Giovanni: “Questo è il fin di chi fa mal.”

  • Eric

    Although I do believe Clinton will win because the data and the analysis of the data are reliable, what I do not believe is that Trump couldn’t win 240 electoral votes. You might indeed have to eat that bug. I’m sure chocolate covered grasshoppers would be acceptable :)

  • Dave C.

    If you trust the >99% odds, I will take that bet. I offer $10 if Clinton wins if you agree to pay me $1,000 if Trump wins. Do you accept?

    • Sam Wang

      No, silly, because that is a breakeven bet for me. For example, I would take a $20 vs. $1000 bet from someone who was on public record with a calculated probability. Not you, though.

  • Deb

    So upshot and pec still favorable but why does huff pollster differ so much from RCP averages that have HRc only 1 or so points ahead?

    Which of the two was more accurate in 2012 and 08?

    • Deb

      Meaning huffpollster vs RCP?

    • George

      According to David Rothschild (Predictwise) RCP has a Republican bias as it includes Republican leaning polls including those run and published by the Republican party. I enjoyed his analysis of the current state of the election here https://www.facebook.com/PredictWise/ Please note David uses a very different approach (state level betting markets) than Sam.

    • Mr. Wang

      RealClearPolitics averages only the most recently released polls from a handful of the major pollsters. HuffPollster includes all polls as long as they meet a minimum criteria. (See here http://elections.huffingtonpost.com/pollster/faq). Also, HuffPollster “is NOT a simple average of a certain number of recent polls but smoothed estimate of support as of the most recent poll based on local regression, a statistical procedure that creates a smoothed line when data points are scattered.” http://www.huffingtonpost.com/p/huffpost-pollster-faq.html#2.

      I’m not sure which was more accurate in 2012. However, Sam Wang pointed out in a post four years ago that “national polls were biased by 2.4 +/- 0.4% toward Mitt Romney.”http://election.princeton.edu/2012/11/12/the-final-unskewing/#more-8904. So, support for President Obama was underestimated in the final polls before the election.

    • hubcap

      Re: HuffPo vs RCP

      Poll choice aside, RCP just takes the most recent 5 polls and averages them.

      HuffPo takes recent polls and blends them with historical data using a tracking model.

      As a result, RCP is very sensitive to the most recent polls, while HuffPo weighs new information against previous information.

      For fun, you can:
      1) select a chart on HuffPo
      2) click “customize this chart”
      3) pick Smoothing: Less Smoothing

      You’ll find the “Less Smoothing” results are much closer to RCP.

      It kind of gets to the heart of this month’s popular polling topic: do you think public opinion is spiky (RCP) or stable (HuffPo, Sam)?

    • George

      mmm … watch David’s video for examples of what he considers poll selection bias

    • deb

      But which has proven more accurate in 08 and 12?

    • Kari Q

      In 2012 HuffPost was closer, showing Obama with a 1.5 point lead compared to 0.7 at RCP. In 2008, there was no difference.

  • Joseph

    Is this the colloquial “bug” as in anything that would be considered a bug by the general population? or are you excluding arachnids entirely in favor of an insect?

  • Josh

    In speaking with Lawrence O’Donnell last night, David Frum (who revealed that he voted for Clinton) suggested that rather than “shy” Trump voters out there, i.e., those who will vote for Trump but won’t admit it to pollsters, he believes that there is a dynamic shy Clinton voters, i.e., Republicans, and particularly Republican women, who will vote for Clinton but won’t admit it to pollsters. Any data out there to support that theory? Perhaps the 28% crossover reported in Florida?

  • EDSY

    I’m no geek, I’m just freaked….And as I recall, Sam reccomended less hand wringing and more action. Believe me, I took note.

    I’m in MA. The entire HRC election effort in MA is focused on NH. MA has been hunked into about 6 pieces, all of which have been assigned a different city in NH. I will spend ALL of Monday on the phones calling NH. I will spend ALL of Tuesday driving people in NH to the polls.

    I have NEVER done this before, and I’m a pretty typical moderate, middle aged democrat. I’ve always kidded that though I would love to be unique, the older I get, the more I realize that as goes my opinion, so goes the opinion of the majority of Americans. I’m that typical…. And I’m the most freaked and the most active I have ever been in an election. Active is key. Trump as NO ground game, and it will effect the Senate and Congess as well if everyone hangs in there and GETS ACTIVE

    • Reed

      A sincere thank you from those of us in other parts of the country nursing a sense of helplessness in the face of polling swings.

    • Kearny

      I, like you, have never gotten so involved in an election before (due to the historical uniqueness of Trump’s awfulness). But for everyone one of us, there is also those out there in the rural areas more pumped than they have ever been to vote for someone…and it’s not Clinton. The Trump campaign is trying to make up for his weakness in suburbs (and urban areas of course) by getting massive turnout in rural areas.

      We will Tuesday how that strategy works out.

    • Wendy

      THANK YOU for your work, Edsy. I’m doing what I can from abroad. God help us all.

    • Not gonna be year 109

      @Kearny: While I agree that there are plenty of Trump supporters that are all riled up and ready to go vote, I don’t think the turnout will be remotely 1 for 1 because of three reasons:
      1) The Trump supporters are likely to inadvertently turn more people off than they would actually encourage them to vote. I live in a very Trump-friendly community (it’s a predominantly white, uneducated male Trailer Park where most of the tenants work in oil fields) and while I consider myself to be a dem-leaning moderate, I have been labeled by my neighbors as the local liberal wingnut (mostly because I am in grad school and to them education = liberal). Overall, the majority of the people around me are uneducated, with on average a high school diploma at best. They simply do not have the ability to persuade in a civil manner. They easily get frustrated if you counter with any logical argument and will either give up or become belligerent. That is not the recipe for a successful GOTV door-knocker.
      2) There has been plenty of analysis that the vast majority of Trump supporters are not new voters–potentially more enthusiastic, but not new. To me that means that they tend to “preach to the choir” instead of effectively finding someone that is on the fence and convincing them to vote for Trump.
      3) As has been said by others, they lack organization. The RNC is providing some ground game that is mostly focused on Congress, but Trump’s base is not interested in working for the “establishment”. This is the same fatal flaw that led to downfall of most Tea Party candidates. They simply don’t have the know-how and resources to implement any kind of effective GOTV campaign.

    • Debbie lefkowitz

      Don’t freak but thanks for helping!!

  • Michael

    Sam, One request. In your interviews, please don’t convey such confidence in a Clinton victory so as to suppress turnout through complacency. There are places where there isn’t a competitive down-ballot race that will sufficiently motivate Democrats to get to the polls. As Don Corleone said, “I spent my lifetime trying not to be careless.” Of course, the rest of the quote is a bit sexist, but it was set in the 40′s.

    • Trem

      This doesn’t really happen. People are more eager to vote when they expect a win than when they expect a loss. This is the main thing driving Trump’s rise in the polls, up until the FBI thing came out he was acting like he had already lost and depressing his own turn out.

    • Lorem

      I think proclamations of Hillary’s victory being inevitable are more likely to suppress suppress Republican turnout than Democratic. Most people feel bad about coming out to vote for the loser.

    • Ruth Rothschild

      Michael,
      I agree with you. Before Comeygate a week ago, there was a complacency about a Clinton victory. But, when the email thing came back into the spotlight last Friday, that appears to have shaken people out of their complacency. From what I read, Hillary’s donations went up quite a bit in the aftermath and so did both the number of volunteers helping with her GOTV as well as people actually going out to vote. We don’t want to lose that momentum. So, I agree that it would be better tone down the confidence in a Clinton victory and leave a little shadow of a doubt.

      The subject of complacency brings to mind a glaring case of how over-confidence and complacency can have bad results. Specifically, in an Arizona gubernatorial election many years ago Evan Meacham, a known neo-Nazi candidate, ran against a candidate who was viewed as a lot more reasonable and fit to serve as governor. Because Meacham was viewed as being so off-the-wall and could never win, and many Arizonans believed that the other candidate was a shoe-in, many people didn’t bother to go out to vote in that governor’s race believing that Meacham had no path to a victory, nobody in their right mind would vote for him, and that the other person would win without their vote. Well sadly, Meacham won the race (much to the shock of Arizonans) because too many people were complacent. Fortunately, Meacham was impeached. But, I think that there’s a very important lesson learned from this that none of us should ever forget– i.e., complacency can have some pretty bad results. And as they say, it’s not over until it’s over. So, even if Hillary is ahead and the EV count shows a high probability of her winning, don’t take that for granted. Get out there and cast your vote and don’t get complacent.

    • Jeff

      Meachem is also Morman in a state with 30% Morman population. This was a split ticket election I believe.

    • Rajeev Jain

      I tell everyone their vote is included in the forecast, so they can stay home only if they want to do their bit to spoil that forecast.

      In any case, Hillary win aside, Dems should still turn out for downballot and local races. That is another reason to vote.

    • JFCC

      Why 11? Odd.

    • cvermar

      Yor best bet is Mexico: I can vouch for escamoles (ant eggs) at Los Cardenales in the center of Mexico City , and roasted crickets with chile in Oaxaca (the city in the eponymous state) . I haven’t tried jumiles (hoo-MEE-lehs), little beetles, which are popular in the state of Morelos, south of Mexico City.

      Oh, and thanks for keeping my entire extended family (and many friends) sane!

  • Geoff

    Can someone help me grok Sam’s math better? Decades ago I started college as a math major, but I ended up going into a different field, and now I don’t remember even the basics of polynomials. In particular, how does one calculate the missing coefficient of the polynomial Sam uses to determine the probability distributions for all possible EV outcomes? He presents this polynomial:

    ((1 – P1) + P1 * x^EV1) * ((1 – P2) + P2 * x^EV2) * …

    Where P1 and P2 are the probability of my candidate winning the EVs in states EV1 and EV2. He does this for all 51 jurisdictions. (Er, not for 56 — districts in Maine/Nebraska?)

    Suppose I wanted to calculate this by hand for just two states. How would I do it? E.g., suppose there were only two states, EV1 and EV2, and EV1 has 2 electoral votes and EV2 has 3 electoral votes. Suppose further that HRC has a .7 chance to win EV1 and a .6 chance to win EV2. How do I determine x?

    • Eric

      He’s using a “Probability Generating Function”. There’s a random variable EVi for the number of electoral votes from Clinton winning the ith state. The value is either the number of electoral votes for that state or 0. The idea is that you want the probability distribution of the sum of all these random variables. The easy way to compute this is to notice that for each state there’s only two outcomes (wins, doesn’t win) and that they’re all indepdent. So the probability generating function (the big polynomial) is the product of all the simpler polynomials.

      The variable x is just a formal, algebraic value. In general, it’s only there so that when you expand out the polynomial you can read off the coefficients (probaiblities) of each power of x (the number of electoral votes)

      https://en.wikipedia.org/wiki/Probability-generating_function

    • CW

      You don’t solve for ‘x’. The coefficients to ‘x’ are what matters. Write out the simplified two EV version:
      (1-P1)*(1-P2)*x^0 + P1*(1-P2)*x^EV1 + (1-P1)*P2*x^EV2 + P1*P2*x^(EV1+EV2)

      So the odds that HRC gets 0 EVs is (1-P1)*(1-P2) = 12%; EV1 EVs is P1*(1-P2) = 28%; etc.

      Writing this out for a 538 factor polynomial is tedious, to say the least, but it’s pretty quick with a computer program.

    • Eric

      If you want to play around with the polynomials, give Wolfram Alpha a spin.

      If you ask it

      Expand[((1 – P1) + P1 * x^V1) * ((1 – P2) + P2 * x^V2)]

      (I had to change EV to V for it to work)

      You’ll get the polynomial

      (1 – P1 – P2 + P1 P2) + P1 x^V1 – P1 P2 x^V1 + P2 x^V2 – P1 P2 x^V2 + P1 P2 x^(V1 + V2)

      So the probability of 0 electoral votes is (1 – P1 – P2 + P1 P2), the coefficient of x^0 = 1

      the probability of V1 electoral votes is the coefficient of x^V1 (group all the terms):

      P1 – P1 P2 = P1 *(1 – P2)

      (wins the first state and doesn’t win the second state)

    • Geoff

      Thanks for the replies, Eric. So the model results on the assumption that each state’s outcome is independent of another’s. Is that assumption safe?

      I’d never visited Wolfram Alpha before; that’s a pretty neat site! I’m playing around with it now.
      To understand how the numbers add up, is it useful to plug in actual EV and win-probability numbers into the polynomial? For grins, I tried that in Wolfram alpha, first using my simple two-state election, and then numbers more like the real election. I got a variety of interesting results, always in the form of y as a function of x (which varies between -1 and 1), sometimes S-shaped, sometimes U-shaped, always with a positive y-intercept. I don’t know what this means. This brings us back to my basic math ignorance: is a polynomial effectively a function? F(x) = (polyomial)?

    • Rachel Findley

      You’re not trying to solve for x; you’re just trying to write the mathematical expression as a polynomial. The coefficient of x^n in that polynomial give you the probability that Hillary will get exactly n electoral votes. (for x^n read “x to the n”–sorry this font doesn’t allow me to put the n as a superscript)
      Your xample for two states:
      State 1 has 2 electoral votes with a .7 chance for HRC to win: EV1 =2, P1 = .7, 1-P1.3
      State 2 has 3 electoral votes with a .6 chance for HRC to win: EV2=3, P2=.6, 1-P2= .4

      Then the function is (.3 + .7x^2)(.4 +.6x^3)
      Multiply it out and you get the polynomial
      .12 + .28x^2 + .18x^3 + .42x^5
      remember x^0 always equals 1, and we get
      .12x^0 + .28x^2 + .18x^3 + .42x^5
      which we interpret to mean
      coefficient of x^0 = .12, so the chance that HRC will get 0 electoral votes is .12
      coefficient of x^2 = .28, so the chance that HRC will get 2 electoral votes is .28
      coefficient of x^3 = .18, so the chance that HRC will get 3 electoral votes is .18
      coefficient of x^5 = .42, so the chance that HRC will get 5 electoral votes is .42
      (She can’t get 1 electoral vote or 5 electoral votes with just those two states in the electoral college.)

      Now try it with, say
      state 1 is Florida with 29 electoral votes and .7 chance of HRC win;
      state 2 is Ohio with 18 electoral votes and .25 chance of HRC win.

      HRC then has
      .225 chance of getting 0 electoral votes (neither Florida nor Ohio)
      .075 chance of getting 18 electoral votes (Ohio but not Florida)
      .525 chance of getting 29 electoral votes (Florida but not Ohio)
      .175 chance of getting 47 electoral votes (both Florida and Ohio)

      With more states, you’d get several different contributors to the x^n coefficient; the multiplications and additions get tedious, so it’s nice to have an algebra program to multiply it all out for you.

      Or–Say state 1 is Florida with 29 electoral votes and a .75 chance of a Clinton win.
      Say state 2 is Ohio with 18 electoral votes and a .25 chance of a Clinton win.
      Then the function is:
      (

    • Rachel Findley

      Oops, sorry, typos in my reply below. Looks like you’ve got it anyway.

    • David Elk

      The actual trick to do this uses discrete linear convolution [1]. It’s very clever! It’s all contained in 2-3 lines of code in Prof. Wang’s EV_median.m.

      That’s what powers the EV snapshot, and it does assume states are independent, but the meta-margin and prediction do not. The snapshot is what you can use to find the meta-margin quickly, by taking snapshots at varies degrees of national bias until you find a median EV of 269.

      [1] https://www.mathworks.com/help/matlab/ref/conv.html

    • Geoff

      Thank you for the further replies! Rachel, your analysis really cleared it up for me. I was actually over-complicating things, I think. I’m going to play with the numbers, following your methodology, so I can get a better feeling of how Sam’s model works. Don’t worry about the typos; I get the idea now.

      David, I’ve never even heard of linear convolution, heh. I’m learning a lot from this site. :)

      OK, back to play with the numbers.

    • Arun

      On the assumption of independence between states.; all you care about is whether the current set of polls capture accurately represent the current state of the electorate. So long as the polls are fresh, which at this stage in the election they are, for battleground states, any interdependence is fully represented by the polling. Volatility comes in when you try to adjust for current polls in a state based on national polls or results from another state, especially when you react to individual polls. At that point, you’re probably modeling noise as opposed to something real. Regardless of the outcome of this particular election, I would anticipate that, in aggregate, it should do a great job of predicting outcomes of events where you have good polling data.

  • Jay

    Who will control the Senate?

  • Charles M

    Since polls are a lagging measure of voter intent, has anyone looked at the directional trend of the MM (or EV prediction) in the last week or so prior to election day as a predictor of over or under performance?

    As an example, in 2012 Obama’s MM was heading up and his numbers were somewhat better than polls predicted. The question then is did the upward trend in the MM “predict” his better than expected performance? Or in 2014, the Senate MM was trending down for Democrats and they lost more seats than expected – so was the trend indicative of the greater than expected loss?

    (Yes, I am trying to couch “the dropping Clinton MM has me scared” in more mathematical terms).

    Thanks as always for what you do here, and if you have to eat a bug, I will too (in solidarity).

    • Matt McIrvin

      I think that’s basically what 538′s trend adjustment does. The problem with it, of course, is that finding and extrapolating a slope is numerically unstable and has a tendency to generate big drama out of the vacuum.

      During the early part of the primary season Sam had a hypothesis that Ted Cruz’s tendency to overperform was just an artifact of time lags in polls, during a period when his numbers were rising. But the primary was much more sparsely polled, so it was a larger effect.

    • Matt McIrvin

      …There are enough polls in the real battleground states right now that I don’t think the time lag is more than about a week for most of them. In some states, the polls tend to have survey periods of several days, but in Florida there seem to be a lot of snap polls that have high time resolution (it’s easier to get a big sample in a big state, maybe).

      At the current glide slope, that doesn’t look like a big enough lag to put the end result in danger.

    • Robert M

      Also, we don’t know what the trend will be in the next four days

  • jharp

    I’m glad Hillary is going to be our next President but still deeply regret that Trump ever happened.

    The damage is done.

    • Taylor

      I hear you. Trump supporters don’t like him despite his malicious nature. They like him BECAUSE of it. Its very disturbing.

      I have seen candidates I’ve supported win and lose over the years. Losses are always frustrating, sometimes even infuriating. This, however, is the first time I actually find the thought of a loss absolutely terrifying.

  • Bob Skutelsky

    The big question, Sam, is, would you make the same bug bet today? Hoping the answer is yes. I have pretty much sworn off watching all MSM but for you I’ll make an exception. Thanks for your great work. My wife runs with an anxiety prone crowd and I keep directing them towards >99%.

  • smartone

    I have a question – in your podcast yesterday Dr Wang said to watch for NH where HRC should win by 6 any less might give a clue that polls are off this cycle .
    But latest polls show Trump/Clinton in a tie for NH and Clinton will actually visit NH on Monday so that might suggest that the Poll have in fact tightened a bit.
    Are you still standing by Clinton +6 in NH and anything less means polls are off?

    • Amitabh Lath

      Polls are like the weather in Boston, if you don’t like how it is currently, just wait a couple of minutes.

    • Elian Gonzalez

      That isn’t what he said. He said that if the win there is up to 5 points, you can go ahead and go to bed at the regular time. If it’s about 2 points, then you’ll have a long night. Additionally, why people saying “the race has tightened” as if it’s a mystery is itself, the mystery: Mr. Wang has said many times that tightening of races is the trend.

    • Amitabh Lath

      And presto. Poll ending Nov 3, Clinton +10.

      http://elections.huffingtonpost.com/pollster/2016-new-hampshire-president-trump-vs-clinton

      Stop obsessing over single polls. If you do, the media jackals win.

    • weichi

      Amitabh,

      NH really is making a major move toward Trump right now. E.g., on Tuesday night Sam had NH as Clinton + 5.5. Now, just 2.5 days later, the next update is going to show it as tied … and that will *include* the Clinton + 10.0 poll!

      Looking at pollster, it looks like even last night NH was Clinton +3.5, but the four new polls have moved it to a tie.

      Meta-margin is going to go down again pretty soon.

    • Tim L

      weichi, i think your data is inaccurate – pollster has it at +3.5 including everything current

    • CW

      The most recent update has NH at +3%. For those playing the home game, the algorithm cuts off at the 10/27 Ipsos poll of HRC +4.

    • GuyWhoShowsUpEvery4Years

      Is it just me, or do the polls in NH just seem noisier in general? SurveyMonkey has Clinton up double digits consistently…but they also have Johnson polling in double digits.

      Honestly, though, I don’t know what’s making me feel worse. The fact that this election is as close as it is, or the chilling realization after listening to the podcast yesterday that despite my hopes for the electorate to pull their collective heads out of their posteriors, this election is just prologue to what is likely going to be a terrible 4 years.

      It’s feeling like, come November 8th, our potential outcomes are going to be bad or worse.

    • SP

      The last 5 NH polls (post Comey) are C +10, Tie, T+1, T+2, T +5. That should not put the median at a tie.

    • JeffE

      No early vote in NH, so makes sense to make a late visit given that and the fact that it looks semi-competitive. Need to make sure you get your people out to vote!

    • Brian Gray

      PPP just came out with a New Hampshire poll today showing Clinton up 48-43 in New Hampshire, 48-45 in Nevada and 49-47 in North Carolina…

    • Sridhar

      Also consider competitive senate race there in NH.May likely be a joint Clinton/Hassan event

    • BrianTH

      I think it is worth keeping in mind that just as it is bad to cherry-pick one poll because you particularly like or don’t like it, it is also bad to do the same thing with any small set of polls.

      And at this juncture, small sets of state polls are bound to do that, meaning you are bound to get runs of three or four “bad” polls in some state or another.

    • weichi

      My post was prior to the PPP poll showing up on pollster, which shifted the median up +1.5 all by itself.

      But I was also missing that the rules includes polls from last 7 days relative to most recent poll! I had assumed for some reason that it was last 7 days from today, so I wasn’t including the ipsos poll. Sorry for the confusion!

      So rather than saying that there is a clear and strong shift to Trump in NH, I think we can only say that the polls are quite volatile there. Whew!

  • Mike P

    Gives new meaning to the phrase butterflies in the stomach . . . . which I can’t seem to overcome, notwithstanding the reassurances of the EV Estimator. I think it’s time for me to stop reading the headlines and trust in science.

  • bks

    Hmm, Sam’s tweet actually leaves the door open for an Evan McMullin victory.

  • Tony Nickonchuk

    Will you fry it first? Cover it in chocolate? Will the consumption of said bug be live streamed? FWIW, I don’t think you’ll have to consider any of these questions :-)

    • Froggy

      Raw and fresh is best. (Can we focus on the election — all this bug talk is making me hungry.)

    • SP

      Ah, but Froggy, have you tried it any other way?

      Should it come to pass, if Dr. Wang wants to adhere to the letter of the tweet, but not necessarily the spirit, Oyamel Cocina Mexicana makes pretty decent grasshopper tacos. Tastes good, but the legs (or something) getting stuck between teeth is a bit of a problem.

    • Erik N

      given Trump’s and his surrogates statements on Mexicans and their cuisine – a grasshopper taco is the most fitting response.

    • pechmerle

      Yunnan-style fried grasshoppers are a delicacy. Had them myself once — not bad.

  • Amitabh Lath

    Yes, the presidential race is pretty boring and has been for some time. Watching freakouts can be fun but only for a while.

    As you discussed in your latest podcast with Julian Zelizer, the real issue is governing. Given that the House and possibly the Senate will be Republican, can President Clinton get anything done?

    I believe she will be far less accommodating than President Obama. Most districts have some federal support that ultimately comes under Executive branch purview, but are not usually messed with for partisan purposes. In some cases, like military base closures, there are agreements. But a president has great leeway within those parameters. For instance even if she cannot close an army base in an R district, she could reassign the armored division stationed there, and let it be known the pain will continue until congressman X relents. Given the high level of polarization I doubt she will pay much of a price. She will be seen as doing what must be done to get bad behavior under control, because as Obama has clearly shown, appeasement does not work.

    • alurin

      I don’t think the President has that kind of leeway. Anything seen as using Federal resource allocations to punish uncooperative lawmakers would (rightly) backfire politically.
      Appeasement does not work, and executive orders can only go so far. The only force that can bring Congress to heel is the voters.

    • Amitabh Lath

      Presidents define the job to a large extent. Andrew Jackson and LBJ come to mind as examples of chief executives who stretched the notion of how much leeway there is in extraordinary times. I believe President H. Clinton can also, given a large enough mandate, now that there is a clear history of irrational obstructionism.

    • Ruth Rothschild

      Amitabh,
      I think that, in addition to Hillary likely not being as accommodating as Obama, we need to take into account that in her past positions as NY senator and as Secy of State (and likely even before that in her other political work prior to these positions) she has effectively been able to work across the aisle to get consensus from both parties. So, I suspect that when necessary, she’ll use her talents of consensus-getting. But, if obstructionism blocks consensus-getting, she’ll use the powers granted to her by the Constitution and not be accommodating. She’ll put the necessity of what’s good for the country before the political game playing. I also read that over the past few weeks she’s been quietly contacting Republicans in both houses in an effort to reach across the aisle. So, it appears that she’s trying to set the groundwork to get our reps from both parties and in both houses to work together. We can only hope.

    • GC

      @Amitabh – I find that perspective troubling from a constitutional separation of powers perspective. One beneficial outcome of this divisive election would be Congress clawing back the Article I powers it’s unwisely delegated to the executive branch agencies over the years. The Congress is Article *One* for a reason — and must stay that way for the long-term preservation of a constitutional republic.

    • Amitabh Lath

      GC, a president can apply significant pressure on members of the legislative branch while staying well within the constitution. For instance, as commander in chief, there is nothing unconstitutional in her deciding to shut all military bases in TX01. I agree that if she did something that nakedly punitive there would be a crisis, but it would not be a constitutional crisis.

      More generally, documents like constitutions cannot fully define systems of government. Some political version of Godel’s incompleteness maybe? That’s why active political systems depend on precedence, English common law, etc.

    • ADC Wonk

      “Anything seen as using Federal resource allocations to punish uncooperative lawmakers would (rightly) backfire politically.”

      And, potentially, legally.

      See, e.g., the two convictions today in NJ’s “Bridgegate.”

    • Will Hutchinson

      @Amitib, let me add Ronald Reagan’s famous comment, “If you can’t make them see the light, make them feel the heat.”

    • Ed Wittens Cat

      Amitabh:
      if the dems have the Senate Bernie becomes the chair of the Senate Budget committee– so while all legislation must originate in the House, Budget is a chokepoint for bills to get to the Senate for a vote– an oppo to make some sausage.

    • Josh

      I find it fitting that a New Jersey resident is (unwittingly?)advocating a Bridgegate-esque solution to political gridlock.

    • Amitabh Lath

      When bridgegate hit the news I primarily reacted to the sheer incompetence on display. It was high risk/no reward behavior. Idiots.

      A competent crew would have planned better. There would have been meeting minutes planning the traffic study, pictures of the Gov. in a hardhat inspecting decaying girders six months ago, and the whole thing would have lasted about an hour, until the mayor was forced to make his frantic calls. Then traffic back to normal, message relayed.

      And it would have happened much earlier than the election to give the mayor time to endorse.

      That would have been properly Machiavellian. The way it went down was just plain stupid.

  • Edward Song

    Prepare to eat a bug. There is no way Hillary has a 99+% to win this election. Given that undecided voters are breaking toward Trump, a 60% chance of winning on election day is more realistic. On the other hand, I do like the fact you are making a strong stand and putting your reputation on the line. I would not be surprised that Nate Silver will have about a 50-50 election at 11:59 pm Monday night, where he will be able to claim he was right no matter what the results will be.

  • Bob McConnaughey

    Do polls get added in and then dropped? or is my mind at sea? I thought i saw 206 state polls earlier? Whatever. I’m sure i’m delusional at this point.

    • Tony Nickonchuk

      I think in Sam’s methodology he states that he takes the median of the last 3 polls or last 7 days, whichever is greater. So yeah, I think he drops older ones out as new ones come in.

  • A DC Wonk

    Count me in a among the large schizophrenic crowd that on one hand hears what you’re saying (98+% probability of victory), but goes nuts when _seeing_ the sustained dropping, and steep downward slope of the EV and MM over the past few weeks.

    Rationality and Emotion don’t always align.

    • SP

      jculb69, I think the difference, and what has me a bit concerned in the presidential election, are the trendlines. Obama was trending up same time in 2012. The drop-off here has been at times, precipitous. My hope is that the MM stabilizes over the weekend, since we’ll be a full week out from the Comey revelations.

      That said, I’m pointing everyone I know, who is pulling their hair out by reading the prognostications elsewhere, over here. The math, I trust.

    • Matt McIrvin

      The psychology for us was a little different in 2012: Obama was almost exactly where Hillary is now, but his numbers had been rising at the end, not falling.

      Still, it was the same in that the national polls and pundits were all saying it could go either way, but Sam’s model was giving the Democrat a safe lead.

    • Brian Gray

      Clinton’s numbers dropping? It sems the much touted ABC/WP poll is showing her rising now with momentum. There is other polling showing this ..

    • Brian Gray

      and in Rasmussen Hillary went from being behind 3 to a tie today…

  • Patrick E.

    What kind of bug? Will you record and post it for our amusement? We’ll be in desperate need of a little levity if Trump pulls off a win. Can we count on you?

    • Sam Wang

      Of course, though you realize that I calibrate my biennial bug promises to avoid paying off more than once in my actuarial lifetime.

    • Steven

      Seems like it all hinges on NC +2 and FL +2. Must win them both. I hope it happens!

    • MikeW

      Do gummy bugs qualify?

    • Matt McIrvin

      The exact phrasing “more than 240″ may turn out to be important.

    • Brian Gray

      Steven, I don’t think it all hinges on Florida or North Carolina . IMHO her blue wall will hold.

    • anonymous

      If Trump wins, I think the pleasure that some people will feel by seeing Sam eat a bug will be reversed when the same bugs become a food staple for their grandchildren due to global warming.

    • Steven

      I meant the bug bet hinges on NC and FL. The election is already over. Hillary’s floor is 272.

    • Brian Gray

      Ok sorry Steven!!!!!…lol

  • Arun

    Aside from my personal interest in the election outcome, I’ve found it interesting to compare the various statistical tools used to make predictions of the outcome. Personally, I feel a simple probabilistic model that expresses our estimate of the outcome in terms of confidence intervals around a median is far better than some overly complex model whose underlying assumptions are can probably not be validated. One can fall in love with the complexity and spend too much time trying to understand small fluctuations, but simpler models generally work better.

    • JSA

      I agree with you. From my own experience in pricing securities, more coefficients and input variables in the MV linear equations makes the resulting variable unpredictable.

    • Eric

      As my grad school adviser would say, “Simplicity is the hallmark of truth.”

  • Jono

    Hey, some bugs can be deliciously prepared. I’d rather not see you experiment with Entomophagy under those conditions, though.