Princeton Election Consortium

Innovations in democracy since 2004

Outcome: Biden 306 EV (D+1.2% from toss-up), Senate 50 D (D+1.0%)
Nov 3 polls: Biden 342 EV (D+5.3%), Senate 50-55 D (D+3.9%), House control D+4.6%
Moneyball states: President AZ NE-2 NV, Senate MT ME AK, Legislatures KS TX NC


October 27th, 2012, 8:00am by Sam Wang

Hurricanes Sandy and BarackIn Princeton, we’re making sure we have bottled water and other supplies. It’s not clear how serious Hurricane Sandy will be. But we are grateful for the advance warning that is made possible by the National Weather Service.

Seeing as how predictions are so useful, Andrew Ferguson and I have decided to put the Obama re-elect probability in the topline. We give two probabilities, which are built on the same assumptions that went into calculating the “strike zones” in the history graph. The “Random Drift” number is a minimum (conservative) probability, and the “Bayesian Prediction” is my best shot at calculating the actual win probability. In the coming 10 days, the two numbers will converge.

I will list the assumptions again. This will make the most sense if you know a little about what we do here at the Princeton Election Consortium.

Starting from a snapshot of today

Both predictions (“random drift” and “prediction”) start from a current snapshot of polling conditions, the Meta-Analysis of State Polls which forms the core of this site. The snapshot is listed in the top line above. It is currently Obama 297 EV, Romney 241 EV, Meta-margin Obama +1.96%. This predicts what would happen in an election held today.

To calculate this snapshot, we (a) use recent polls for each state (3 polls or 7 days, whichever is greater) to calculate the probability that one candidate is ahead, (b) calculate the exact distribution of all 2^51 = 2.3 quadrillion outcomes, measured in terms of electoral votes (EV), and (c) take the median of the distribution to get an expected outcome.

In addition, we calculate the amount by which polls must swing overall to create a perfect toss-up. This quantity is just like a two-candidate margin that people are used to seeing in polls, so we call it the Meta-Margin. Both the EV estimator and Meta-Margin are extremely precise, and performed very well on Election Eve in 2004 and 2008.

Projecting into the future

Between now and Election Day, opinion may move toward Obama or toward Romney. But by how much? To turn the snapshot into a prediction, we have to estimate how much movement may occur. There are two ways to do so. I have explained these before (“The Presidential predictor sharpens,” September 29). Here is how they fit into what’s listed above.

Random drift. Using past races, I have estimated how much the Meta-Margin is likely to fluctuates over time. In this “random drift” model, I assume that opinion is equally likely to move in either direction. (Nerds: at N days before the election, the drift has a standard deviation of 0.4% * sqrt(N).) If the Meta-Margin stays above zero, then Obama wins. Today, the probability of an Obama win is 89%.

Bayesian prediction. Here I make an additional assumption, that the final outcome is likely to be drawn from the values that the Meta-Margin has explored this year. This is equivalent to the idea that the Meta-Margin is more likely to move towards its average (Obama +3.1+/-1.3%) than away from it. This has been the case in past elections. In statistics this is called a “Bayesian prior,” as in prior assumption. Today, including that prior gives a win probability of 97%.

The prior is also used to calculate the red and yellow “strike zones” in the history graph.

In my view, the prediction is the correct probability. But if the prior seems like an unwarranted assumption to you, then use the Random Drift probability instead. This is a more conservative estimate. Anyway, over the coming days these probabilities will converge to the same value.

Tags: 2012 Election · President

181 Comments so far ↓

  • NY Romneyite

    The clearest sign of a valid/confident prediction is whether you’d take the odds. You have Romney as a 32 to 1 shot, I’ll pay a casino vig and bet as much as you care to offer at 25 to 1.

    • Czech nerd

      I believe that for Sam it is much more profitable to go to Intrade and sell Romney at about 2 to 1 and make fortune. And it’s exactly what I am doing.

    • Strabo

      The public and professional humiliation if he is wrong is probably a lot bigger than losing a few hundred or thousand bucks. So the whole “put your money where your mouth is” seems rather… misguided in the “bet you 10,000 $, Rick” sense.

    • DanielMiller

      Is that offer open to everyone?

      The clearest sign of a valid prediction model is past performance. The willingness to put your real name out there in the public for everyone to see as you make the prediction is a sign of your confidence in the validity of the model.

      In any event, for all you know, Dr. Wang has placed a money bet on his model, with someone reputable and not hiding behind fake names on the internet.

    • Sam Wang

      Factually, you are all correct. My reactions:

      (1) The probability can, in fact, be interpreted as NY Romneyite (and all of you) say. However, there is a liquidity issue. If it costs $1000 to make $100 in 10 days, this does make sense as an investment. But does a grown-up person really do that using InTrade?

      (2) InTrade (and other such sites) offer many bets. There are even EV-range and exact-EV bets. Rationally, one would apply the Kelly criterion or some other measure to figure out which bet is optimal.

      (3) We have here an asymmetric situation in which all of you know exactly who I am. However, I do not know your names. In fact, I gave NY Romneyite his/her handle. Wagering with strangers…what’s next, cockfighting rings???

      (4) In regard to Strabo’s comment…indeed, if the 3-11% probable outcome (a Romney victory) occurs, the reputational hit I suffer will be large. Perhaps more importantly, since my methods are essentially neutral, it will raise serious questions about the validity of the entire industry of state polling.

    • wheelers cat

      I’m guessin’ you would have lost your shirt on the ACA ruling.

    • Olav Grinde

      NY Romneyite, I’ll take those odds, provided you can get:

      — Tagg Romney and partners to reverse their investment in Hart Intercivic, the third largest voting machine company in the country (A strange investment, wouldn’t you agree?)

      — the Tea Party to reverse its plans to mobilize up to one million “volunteers” tasked with “challenging” minority and other voters at the polls

      — Republican secretary-of-states in swing states to order a cease-and-desist order to a host of measures aimed at suppressing the votes of Democratic-leaning demographics

      — find a way to ensure the integrity of the vote, especially in states that have electronic voting without paper trails that allow auditing of the results

      Regarding the last point: The four most vulnerable states that will heavily rely on Direct-Recording Electronic voting (without sufficient paper trails!) are Pennsylvania, Virginia, Colorado and Florida.

    • NY Romneyite

      Czech nerd – I agree that the intrade odds are more favorable. If you think the true odds are 97% for an Obama win, I hope you don’t have any spare cash lying around because if you do and are not betting it on inTrade you are doing yourself a massive disservice.

      DanielMiller – It sure is open to you. If you are serious I’ll give you an email address we can make contact on. Matter of fact, you aren’t the statistician behind it, so I’ll make it a no-brainer for you and even give you 24 to 1.

      Olav – So you are saying you wouldn’t take the bet, in other words.

    • Sam Wang

      Wow, so lively down here. Erm, everyone take it down a notch? Also, NY Romneyite, I wonder if you would consider using a real email address with me. Most readers do.

    • Olav Grinde

      “…if the…outcome (a Romney victory) occurs… it will raise serious questions about the validity of the entire industry of state polling.”

      @Dr Wang: Or, perhaps, it may be a compelling reason to raise serious about the integrity of the voting and vote counting process. Especially if paired with statistical anomalies and their correlation with voting machines or other factors.

    • Brad Davis

      For what it’s worth, I’ve been betting against Romney on InTrade for over a month now. But for exactly the reasons mentioned here by Sam and others, I wouldn’t touch your offer with a ten foot pole.

    • mediaglyphic

      while we are talking about bets. I remember David Shor of Stochastic Democracy being a pretty shrewd oddsmaker. His blog seems to be private this cycle (or open only to invitees), is he still performaning any quantitative analysis?

    • creedofhubris

      Nice deal for you! Offer Obama at 24:1, hedge with Obama at 2:1 at Intrade, profit.

  • Outloud FLL

    I’m sending good thoughts your way from down here in south Florida.

    In a few minutes I’ll be heading out to cast my vote on the first day of early voting. Will that calm my obsession for PEC? Hardly, but at least my part will be done.

    Thanks for all the time and effort you put into the site!


    • Olav Grinde

      Outloud FLL, I understand that today is the first day of early in-person voting in Florida, yes?

      According to what I read, the Obama Campaign has encouraged in-person voting, which is more “robust” than mail-in voting.

      I see that Republicans currently have a 44.5% to 39.3% edge over Democrats in Florida early voting. I am very curious how those numbers change in the days ahead.

      This excellent site tallies all early voting statistics. It is run by Dr. Michael McDonald of George Mason University.

    • Outloud FLL

      Hey Olav,

      Yes, in person started today and runs through next Saturday. Log lines all over the place here in S Fla. I waited 4 hours and was happy to do it. The beautiful weather left behind by Sandy passing us on Friday helped out.

      As for the the R advantage in absentee voting you mentioned, I’m surprised they were only up by 5 points. The Obama campaign is out in force though trying to GOTV. As I was standing in line, my mom got visited and she confirmed her absentee ballot and my early vote.

      I’m not expecting O to win FL but heavy turnout in S FL and good showing in Orlando and Tampa might make it interesting.

  • Bender

    Sorry, Professor, but everyone knows the best predictor of who will win the election is based on whoever wins next Sunday’s Washington Redskins game.

    So, please, sir, with all due respect, put away your fancy mathematical models and jargon and plop yourself down in front of the tube next Sunday.

    I’m kidding, but what’s sad is that undoubtedly numerous articles will be written about next Sunday’s Redskins game and people will genuinely believe there’s a correlation between the game’s outcome and the election following two days later.

    (Oh, and for what it’s worth, the Redskins play the Panthers Nov. 4).

  • NY Romneyite

    Also a clarification question – the way I understand the model here is to take HuffPo’s Pollster’s last 3 polls, or one week of polls (back to 10/20), whichever is greater, then take the median, rank the states, find the 270th electoral vote in order, and use that margin as the meta-margin.

    If I look at Pollster’s state of play now:

    North Carolina, Florida, Virginia – Romney leading or tied in the median of the polling over the last weeks, this won’t be the meta-margin state.

    New Hampshire – The last week of polling has four polls, including O+3, O+3, R+2, R+2. Median of that would show O up, but one of the O+3 polls (a partisan poll) is going to roll off tomorrow, so R will be up in that median tomorrow.

    Those states put Romney at 252, we need 17 more EVs.

    OH gets you those 17, but has O+5, O+4, O+3, O+2, O+2, O+2, Tie. So median and meta-margin benchmark would be +2.

    But CO gets you 9, and this site’s qualifying polls would show O+4, O+3, O+3, O+1, Tie, R+4. Now I could point out that the O+4 and both O+3’s are from partisan polling organizations, but even so, the median here would be O+2 as well.

    WI and MI both have the latest poll showing a tie and no other polls in the last 7 days. The second oldest poll comes in with a big Obama lead, but let me ask, if the very next poll in Wisconsin happens to show a Romney lead, and one more non-partisan polling org’s showed a CO lead for Romney, wouldn’t the meta-margin instantly re-align to make WI/CO the tipping point combination, and reset the meta-margin down to like one point or less?

    • wheelers cat


    • Arbitol

      You’re asking if polls stop showing Obama leading in the battleground states, will this site show improvement for Romney? The answer is yes. Anything else?

    • Sam Wang

      Well, of course. It’s automated, as follows.

      HuffPost polls > MATLAB > python > your screen

      …and you can even see all the code, over in the Geek’s Guide. I am not in there unskewing, or whatever. What’s the alternative – that I make it up as I go? That would vitiate the entire enterprise.

    • lbrooks

      Ny Romneyite,

      Come on lets be a little realistic. You are takling a RAT poll in WI and saying the race is tied? WI and MI are not in play By the way just to correct you both PPP and Angus Reid did WI polls within the last 7 days with larger samples and live interview and it should o +5, +6..MI is simply not in play that AUTOMATED poll is obviously an outlier..Grasping at straws my friend…

    • Felix

      @NY Romneyit
      what you seem to be missing is that Dr. Wang is a scientist and not a politician. But he is also a citizen. As a citizen he has clearly indicated his preference for the election outcome.
      As a scientist, he does not care. Its about predictions based on models that have been validated in the past. Winning the ‘science game’ is to get the outcome right which is different from having ‘your’ candidate win the election.

    • NY Romneyite

      Okay so there’s some disagreement between the cat and Arbitol. One says no the other says yes, I’m glad my question will be illuminating.

      I’m sorry I did mis-explain one thing, PPP does have a poll in WI in the last 7 days, but my point was more that since there have only been 2 polls in the last 7 days, one new poll with Romney in the lead makes the Rasmussen poll the median poll of the last 3, which in my understanding was how the model worked.

      I don’t know if it’s right or wrong, I’m trying to get clarification on how the model works – if Gravis (who I don’t put much faith in) showed R+1 in WI tomorrow, wouldn’t that mean the model uses the Tie poll as the median for calculation purposes, thus making CO the new meta-margin defining state (since NH is ahead of both those two and those three get you to 271 for Romney)? Genuine question here.

      lbrooks – I’m not making any decisions here, I thought I was working directly off how the model works. I prefer to use Polltracker at TPM and to throw out the explicitly partisan polls (like Grove Insight-D and Pulse Opinion Research-R and Gravis-seems R), but I thought the methodology used Pollster’s polls, so that’s what I did.

    • Arbitol

      I don’t think I said anything controversial or particularly thought provoking. Did I misunderstand your question? If O+ polls roll off and R+ polls roll on, Sam’s system will show a shift towards Romney.

    • VA Voter

      Don’t talk about “partisan polling organizations” when your entire argument is built on using them. The “tie” you mention in Michigan is by an outlier poll that’s been ~8 points off the mark in every one of their polls. The state’s not in play, the campaigns aren’t even spending money there. Wisconsin is only barely in play, because while a hyper-partisan poll with a garbage methodology has the race tied, 3 more-reputable and more-accurate polls within the last two weeks show Obama with a lead.

      Colorado is close and could benefit from a Quinnipiac poll, but PPP was far more-accurate last cycle than Rasmussen so their +4 result is a lot more believable. I don’t think either candidate is at 50% in the state as of now. Romney’s strongest polls in New Hampshire come from the terrible robopolls with excessive Republican leans. The state will likely go to Obama by a narrow margin, but both campaigns are adding visits to the state because it’s legitimately in play.

    • Matt McIrvin

      With Obama running pretty strong in Ohio, we’re in the interesting regime in which Romney can still win, but only if things break his way in multiple states at the same time. E. g. he could carry VA, NC, CO, NH, and WI and win. There are some other scenarios too, which all the state-poll aggregators incorporate.

      Here we get into the big difference between Sam and Nate. Sam’s calculation ranks these combinations as very improbable because he’s treating the probabilities as independent; Romney winning all those really close states would be kind of like winning a series of coin flips. Nate, I believe, incorporates the possibility that they are correlated, by including national polls as a contributor to every state’s win probability. That’s one of the main reasons the probability of a Romney win is much higher in his model.

      (Sam tries to give this possibility a nod, I think, by making his probability distributions for the individual states fatter-tailed than a Gaussian, but will that help if all the individual states are near 50%? I guess they’re not all near 50%: Romney probably has, for instance, a much higher win probability in NC and a much lower one in WI and IA. Making the distributions fatter-tailed would tend to drive them closer to 50%.)

      My gut feeling, honestly, is that the tail corresponding to a Romney win is fatter than Sam is saying. For instance, if Obama makes some blunder that screws up the response to Hurricane Sandy, or Bibi sends in the bombers while Obama is busy with FEMA and Obama’s response is somehow not good, etc., etc., that could hurt him nationally. But that’s mostly me being a pessimist, as is my tendency.

    • wheelers cat

      I said No because Dr. Wang’s model is pretty much immune to singleton polls and outliers.
      Go Central Limit Theorem!
      Rah, rah, rah.

    • Matt McIrvin

      It occurs to me that in my comment above I was mixing up Sam’s Meta-Analysis and his projection to some degree. (The latter is what would take correlated motion into account.)

  • Mike Chapman

    I seem to remember that you said the only state you miscalculated recently was Nevada two years ago. I spent a week volunteering on the Reid campaign that year and it was clear on the ground when I got there that the Latino vote was going to be higher than was being predicted by the national media and their public polls. I’m seeing reports that we might have a similar situation this year because the polls are underestimating Latino turnout in Nevada, Colorado, maybe Virginia, due in part to language barriers. Have you been able to factor this into your calculations any differently this cycle compared to 2010?

    • William

      Sam Wang doesn’t factor anything into his calculations that the polls don’t. The question is: will the pollsters underestimate Latino turnout?

    • Sam Wang

      I am more prone to suspect that it is a problem with cell phone sampling. When people move to a new state, they often bring their old area codes with them. These people are missed by dual-frame (landline+cellphone) surveys. Nevada has an unusually mobile population. Thus the error in the Sharron Angle v. Harry Reid race that you mention.

      In principle, Latinos like any other group can be accounted for by re-weighting (a.k.a. stratification). And as far as I know, any competent pollster does this.

    • Kevin Kesseler


      I did some canvassing for the Obama campaign in rural North Carolina (Pittsboro) in 2008 and I found (and was told anecdotally by others) that latinos generally declined to answer questions from someone holding a clipboard. I wouldn’t at all be surprised if the polls are underestimating the Latino vote again. I wonder if there has been any systematic study of the effect you mention in Nevada in 2010—it seems like that could at least give you a rough estimate of the magnitude of the error.

  • Jay

    Dr. Wang, you mention that the Random Drift number and your Prediction number will eventually converge as we get closer to election day. Nate also predicts that his Forecast and Now-Cast will converge. Is it fair to say that the relationship between your Random Drift/Prediction is similar to the relationship between Nate’s Forecast/Now-Cast?

    • Sam Wang

      No. Both of the numbers given are predictions. If you really insist on a comparison:

      Snapshot (topline EV and MM) = Nowcast, probably (though I have doubts as to whether his is a true snapshot)
      Random drift = Prediction using a neutral-drift assumption
      Prediction = Prediction using a Bayesian assumption

      In all cases, PEC uses far fewer assumptions. The Bayesian thingie is sort of like “fundamentals” but based on polls only.

    • AndrewJJ

      Using fewer “assumptions” doesn’t necessarily make any prediction better. But, I am curious what you would take as a test between your model and Nate’s that outside observers could view as a relative validation of either method.

    • Sam Wang

      Good question, not only for that model but other predictions as well. Will have validation criteria soon.

  • victor

    Of course he will not give you 25-1 when he can get 8-5 at Intrade. If you placed a bet on Sam every time he was away from the market you would make $$
    You would probably have said nothing to say if he made Romney the big favorite.

  • Jay

    Thank you Dr. Wang. I know 538 takes into account economic factors (stock market, etc.) in its model, which gradually phase out, and which might explain the convergence of the numbers. To a casual observer like myself, it seems as though the more data that is included beyond polling data, the more subjective the model becomes, because once you open the net to other factors, how do you decide what to include and what not to include?

    • Sam Wang

      Indeed, how does one decide? This is why I use only polls. The closest I come to subjectivity (in my view) is in interpreting how to use polling from past races to set some of the parameters. The arguments are mostly laid out on this site, though by now it will require reading a few different essays.

    • MarkS

      I would just like to make the philosophical point that NOT using economic data (and its correlation to past election results) is just as much a subjective choice as using it. Before inputting any polling results, Sam’s model says that the election is equally likely to go to the Republican or the Democrat. This is reasonable only because past results indicate that both parties have a good shot at winning (and 3rd parties have a very small shot). Nate’s model tries to do a little better on the starting point than 50/50 by using apparent correlations of election results to economic conditions in the past. This is not MORE subjective that Sam’s 50/50 assumption; it is equally subjective. But it is more complicated, and therefore harder for an outsider to judge without knowing the details of the model.

    • Craig

      It may not be more subjective, but it is objectively noisier – there is a relationship between economic data and public opinion, but if you’re already measuring public opinion, then the econometric data should be priced in. Silver’s model is likely double-counting in that respect. And of course the six or seven variables he uses is far too many for a sample size of a few dozen presidential elections.

  • Gordon Cormack


    I’ve loved your site since I discovered it in 2004 (notwithstanding being burned by your undecided prediction) but never previously commented. I much prefer your site to the one in which all sorts of hocus-pocus predictors are considered.

    I am concerned that your current predictions don’t take into account uncertainty of measurement of the meta-margin. Shouldn’t you add the variance of your snapshot to the temporal variance in the random model? Perhaps for the Bayesian model as well, but that is not so clear to me.


    • Sam Wang

      Thank you for that input. It’s a good question. It’s time to revisit the issue.

      The yellow zone on the history captures the uncertainty you mention. So for the graph, it is there. Your concern affects the red zone and the numerical probabilities.

      For calculation of a probability, the entire snapshot variance should not go into the prediction. Based on past performance – as well as stability over time – the meta-analysis is considerably more accurate than the 95% gray CI indicates. This is because pollster biases are included, yet we know that they cancel one another out.

      Here is how I will probably calculate the combined uncertainty. If drift from now is D, and our uncertainty about current conditions is U, then the total uncertainty for Election day is sqrt(D*D+U*U). U is no more than 0.5%. Since that is much smaller than the current value D, it will not affect what appears today. However, as the election nears, you will see some residual uncertainty.

    • Sam Wang

      Gordon Cormack, I have now implemented the change I mentioned just above. If you can read MATLAB, I changed this

      to this

      The 0.25 term is the U*U that I mentioned above.

    • Gordon Cormack

      Right. Immediately after I posted I noted that the yellow region appeared to do what I suggested. You have a confidence interval for the instant in time, and then it grows to account for drift.

      Presumably, the bottom edge of that confidence interval is what you call 97.5% probability (assuming a 50/50 prior).

      I’m still a bit concerned that you’re venturing close to Nate’s Neverland by using the word “probability.” But I do appreciate that people demand such an estimate and aren’t interested in an essay on the Bayesian/Frequentist wars.

    • Mustapha Augustus Gbassa

      Wish my elder brother was on here-he is the statistician, but my two-cents question for Dr. Wang? Since there are other “minor” party candidates, Johnson, the Greens etc. are these accounted for in your forecasts? Won’t Johnson -the Libertarian candidate in Colorado for instance take away from Romney, and similarly a strong Green Party showing in another state diminish a predicted Obama outcome? As close as the polls are showing-one or two percent margins in some state averages- won’t the scenario above impact any predictions you are making now? Or as the uninnitiated that I am, not noticed how that has been factored in?

  • Dennis

    This is the first sentence for an AP article by Julie Pace:

    “With an eye on the weather forecast, President Barack Obama and Republican Mitt Romney are launching a 10-day sprint to the finish line in a contest increasingly about momentum vs math”

    Personally I chose the math.

    • Sam Wang

      Proof positive that when political writers use the word “momentum,” either they don’t mean anything, or they mean “morale.”

    • grandpa john

      AP is just another of the organizations who have become ideologically inundated so that now instead of being a source of news they try to create news and headlines in order to attract more readers.
      Reporting of facts and factual events is passe and irrelavent to the primary task of making money

    • Tractarian

      I think reporters generally use the word “momentum” just the way it’s supposed to be used – in the election context, it’s when a candidate is rising in the polls.

      They just seem to be misinformed about which candidate, exactly, is currently rising in the polls!

      It’s not a semantic issue; it’s an ignorance issue.

  • DrOrbit

    Question. Is this model also tracking early voting trends? Example: In CO, the latest breakdown by party affiliation has R ahead by 3% with around 26% of the total electorate voting. Is this included?

  • Amitabh Lath

    An interesting Bayesian prior would be to assume that fluctuations above a certain frequency are simply jitter, and filter them out.

    Then if you look from August on, you get one big sine wave, going up, then down, and now up again.
    It ends up at 300-310 ev.

    Which is probably where your prior also gets you.
    All roads lead to Rome.

    Stay safe Sam. The Rutgers weather center
    gives good localized weather prediction, probably also for Princeton/West Windsor areas.

    • wheelers cat

      Eventually we will have to have a throw down, Amitabh.
      Spectral vs Fractal.

    • Sam Wang

      Thank you, Amit. You stay safe too.

      I am indeed starting to wonder if the EV estimator is periodic. Over lunch yesterday a friend and I were pondering whether “momentum” is the right concept. It’s really more like a weight on a spring. Pull it and it moves, but it will tend to go back to some central point. The idea of “impulse” is still OK – debates and conventions are impulses – but the guiding principle is Hooke’s Law.

      By the way, weeks ago you had a neuroscience question. I never answered that. In my view, neuroscience is further along than you implied. I think lots of phenomena are right on the verge of being explained in a satisfactory manner. The explanations won’t look exactly like those found in physics, but we’re getting there slowly. Ultimately it will require a bridging of psychology, neurobiology, physiology genetics, molecular biology, and development. That’s all. (ha)

    • Matt McIrvin

      It’s really easy to imagine a periodicity in a random series. I suppose it wouldn’t be hard to tell with some calculations.

    • Amitabh Lath

      Hi Sam, I was looking at your code but there doesn’t seem to be anything that could artificially create a periodicity in the EV estimate.

      One way to get an harmonic-oscillator like artifact did spring to mind: If pollsters have +R and +D biases, and say, the +R guys report results on the 1st and 14th of the month and the +D guys report results on the 7th and 21st of the month.

      Then you would get some oscillatory behavior.
      Aggregators who adjust for pollster house effects like Nate Silver would not see this.

      Having said that, I think what you are seeing is a real effect. As to why no one else picked up on it, probably no one else has an instrument this sensitive.

      As Matt McIrvin says, the human brain wants to see patterns. An FFT would settle the matter. The dominant frequency should be unmistakable.

    • MAT


      I really like your harmonic idea, I’ve been toying around with some half baked ideas on how polling frequency tied to house effects impact polling aggregators. Hopefully someone with stronger skills than me will follow up. If nothing else, it’ll be
      a good topic for discussion after the election

    • Partha Neogy

      I hope you gentlemen will pardon my intrusion. If you are looking for a mechanism that would produce oscillations, wouldn’t this do? If the likely voter screen amplifies and produces positive feedback on the unscreened poll results (as it seems to do for disruptive events), wouldn’t it produce instability and oscillations? The oscillation period will have to be some combination of the frequency of poll taking and the rate at which disruptive events (i.e., events that trigger the reinforcing effect of the likely voter screen) occur. Just a thought.

  • A New Jersey Farmer

    The RAND Intention to Vote graph has shot up. Looks like Democrats are getting in the mood.

    • Amitabh Lath

      Hi NJ Farmer, this RAND thing is really interesting, but it’s one data point, and a non-standard one at that.

      That being said, even if one has doubts with the overall values, the day-to-day changes that you point to are very interesting. Even if the value of a function has some offset bias, the first derivative of the function is ok.

      You stay safe also. Even if the frankenstorm veers to Delaware, we take a substantial hit.

    • A New Jersey Farmer


      Thanks for your response. It’s just interesting to note the changes over the past week. They’ve moved more towards Obama.

      You stay safe as well.

    • Matt McIrvin

      Today’s breakdown graph is amusing compared with yesterday’s. Yesterday they showed their forecast separated into income brackets. The $50,000-$99,999 range was most consistently loyal to Romney, with poorer voters now breaking for Obama in a huge way and richer ones moving a little more to Romney after the first debate.

      Today, they break down who the respondents predict will win by income range. This time, while Obama leads all brackets, it’s the above-$100,000 crowd who are least certain about that. The richer you are, the more plugged in you are to the Ro-mentum story.

    • Jack Rems

      I *think* what you see there is some people have already voted, so when they get their weekly RAND email they give a 100% probability for voting. I looked at the questionnaire, there’s no other way to indicate you’ve already voted. If I’m right, both “intention” lines should trend up substantially day-by-day from here on.

    • Pete the Statistician

      Yes, that is consistent with the fact that in polls among “likely” voters Obama’s strength is underestimated vs. among “registered” voters. This is because Obama’s superior get-out-the-vote machine tends to convert many registered voters to likely voters and, ultimately, actual voters as election day draws near. The RAND data tend to support this. And we should see a gradual movement of “likely” voter and “registered” voter polls over the next 10 days.

    • Pete the Statistician

      In my previous reply I accidentally left out a word. When I said, “And we should see a gradual movement of “likely” voter and “registered” voter polls over the next 10 days,” I meant to say “convergent movement.” I.e., as election day approaches, and as more registered voters become likely voters (and then actual voters), we should expect to see an increasing trend that is starting to appear already in the RAND data.

  • Scott

    Now that the GOP is paying more attention to early voting, I’m curious to know if for 2016 you think polls of early voters might factor into the PEC prediction? Next time around, it appears 50% or more ballots could be cast before Election Day.

  • E L

    My simple minded observation: The more the Right Wing attack Nate Silver personally on Twitter and elsewhere, the less they actually believe in Ro-mentum. Here’s an example: “Nate Silver is a man of very small stature, a thin and effeminate man with a soft-sounding voice that sounds almost exactly like the ‘Mr. New Castrati’ voice used by Rush Limbaugh on his program.”

    • Craig

      Have you seen this guy’s projection? (The author, not Silver.) Romney takes everything but California, New York, most of New England and Obama’s home states. Since he clearly can’t compete with Nate (or Sam or Drew Linzer) statistically, he’s resorting to particularly ugly and childish personal attacks.

    • Ms. Jay Sheckley

      I cannot return to Nate Silver from Sam Wang, but what a preposterous ad hominem attack. What sort of build and voice is required of a state poll aggregator? I’m miffed.

  • Hedgehog

    Can you address the difference in national polls with what you get from your state poll focus? The national polls seem to have Romney up. Nate Silver addressed it yesterday but I thought papered over it by using Rand (Obama’s most favorable result) which isn’t really a poll but a survey of the same people again and again to make the national results more even.

  • smartone1

    My feeling that Romney just blinked- A report in huffingtonpost says that he may be shifting strategy to Wisconsin instead of Ohio. If this is true then it might be the first indication that the EV is slipping away from Romney.

    • Froggy

      Here’s the article:

      Hard to tell if this is the real deal, or just another feint by the Romney campaign. WI looks to be a tougher nut to crack for him than OH. Also going for WI means that Romney needs to get two additional states (CO and any one of IA, NH, or NV, or IA +NV), wheras he’d only need any one of these states if he gets OH.

    • A New Jersey Farmer

      Ohio has always been solid for Obama and the debates didn’t change that. Romney has to pivot because of the math and now is the time. Wisconsin was supposed to be in the GOP column because of the Ryan pick, but obviously that didn’t work out. He’ll also try PA and MN, but as we all know here, those are both losing propositions.

    • 538 Refugee

      ” If this is true then it might be the first indication that the EV is slipping away from Romney.” I wouldn’t say first. :D

    • Matt McIrvin

      Shifting to Wisconsin would, I’d think, be an attempt to project confidence, since Rasmussen and Ryan notwithstanding it’s bluer than Ohio.

  • Steven J. Wangsness

    I’m sorry, but a 97% chance of O victory is NOT enough. I demand 100%. Or at least 99.9%.

    Thank you.

    P.S. Though I got an “A” in stats in grad school, that was 30 years ago, so I’m a little rough. I wonder if this Frankenstorm could be one of those dreaded “black swan” events I read about. I worry about northern VA and what effect on the pro-O vote could be in the state overall, given the importance of NoVa to that. I used to live in Arlington and if my experience then is any guide, any serious wind damage leaves NoVa effed up for a long time and could conceivably dampen the vote there vis-a-vis the red part of the state.

    Also, the only “Black Swan” I understand is the movie of the same name.

    Thanks again.

  • H Levenson

    Dr. Wang,

    Could a reasonable federal response or the lack thereof to damage by Hurricane Sandy effect the outcome for election of President Obama in the Northeast and Eastern seaboard of the US by election day on November 6, 2012???

    • Hedgehog

      Unless they totally blow it, I’d think the more likely effect would be if turnout is depressed due to the storm and the cleanup. Who’s voters are most likely to make the extra effort to go to the polls?

    • Matthew M

      The state-by-state impact is important here IMO. The only swing states where the storm is likely to affect turnout will be VA.

      On the other hand, the impact could be more telling in terms of popular vote than EV. That would increase the likelihood of Obama winning the Electoral College but losing the national popular vote.

    • Matt McIrvin

      If Philadelphia were to end up with Katrina-level devastation, it could swing Pennsylvania to Romney just by dispersing a heavily Democratic-voting population.

      But that (extremely unlikely) event would be a poor enough reflection on federal disaster management that Obama might lose for that reason alone.

  • Steve Norton

    Sam, I’ve heard it reported that (a) more undecided voters are women and (b) in the past women have been somewhat more inclined to favor the incumbent (everything else being equal). Is there any evidence to support these statements?

  • LA_renter

    “the reputational hit I suffer will be large”

    I don’t understand this. An odds prediction is not a certainty. Every week there are sports teams that defy overwhelming odds against them and win. Of course there may be more variables in a sporting event but there’s an uncertainty in any prediction. Even if you found there was 99% chance, there’d still be a realistic but rare chance that Romney would win.

    • Sam Wang

      That is true. But any probability over 95% would be interpreted by most readers as a prediction.

      A better approach would be to have advance criteria for evaluation. For example, if I make 20 predictions at >95% probability, then 0 or 1 of them should turn out contrary to the prediction.

    • Matt McIrvin

      In most cases where Romney wins, though, the overwhelming likelihood at this point is that you’ll have seen the possibility coming at least a day or two before, and will have changed your prediction to bring Obama’s win probability far below 95%.

      If it goes down that way, it should limit the damage to your reputation: the lesson will just be not to trust your longer-term predictions, not your Meta-Analysis or the validity of state polling itself.

  • Futurist

    Hey Sam,

    Long-time lurker (since 2004), first time responder. As an obsolete math nerd, I appreciate your site, and worry over the fact that an 89% probability means that Romney would win 11% of the time.

    However, what really worries me is the potential for vote flipping for Romney. This is especially of concern as there is substantial circumstantial evidence for electronic voting machine fraud in the 2004 presidential election (although no “smoking gun” evidence), plus reports of such fraud in the Republican primaries this year.

    If Romney wins, and people then start talking about election fraud, they will be greeted with two sets of opposing arguments: first, “Both sides cheat”, and then, “Tin-foil hat conspiracy theorists!”

    Can you outline, now, what would constitute sufficient conditions to conclude election fraud had occurred? I’d appreciate having such a description in-hand by which to gauge the results. Part of my concern is that the current “Ro-mentum” hoo-haw may be part of the cover story to explain how Romney won (or stole) the election.

    Thanks for all your work. Much appreciated!

  • mc

    Dr. Wang, thank you so much for this essential work. Without your site, I’d be a basket case.

  • Wendel Schneider

    I have read several comments on this and Silver’s website criticizing political types for using the word “momentum” with respect to a given candidate’s “surge” in the polls.

    I think the usage is valid if we give momentum a second definition: If, in a given period of time, the second derivative of the support curve is zero or positive, a candidate is experiencing “momentum” in that interval.

  • Simon Tang

    What do you make of this Sam? –

    “According to their updated analysis, Romney is projected to receive 330 of the total 538 Electoral College votes. While many election forecast models are based on the popular vote, the model developed by Bickers and Berry is based on the Electoral College and is the only one of its type to include more than one state-level measure of economic conditions”

    • ML

      I can’t speak for Dr. Wang, but I imagine his criticism would be very much the same as it is of Silver’s use of econometric analysis, which is that those models might make sense for predicting elections a year or two out, or describing the conditions under which a candidate is or is not likely to win, but at this point in time, actual support as measured by polls is a far more accurate gauge of the current state of the race. All those econometric factors are factored into people’s preferences and as such accounted for in the polls, whereas models that look only at those factors discount actual voter preference.

    • Craig

      In general, econometric models have a very, very poor record. Offhand I can only think of one year, 1988, where they outperformed polling aggregates. Even in years where the polling missed somewhat, such as 1996 or 2000, the models on average missed by more.

    • 538 Refugee

      Science develops models based on observations. If observations don’t agree with the model, you change the model. Here they are saying the observastions (polls) disagree with their model so the observastions must be wrong. Interesting take.

  • Olav Grinde

    Dr Wang, may I make a small suggestion:

    How about expanding the number of entries in the “Power of Your Vote” list in the right-hand column?

    It’s very handy to be able to see the current PEC margin for the various states, but I miss some — for instance Florida.

  • Adrian in Seattle


    I’m curious why you decided to go with the three most recent state polls. Why three and not five or some other number. If the three most recent polls are by Gallup and Rasmussen wouldn’t that skew your results? What if concerted series of “push polls” begins appearing in a swing state masterminded by, say, Karl Rove. . .How much does a poll cost to actually cost to run? If it isn’t that much why wouldn’t a campaign in trouble hire a disreputable pollster to poll a swing state and give their campaign the appearance of a close race? After all the closer the race the more headlines and media attention…

  • Pilgrim

    Hi Sam,

    Great site! I visit several times to get the updates and read the comments.

    I am little confused by today’s post.

    Today, you mention that

    To calculate this snapshot, we (a) use recent polls for each state (3 polls or 7 days, whichever is greater) to calculate the probability that one candidate is ahead, (b) calculate the exact distribution of all 2^51 = 2.3 quadrillion outcomes, measured in terms of electoral votes (EV), and (c) take the median of the distribution to get the expected EV count.

    Yet, in the FAQ for the metamargin. you say that you don’t do 2.3 quadrillon possibilities;

    In the Meta-Analysis, how can you possibly go through 2.3 quadrillion possibilities? Wouldn’t that take forever?

    The Meta-Analysis doesn’t actually calculate the probability of every combination of states one at a time. At a rate of going through a million combinations per second, that process would take over 71 years.

    Am I missing something here? (Sorry, I don’t know how to format to make it clearer.)

    • Sam Wang

      There’s a shortcut. It can be done very fast using binomials. All in the FAQ.

    • Roger, a puzzled reader

      Pilgrim, Dr. Wang shows the precise method in the FAQ, which I first tested on my own hypothetical four-state country where I could calculate the probabilities in the conventional fashion and then compare the results with Dr. Wang’s method–and of course they were identical. But I then closely examined the method and quickly understood how it worked mathematically, and it’s clever but very simple. A one sentence explanation: using conventional probability methods, you’d have to do 2.3 quadrillion calculations, each of which had 51 terms, but with Dr. Wang’s method you do ONE calculation with 51 (slightly more complicated) terms that produces 2.3 quadrillion results that are automatically arranged into 539 entities, that correspond to the probability of each electoral vote outcome for Obama, from 0 to 538. But this 2.3 quadrillion results I just mentioned is purely theoretical in that, due to the nature of the calculation, you can consolidate the results at every step along the way so that the computer doesn’t have to deal with anywhere near that many entities. And in thinking about the method, I immediately recognized many other situations in which it would be extraordinarily useful.

  • Roger, a puzzled reader

    Hi. I’m hoping someone will explain the following to me concerning the 89% random drift model prediction:

    Dr. Wang says that the standard deviation of the Meta-Margin is 0.4 % multiplied by the square root of the number of days remaining. So in this case that is .4 * 3.15=1.26 %. The Meta-Margin currently is 1.96 %, so it seems that the z-score is 1.96/1.26=1.56. So, that leaves only 6 % of the distribution for Romney, giving Obama a 94% chance, not an 89% one.

    I hope someone can resolve this perplexing contradiction!

    • Sam Wang

      t-distribution to allow for long tails. being conservative. in MATLAB it’s tcdf(t,3) if I recall correctly.

    • Roger, a puzzled reader

      While the t-distribution with 3 degrees of freedom would result in an 89% chance for Obama, why would 3 degrees of freedom be the correct number in this situation? Isn’t it n-1, so 10-1=9? And 9 degrees of freedom results in a 92.3% chance for Obama.

    • Sam Wang

      Allows black-swan outcomes.

  • Ram

    I am just surprised that the national polls still have Romney up by 1% on an average. I know folks here debunk the Gallup and Ras polls but could they be that way off – 4 to 5%??

    Dr. Wang, you are a real stud, if you get this right. It will be very interesting to do the Wednesday polling firm analysis to see who had it right all along

    • Craig

      This isn’t to pick on Gallup – the only reason I can point this out is because they have a lot of historical data online, far more than anyone else – but yes, there’s almost always a pollster or two that misses large, and Gallup has been that pollster before – check out their final trial heats from 1996.

    • Froggy

      Yes, Gallup can be, and several times has been, that far off this close to an election.

      Gallup 10/27/1980: Carter 45, Reagan 39, Anderson 9

      Gallup 10/27/2000: Bush 49, Gore 42, Nader 4

      Gallup 10/27/2008: Obama 49, McCain 47

  • Marco

    Dr Wang:
    would it be possible to get the data that make up the Median Ev outcome and the Meta Margin graphs as simple two column files, EV vs. time and MM vs time (preferably with time being days). I would be curious to see if there is an underlying periodicity and, if there is, if the two have the same period and how long this period is.
    Thank you!
    (a physics nerd that does search for periodicity in light curves of stars).

    • Craig


    • RDT

      If polls with different biases are released on periodic time scales that may show up as periodicities in the in both EV and MM; both clearly fluctuate at levels larger than the precision based on polls entering and leaving the model.

  • Tom Gavin

    That is reassuring Froggy. Especially the last two elections you site that both underestimated the Dem nominee by 5 points or so. Got anything on Rasmussen?

  • Mike B.

    Dr. Wang,
    Could you correct me if I am wrong? (I am sure I am.)

    But according to the model here…Shouldn’t NH be at +3 with the week interval.

    Also shouldn’t WI be at +5 due to the top 3 polls (not many polls this week surprisingly.)

    Another quick question…
    If applicable, when does the 7 day period fall off for a state? Is it when poll is published the clock starts? When the sampling begins the clock starts? When the sampling ends the clock starts?

    And is there a universal time of the day when a poll is dropped due to it being out of date?

    Any help as always would be hugely appreciated.

    Thanks for all the good work you do!

    • Froggy

      The model uses as the polling date the average of the starting and ending polling dates for a poll, with fractions dropped. The seven days is counted back from the latest polling date.

      For NH the latest polling date is 10/24, and there are 6 polls 10/17 or later, and therefore in the pool.

      Since the 7 days is counted from the latest polling date, the only time when a poll can drop off is when a new latest poll makes it to the model. The dropping of any poll from the pool is immediate when the new poll is included.

    • grandpa john

      Yes this is a very good analysis of Ras, AS he noted since they try to overload the states with biased polls , what they are trying to do is push the narrative to favor republicans hoping that uninformed voters will be swayed.]
      Probably within the last week, they will adjust their polls , as they have done in the past, so that their final polls will closely agree with all the others and they will not seem so biased.

    • ChrisD

      Oops. I posted the Ras article above before reading all the way down. Sorry.

      John: Maybe, maybe not. Here are RCP’s 2008 polls for WI, which Obama won by +13.9%. Can you guess which of these final week’s polls was Rasmussen’s? O+13, O+16, O+11, O+10, O+9, O+7, O+13. Answer: O+7.

  • Adam

    I know it’s only one poll, but I find it interesting that Gravis Marketing (Right-leaning) has the race in Virginia tied today when they had Romney +5 in their last poll.

  • Steve

    Prof. Wang and others: would like your thoughts on Andrew Sullivan’s analysis her illustrating the gap between Gallup/Rasmussen (GR) and the rest of the national polls. If you just graph GR they would indicate Romney has had a consistent lead since Sept. 1 with very little variation. Graphing the other polls illustrates the race the rest of us have been seeing: Obama opened up a big lead in Sept. after the conventions and 47%, that lead collapsed after the first debate and since the second debate he has regained a small but meaningful lead. So which one do you think better represents the reality of this race?

  • Matt McIrvin

    This guy claims Romney is guaranteed to win because he’s rigged the election:

    These claims, of course, appear every four years. I guess we’ll see.

    • Matt McIrvin

      …the claim is that the largest precincts in every single state in the Union are rigged, and have been so in every single election since 2008, which would be a pretty amazing conspiracy to organize if it were true. I guess it would explain why state polls were low on the Republican margin in 2010.

    • Froggy

      Evaluating this would take someone with better skills (and more time) than I have available, but count me as extremely skeptical. I didn’t get past the claim that his analysis “showed that Governor Brewer actually lost her election” without performing a sanity check.

      Brewer led that race for six solid months in the polls ( prior to election day, with margins of between 8 and 22 points. The official result was that she won by 12.5% — it doesn’t pass the sniff test that she had to cheat (or that cheating was done on her behalf) for her to win.

    • Matt McIrvin

      What made me skeptical is just the claim about the sheer vastness of the conspiracy, which would have to be coordinated across 50 state electoral apparatuses and a huge number of local ones. It’d actually be more plausible if the US actually had a central election authority.

  • Froggy

    Sam, thanks for the additional Power of Your Vote states. In future I’m not going to be the only one who notices moves like today’s shift of MN from O+6.5 to O+8. Woo hoo!

  • Nancy Cadet

    Dr. Wang, thanks for the site. I’ve got a Ph.D. In Romance Language & Literature and rely on trusted others to crunch the numbers. My husband is going crazy with anxiety about the election, so your analysis provides a respite.

  • Susan

    Sam….great site and commenters. Thank you.

  • JimmHck

    Since the yellow bars mark the 95% confidence interval it seems counterintuitive that Obama could have a 96% chance of re-election while the yellow bars cross over the 270 EV line.

    Are you accounting the confidence band into your calculation?

    • Froggy

      The 95% confidence interval leaves 2.5% above and 2.5% below that interval. So the bottom of the yellow bar marks the location where Obama’s chances are 97.5%.

  • Brian C.

    The PEC extension for Google Chrome has been updated to include the new Obama Win Probability data. If you already have the extension, it should update automatically. If you don’t, you can download it here:

    • Sam Wang

      That’s great. Thank you for making that!

    • E L

      Thanks, Brian. I just installed it on Mac OS 10.8.2 Chrome and it works just fine. Fortunately, it does not record how many times I will click it per day. I read several blogs daily and PEC is the only one on which I read comments. I really appreciate how Dr. Wang has kept it clean of trolls. Perhaps, it just too quant/wonk/geek for the flamers.

  • bflobillw

    I am still frustrated that almost no polling is showing Gary Johnson or Virgil Goode. Either one may tip a state or two.

  • Joel

    Looking like ~1.75 is the convergence point?

  • pechmerle

    Love the “Landfall” title of Sam’s post today.

    On Nov. 6 we’ll all — finally — make landfall for this election. But unlike so many out there, we PEC readers have been sailing through well-charted waters!

  • Ms. Jay Sheckley

    Very much appreciate the additional probabilities line up top and its explanation. Though I have no power here, I’d like you to promise me something: If the alleged vote totals fall outside of the final yellow zone AND there’s good reason to believe this is because of vote tampering, don’t drink the tabasco. It’s bad for you, and this was about votes not crime. At least let your family vote on this.

  • A New Jersey Farmer

    Yes, I know we’re not supposed to watch individual polls, but this one will warm most hearts here.

    VA: Obama 51-47

    • Brian

      My heart has been warmed

    • ChrisD

      Thanks. The WaPo article is headlined “Obama clings to slim lead” and it uses “against the surging Romney” in the text. Then again, they’re comparing the poll against the last one they dis one in mid-September that was O52, R44.

    • Dean

      It brings a smile to my face. A Gravis poll released today shows a tied race. The O +4 poll has yet to be posted at Pollster.

    • Ross C

      I was out canvassing in Northern Virginia today, and I must say the mood is very high for Obama. No enthusiasm gap here. Maybe less giddy than 2008, but still very positive and also more determined. Just enough cautiousness about the tightness of the race to want to make absolutely certain to vote.

      Plus, I was canvassing in an area that was mostly young and/or minority, and there was a palpable fear of the damage that would be wrought by a Romney presidency. I’m liking our chances, but will phone bank and canvass to the end, then do GOTV on election day.

      My anecdote, FWIW. And one more thing — working with the Obama campaign organizers, there is pretty much zero talk about polls, media headlines, or Obama’s debate performances, good or bad. Just extremely focused hard work, based on excellent, highly targeted supporter data. I’ve been very impressed. The focus is on making sure already-convinced Obama supporters get to the polls, rather than trying to persuade marginal supporters. Very smart.

    • Martin

      This is a site about the election. How can anyone avoid posting individual polls? That’s like asking a starving person to avoid a big sweet potato pie just out of the oven while it’s sitting right in front of their face! I think most people here are adults and know how Sam treats individual polls and not to put alot of stock in them. I think not posting polls insults people’s intelligence. Don’t think there’s a need for that rule.

    • Ross C

      Dateline Nov 7: While Obama wins 330 EVs, the upbeat mood at Romney’s concession speech is unmistakable, a testament to his continuing momentum, which pundits now believe will carry him to victory in 2016.

  • Jay Bryant

    Thanks for the explanations, Dr. Wang.

    Also, may the storm miss you and yours.

  • Mike B.

    Ha, Gravis, utterly incompetent. cancels the real WAPO poll in the EV +/-.


  • Ohio Voter

    Just completed my poll worker training today. I’m really looking forward to this election.

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