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“Re: Nate Silver, most amusing thing about this election is watching political pundits make sports fans look like PhD mathematicians,” tweeted ESPN basketball writer John Hollinger earlier this week.
Hollinger was referring to the mainstream media’s largely ignorant criticisms of Nate Silver, the New York Times writer who uses polls and other information to assign probabilities to political outcomes, including, most prominently, the presidential election. Earlier in the day, Politico’s Dylan Byers argued that because Silver had given Barack Obama nearly three-in-four odds, then if Mitt Romney prevails, Silver will not really be worth paying attention to anymore: “should Mitt Romney win on Nov. 6,” Byers wrote, “it’s difficult to see how people can continue to put faith in the predictions of someone who has never given that candidate anything higher than a 41 percent chance.” (Byers is actually wrong on this fact as well: one year ago, Silver gave Romney a 60 percent chance should 2012’s GDP grow two percent, which was last quarter’s annualized rate. But as we’ll see, that’s beside the point.) Byers also cited pundits like Joe Scarborough and David Brooks disparaging Silver after similarly misunderstanding the concept of probabilities.
In addition to this line of criticism, one need only do a quick Google search—or check of John Podhoretz’ Twitter feed, or Matt Lewis at The Daily Caller—to find accusations that Silver, a liberal, is skewing the numbers to help Obama. (Here is Podhoretz, who can be very funny even when he is wrong: “Battleground poll has Romney 52-47. In response, Nate Silver raises Obama probability to 99 44/100% pure.”)
Hollinger, a stats-savvy journalist, is right: the world of sports prognostication is more enlightened than the world of political prognostication. The analogy holds in part because what Silver does as a political statistician is strikingly similar to what he did as a baseball statistician. “When Nate Silver worked at Baseball Prospectus,” notes Columbia political scientist Robert W. Erikson, “he did a lot of statistical analysis of the sort he’s doing here.” His most famous invention was a model called PECOTA that guessed how a player would perform based both on his past performance and the past performances of “comparable” players (much as Silver adjusts for polls’ Democratic or Republican leans). According to Erikson, PECOTA was a slightly more accurate forecaster than any other models that attempted the same thing.
But nobody in baseball today bats an eye when PECOTA is cited. No longer would the basketball equivalent of Scarborough or the football equivalent of Brooks be permitted to make claims that are based on such basic misapprehensions of math without facing near-universal reprimand. A look at the way the sports world has assimilated new, smarter ways of dicing up the numbers contains several lessons for whether and how the political universe’s gatekeepers will admit Silver and his ilk. Chances are that Silver will not earn similar mainstream recognition—even if Obama wins.
IN 2009, UP SIX points late in the game, New England Patriots coach Bill Belichick famously decided to go for a first down on fourth-and-two rather than punt. The moment catalyzed football’s advanced stats community: it was a perfect demonstration that the more unconventional option nonetheless gave the Pats a greater chance of winning. Just as importantly, the gambit didn’t work—the Pats failed to convert, and Peyton Manning’s Indianapolis Colts proceeded to score a go-ahead touchdown to win, 35-34. While this may have appeared to the less-enlightened as a repudiation of the stats, it actually allowed the geeks to make a crucial point: namely, that doing the thing that gives you the best chance of succeeding doesn’t guarantee success. As Bill Barnwell, who was agnostic on whether Belichick was right or wrong, wrote: “you can’t judge Belichick’s decision by the fact that it didn’t work” (bold and italics his).
That probabilities do not ensure outcomes—something every blackjack player who has busted while hitting against a face card has long known—has escaped Silver’s detractors. Brendan Nyhan at CJR and Ben Jacobs at Daily Download have emptied an ample volume of bullets into this barrel of fish. Ezra Klein put it succinctly: “If Mitt Romney wins on election day, it doesn’t mean Silver’s model was wrong. After all, the model has been fluctuating between giving Romney a 25 percent and 40 percent chance of winning the election. That’s a pretty good chance!”
But Silver and his defenders have run aground on the same problem sports statisticians used to face: the failure of laymen to grasp the difference between predictions and probabilities. “The criticism of Nate is that he’s predicting something, when he’s trying to explain that’s not what he’s doing at all,” said Dave Cameron, a baseball statistician at FanGraphs who briefly worked with Silver at BP. “He’s putting the odds on something.” Cameron added, “It is kind of like what we do in baseball. We recognize there are multiple outcomes. A utility infielder can hit a home run off [reigning Cy Young winner Justin] Verlander. It’s just not probable.”
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Aaron Schatz, head of the stats site Football Outsiders, defined three categories of criticisms he typically receives beyond fans’ failure to understand that he is providing probabilities, not predictions. Not surprisingly, Silver has faced political versions of all three.
One is that there is something wrong with the model. “That’s the equivalent of complaining that John Hollinger's measurements of defense aren't accurate enough, or complaining that we don’t give enough importance to red zone [play],” explained Schatz. “Those are technical criticisms. Those are valid.” They are also the ones least likely to be hurled at Silver, in part because his proprietary model (like many sports models, and like Google’s algorithm, for that matter) is secret.
The second is that the expert is biased. Football Outsiders routinely gets accused of jilting fans’ favored teams. Schatz has been particularly accused of this for a particular reason: he is a Pats fan, and, as he put it, “It’s not my fault that I started doing this in 2003 and the Patriots have yet to suck in the decade since.” But he insisted none of his staff are flag-wavers, and neither is Silver: “If this was the 1984 election,” he said, “I don’t think Nate Silver would be afraid to say that Walter Mondale will get his ass kicked.” Schatz further noted, as others have, that in 2010 Silver correctly predicted huge Republican gains in the House.
The third is the attack on the forecaster’s character. The sports version of this is that the statistician is a nerd in his underwear in his mother’s basement. The politics version of this is that, as the Washington Examiner noted, Silver is thin, high-voiced, and maybe gay. It isn’t worth dignyifying this “criticism” with a “rebuttal,” but it is worth noting the parallel. “That kind of ad hominem nonsense—that’s exactly like what we go through,” said an exasperated Schatz. “My God.”
BUT YOU HEAR THESE criticisms leveled at sports geeks less and less frequently. Ever since Michael Lewis published Moneyball, in 2003, and the Boston Red Sox’ sabermetric-driven championship in ’04, you would be hard-pressed to find a Major League front office that doesn’t crunch sabermetric numbers. Where 15 and even ten years ago, broadcasts would list a hitter’s batting average, today they also list his on-base percentage—which sabermetricians pointed out is the more valuable stat. The legendary second-baseman-turned-announcer Joe Morgan, so disdainful of advanced stats that fan Michael Schur (better known as Parks and Recreation’s creator) started a blog called Fire Joe Morgan, has departed the booth.
“I’m part of the Baseball Writers Association of America,” Cameron marveled. “In 10 years, I’ll have a Hall of Fame vote.” Similar revolutions have happened in football, basketball, and even sports like golf, tennis, and soccer. But this happened because the sports statisticians had a bunch of advantages on their road to mainstream acceptance that Silver appears to lack.
A prime leg-up the sports forecasters have over Silver is vastly, vastly more opportunities to see how good their numbers really are. “He only gets to test his model once every four years,” observed Schatz. “I get to test my model 16 times a week.” Of course, and as Schatz noted, there are more ways to test Silver’s numbers—state-by-state, Senate races, primaries—but still no substitute for the NFL’s few hundred games each year, much less MLB’s several thousand.
Another advantage the sports guys have is that while Silver is more or less purely descriptive in his analysis, they tend to be at least partly prescriptive. “We’re not necessarily just trying to forecast the outcome of a forthcoming event as much as making suggestions and helping inform decisions and actions,” explained Cameron, adding, “He’s saying, ‘Obama’s probably going to win.’ We’re saying, ‘That guy’s terrible, trade for someone else.’” (There are ways to divine advice from Silver’s numbers, but the numbers are not really set up that way.) In other words: at this point, sports teams—and therefore the sports media—ignore advanced numbers at their peril; political teams—and therefore the political media—ignore them at their convenience.
But the campaigns themselves are not innumerate. Team Obama has been famous since 2008 for rigorously understanding the numbers, and a longtime business consultant sits at the very top of Team Romney. So the logjam right now may be the media itself. “ESPN in particular decided they were going to grab onto this and ride it,” said Schatz, whose site has had a deal with the ESPN Insider subscription service for several years. By contrast, many members of the political media perhaps perceive the threat Silver poses: they have a horse-race narrative that not incidentally requires interested observers to refresh their websites several times a day to catch wind of the latest episode in the grand unfolding “narrative”; Silver has numbers that suggest a strong likelihood of what the outcome will be. Having perceived Silver’s threat, they have fought it.
Perhaps most dispiritingly, politics’ closest equivalent to ESPN—the ambitious, all-consuming, disruptive media force—is probably Politico, and Politico features authors like Byers, Mike Allen, and Jonathan Martin who in recent days have been among the most vocal opponents of a Silver-style, three-in-four-odds read of the race. (Politico headline yesterday: “Media Stumped by 2012 Outcome.” Silver’s response: “7 polls released in Ohio in past 48 hours: Obama +2, Obama +3, Obama +3, Obama +3, Obama +5, Obama +5, Obama +5 #notthatcomplicated.”)
Then again, maybe the chief distinction between sports and politics is that politics is a decade or so behind. Forward-thinking ESPN was also the place that gave Morgan the most prominent baseball broadcast job for so many years. And Sasha Issenberg’s The Victory Lab or some other book could prove the necessary, Moneyball-esque popularizing tome. Although one thing seems likely to stay constant: as Silver said in a recent New York article, “there weren’t nearly so many assholes in sports coverage.”
30 comments
Ha! The problem in a nutshell--too many assholes in political journalism. Silver's solid as far as I'm concerned. InTrade does pretty well too. Vested interest will struggle for every inch, as in all fields. I still haven't ruled out a last-minute avalanche to Obama. If he can arrange a conciliatory meeting between Springsteen and Christie for the weekend before the election, this could go Big.
- Robert Powell
November 1, 2012 at 2:59pm
Bloomberg just endorsed Obama. Hooray.
- Sophia
November 1, 2012 at 3:56pm
" If he can arrange a conciliatory meeting between Springsteen and Christie for the weekend before the election, this could go Big." Thanks for the good chuckle Robert. You made a dreary day more bearable.
- tmmats
November 1, 2012 at 3:59pm
1. Never misunderestimate the breadth & depth of innumeracy. 2. In the probable case civilization abides (c.f., superstorm, NYC), #1 will become false among elites within our lifetimes, probably much sooner. (Numeracy will be as desirable as literacy; indeed, it may be our only hope (ibid).) 3. The happy outcome in #2 is more probable if Silver's more probable outcome survives Tuesday.
- Wonderland
November 1, 2012 at 4:13pm
Did I hear someone mention Buzz Bissinger? http://nymag.com/daily/intel/2012/10/buzz-bissinger-the-consummate-swing-voter.html
- mldarby
November 1, 2012 at 5:01pm
Chances are that Silver will not earn similar mainstream recognition—even if Obama wins. No, if Silver's final prediction is on target then liberals will use it as a cudgel against every single Silver naysayer from here on out. I agree it will be bullshit, but it will be just as valid a kind of bullshit as the naysayers are laying out. These people will have no response, what can they say. Silver was right about the reasons he was right, that he was working in probabilities only, or that Silver was right in his "prediction" which will only reinforce their own reputation for bullshit in the face of reality. I gotta admit I started to panic when Obama went down to 61%. The next debates have erased that doubt, and Romney's flailing ads have only reinforced my convictions. Still though, we have to wait.
- blackton
November 1, 2012 at 5:14pm
There are plenty of folks in sports who are every bit as dismissive of more advanced modes of statistical analysis today, and a fairly sizeable chunk of them are concentrated in broadcast media, as play-by-play announcers or color commentators. The difference is that there are now more fans who know that these people are little more than sports blowhards in the mode of some of your political voices noted above, and have plenty of spaces available to make that case in witheringly effective dissections of the stupidity of those bloviators, something sorely lacking in the political world--a deeper bench behind Silver, so to speak. That will take time, especially since sports is more fun and far less likely to destroy the world.
- cspencef
November 1, 2012 at 5:21pm
For two decades, I have made my living with statistical analysis. I too am a great fan of Nate Silver, even if the guts of his model are proprietary. The guts of my model are proprietary too, but it works. At this point, you really don't need to accept Silver's odds to see what is happening, and I think his odds are if anything conservative. When an overwhelming majority of the polls in a given state start coming in blue, the margin is not that important. Collectively, they offer a very clear picture of the sense of public opinion. This is happening in Nevada and Ohio now, together sufficient for Obama victory. It also appears likely that it is happening in New Hampshire and Iowa. These races are gelling. Together with Colorado, NH and IA suffice even without Ohio. Colorado, Virginia, and Florida are still wobbling. There are both blue and red results, but the tendency is blue in Colorado and Virginia and becoming less red in Florida. Obama is now in a very strong position as there is very little time. Once a race has gelled, it requires one of four things for an upset: that the polls are systematically wrong, not likely in places so heavily polled, that there is some external event that redirects the race, increasingly unlikely with so little time, or a failure of the party to turn out its vote. I don't think the Obama campaign is going to drop the ball in any of these states. Finally, the expressed opinions may not reflect how people are actually going to behave on election day. This is sort of summarized at times as "an enthusiasm gap." There is plenty of controversy about this and it may be the reason, rather than sampling error, why polls are off from the results. This is where the importance of Obama having so many routes to victory comes in. In the abstract, it is as likely that a poll will fail in his direction as against him. The odds that all the failures of the polls to predict behavior go against him are pretty low. I noticed a while ago that Silver's "adjusted poll averages" were in every case more favorable toward Romney than the actual poll averages. I inquired about this in an e-mail but got no answer. I think it is because he says he pushes his state averages in the direction of the national polling -- in effect reducing their information content by design. I don't really see a sound theoretical reason for this, but it is very cautious. I think it is the reason why, in my view, Silver's overall probability of 80% for Obama is low at this point. I also have a theory, that no one will likely investigate, that the information coming out of states that are not competitive is of lower value and reliability than that coming out of the swing states. I think this has to do with the behavior of people in response to polls when they know that their states and votes are extremely unlikely to determine the outcome. In the swing states, people know it matters and I think this accounts for the relative stability of the results in those states. There was less noise in there all along because people are aware of polls. Thus, the polls are now having a feedback impact on the polling as well as on the contours of the campaign. The lowest information is 50-50. Thus, if the national polls have lower information content than the state polls in competitive races, the will move toward the information null of 50-50. I think that by blending these results with the state-by-state results in the swing states Silver is degrading the information content and hence skewing the odds toward the neutral.
- roidubouloi
November 1, 2012 at 9:41pm
I think Marc Tracy has a lot to learn about statistics and especially probabilities vs outcomes. Consider this example.. Suppose I told you that you had a 70% chance to flip heads and 30% to flip tails on a fair two sided coin. If you flipped heads you may conclude that I am a mathematical genius. If you flipped tails, I always have an out, after all, I told you there is a 30% chance to flip heads. So how can you judge my abilities as a prognosticator on a single coin flip? Obviously, you can't. You would have to flip the coin a large number of iterations until you had a statistically significant sample, enough to see if heads is running 70% on average. So is Silver a genius or a hack? Who the heck knows, he has only measured a handful of elections. Each election runs only once. We don't have a large enough sample to make a judgement. Whether his models are statistically correct or not, if Romney wins, people will stop paying attention.
- Nicomachus
November 1, 2012 at 9:44pm
PS I think the fact that Romney is campaigning in Florida and Pennsylvania is all the evidence we need that he has abandoned hope of winning Ohio. At this point, he is trying only to avoid the embarrassment of being crushed by a loss in Florida and putting on a brave face by pretending to be "expanding the map" in Pennsylvania. If he had a prayer in Ohio, I think he screwed it when he aired is Jeep ad and was called out as a liar by both GM and Chrysler. I think it was a dumb move, but it was certainly a desperate move.
- roidubouloi
November 1, 2012 at 9:46pm
In my town, I have been responsible for election polling in five elections. I don't take the polls, we hire phone banks for that, but I generate the questions, the samples, and interpret the results. We have never been surprised by an outcome as compared with our last pre-election poll, although we have occasionally been surprised by a margin, in both directions. We do not think the polls prior to October give us a good idea of who is going to win. We use polls from the end of August through mid-October as a means of gauging whether our campaign is working. If we are converting undecideds faster than the opposition, we keep doing what we were doing. If not, we may shift tactics. The last poll, taken around the third week in October has always been correct as to outcome. Sometimes we have taken a tracking poll just before the election, but that is more to steady our own nerves than anything else. Until the last 10-14 days prior to the election, I think the public opinion polls essentially show the same thing ours do, which campaign's strategy is succeeding and which is failing. The story until the first debate was that Obama was succeeding. The story of the first debate is that he made a major tactical error and paid for it. Then he stabilized the situation with a good VP debate and second and third presidential debates and the situation slowly began to return to its norm. At this stage, the polls are showing us how the race has gelled, where the outcome is likely set and where it still remains captive of random fluctuation. To my eye, it has gelled for Obama in Nevada and Ohio, enough to win, with statistical likelihoods, with more uncertainty, of achieving the necessary Electoral College votes by other routes. As Silver says, given the polling evidence, the idea that the race is too close to call is silly. You don't need a fancy model to see that, just some experience reading election polls. Of course, from the outside we do not know the polling methodology in detail. The possibility does exist that there are systematic errors, but I think that unlikely. A lot of polltakers have been doing this for a long time. I think that what Nate Silver does is sound. To the extent that there is slosh in a polling number as an indicator of voting behavior -- which he gives you as a +- percentage that is probably a 95% confidence interval -- and then runs Monte Carlo simulations to see how many times the random variables produce victory on one side or the other, it is hard to take any issue with his technique. He is just reporting what on a macro level the polls mean, giving comprehensible meaning to the welter of information. To the extent that he uses economic and other information, as he says he does, it is much harder to gauge what he is doing, but that information exits his model as Election Day approaches. I don't know what else is in there -- derisively referred to as "special sauce" by his critics - but I do know that I made a very good living for 20 years applying the same sort of techniques to financial markets. Thus, i know it can be done. However, whereas we had literally thousands of throws of the dice every day, he has very few. This is generally the case with economic research. So what? We cannot know more than the available information permits. But we can try to know what the available information permits. The poll averages have a pretty good predictive history. My sense is that Silver's refinement of them is likely to be somewhat better, but it is really the polls that are telling the story, not Silver. He is collating and presenting the information they contain.
- roidubouloi
November 2, 2012 at 12:02am
Two things to note: Over on Nate's blog today, someone pointed out that the Princeton guys, who've had their own model for a few years now, consider Nate to be extra complicated, and possibly double counting some uncertainties in his model. Their model has a 99% chance of an Obama victory right now :-) Politico - I think they've single handedly contibuted more to Beltway cynicism than any publication around. Nothing is seen through any lens other than the political. These days, the only reason I go there is to see what unflattering things they're saying about Obama.
- austinous
November 2, 2012 at 12:11am
That is cheery news, austinous (of Austin, TX I assume). It is also nice to see any objective confirmation of my sense that the combinations of the state numbers, even with co-integration thereof, should result in a lower risk of an Obama loss than Silver is showing. (I tried to set up the combinations of the swing states in a spreadsheet earlier this evening to see what I came up with if they were treated as statistically independent, but there were too many combinations and it was too much work, so I gave up.)
- roidubouloi
November 2, 2012 at 12:30am
After austinous' comment, I took a look at the Princeton election model, with which I was unfamiliar, and a bunch of other ones. Sam Wang, who authored the Princeton model, eschews national polls entirely, relying on his method of aggregating and meta-analyzing state polls only. I think his approach makes moderately more sense than Silver's for some of the reasons I described above. Among other things, I relies on the poll median rather than the mean so that outliers don't have an excessive impact. Silver takes the polls and weights them based on accuracy, bias, and other factors, including the number of subjects in the poll. Silver's method on this strikes me as theoretically more appealing, but I wonder whether the data really exist to establish the weights and how he can cope with changing poll methodologies. Wang has a simpler approach that may be more consistent with what is knowable given the present state of the world. For what it is worth, Princeton/Wang does give Obama 99% odds at this point. It would not surprise me if one took Silver's odds by state and ran all the combinations, as I started to do earlier but gave up on, you would come up with something very similar. An awful lot of seemingly low probability combinations are required for Romney to win -- unless the polls are systematically wrong or one is including some other risk of meta-events that could change the whole race. I would reiterate that Romney's behavior says to me that he considers Ohio (and therefore any serious prospect of winning the election) lost and is engaged in face-saving, a bit of Hail Mary, and some head-faking to sustain enthusiasm so that his turnout doesn't crash, further embarrassing him.
- roidubouloi
November 2, 2012 at 2:02am
Chris Cilizza at the WaPo speculates that Romney is spending now in Michigan and Pennsylvania not because he really thinks he can turn things around there but because they've raised more money than they know what to do with, and it's an attempt to save face as roi suggests above (including Florida). Makes sense to me.....
- Robert Powell
November 2, 2012 at 4:46am
Roi, I agree broadly with what you're saying. At some point pretty close to the election, Nate should have dropped a lot of the external factors that he includes in his model - stock market, unemployment, GDP, etc., since those are effectively priced into the polls. And I think the possibility that the Republican party is gaming his system is very real. After the first debate, when Obama was dealt a near mortal blow, and it became apparent that Romney actually had a shot at this thing, the number of right leaning polls that came out of swing states was tremendous and unusual. And yes, I am from Austin, so pretty much a wasted vote for the next couple of presidential elections, at least.
- austinous
November 2, 2012 at 8:51am
Roid, austinous, I make no pretense at being an expert, but here is someone with an opposing view: http://www.redstate.com/2012/10/31/on-polling-models-skewed-unskewed P.S. my Austin vote is also wasted :)
- Nicomachus
November 2, 2012 at 10:57am
Sorry, Nichomachus. I can understand why that article would appeal to people who don't understand statistics and sampling. 96% of it consists of inappropriate analogies that can leave an uneducated reader feeling that he has come to understand what this is all about. But that is flim-flam, a distraction for the purpose of giving the article "truthiness." The punchline is in the claim that the polls are incorrectly weighting the ideological/party IDs of the electorate and that this can be undone ("unskewed," in the favored term of the right) by, for example, taking the preferences expressed by self-IDed Dems, Republicans and independents and assigning new weights to each of those groups based on pre-determined or normative percentages for the groups in the population. The problem with this notion is that self-IDs are volatile and unreliable. If, over and over and over, random sampling by a wide range of polling firms gives you self-IDs that diverge from information about actual party enrollment, the correct conclusion is, not that the sampling is wrong, but that self-IDs diverge from actual party enrollment. In particular, lots of people like to call themselves independent. If there is a divergence of this kind, you cannot re-weight the poll results using the candidate preferences expressed in the polls and different weights for the party IDs. The reason is that the candidate preferences are correlated (technically co-integrated) with the party-IDs. If you are going to adjust the party-ID weights, you also have to adjust the preferences that accompany those party IDs. But you have no information with which to do this. That would require having a meta-poll that shows you the preferences, separately, of those whose self-ID matches their registration and those whose self-ID does not. But there is not meta-poll with which to do this. If there were, then that would be the poll and there would be no possibility of raising this issue. In the absence of better information than the polls themselves about the "true" distribution of preferences, the best information is the polls themselves. There is no means of unskewing them even if they were skewed. Is it possible that a multitude of polling firms do not know how to take a random sample and therefore all come up with the same skew? It is possible. We have no information upon which we can rule out that possibility. However, the poll averages have been accurate predictors in the past -- according to Sam Wang of Princeton, the state polls in particular. Thus, we don't have any good reason to believe that all these pollsters have forgotten how to draw a random sample. The right claims that this election is different. Perhaps. But it has no evidence for that claim. So, we cannot rule out the possibility that almost all the polls are systematically wrong. However, the claim that they are does not have an evidentiary basis. The claim that the "internals," the sub-breakdowns within the polls, disagree with the "top line," the poll conclusion about candidate preferences, is simply false. It is yet another "faith-based" claim.
- roidubouloi
November 2, 2012 at 12:07pm
@Roid- Wow!
- Wonderland
November 2, 2012 at 12:50pm
Roid, you may very well be correct. One thing for sure, one of these guys has the wrong end of the stick. My simple view of the RCP poll averages suggests to me Obama has the edge, leading the polls in a significant majority of battleground states. I give respect to the Princeton guys, 99% is a real prediction :) .
- Nicomachus
November 2, 2012 at 3:53pm
Yup. The Wang model takes no prisoners.
- Robert Powell
November 2, 2012 at 6:25pm
At this stage of the race, Nichomachus, you don't need more than the simple view. You can just look at the preponderance of the state poll results in the swing states, see whether they are red or blue (in effect adopting Sam Wang's preferred technique of looking at the median rather than the mean), and see what is going to happen and where it is still wobbling -- Florida, Virginia, and Colorado. But Obama wins with Ohio even if he loses all three. And yet, VA and CO look to be wobbling -- meaning both red and blue polls -- but more in Obama's direction, and FL is becoming less red, getting close to a true 50-50. Unless the state polls are systematically wrong, as the right claims, then I would put the current odds about half way between Nick Silver's 81% and Sam Wang's 99% -- that is at 90%, 9:1 Obama. I don't think the campaigns matter any longer -- they will simply drown each other out between now and Tuesday. An event that upsets the narrative is highly unlikely. I don't think the sampling error is relevant as the preponderance of the polls method pretty much eliminates that. Rather, there is a variance in the behavior implied by the public sentiment measured in the polls. That is to say, even if the poll is drop-dead accurate that 51% of likely voters prefer Obama, there is a variance, according to Silver about +-3%, in who turns up to vote. In the places where the margin is less than this variance (I believe it is a 95% confidence interval), random wobble could put the result in Romney's hands even if the sentiment in fact favors Obama. It is not very likely that all the wobbles go one way, toward Romney, which is about what would have to happen given that most of the swing states are leaning Obama, but it is statistically possible. One could do Monte Carlo simulations to figure out what the average outcome is from the wobbles (something Nick Silver does). I don't have the tools, but my seat of the pants puts this in the range of 10% perhaps down to 5%. I don't know how Silver's model works, but I would not be surprised if his odds move up to between 87% and 90% by Monday if the polls don't change in tone between now and then. Myself, I would then still put the probability about half way between Wang and Silver. 93% on Monday is my guesstimate if the polls in swing states are no worse for Obama than they are today. Of course, we will NEVER be able to tell if the probabilities were accurate because there will be only a single trial with a heads or tails, Obama or Romney, outcome. Even if you have an unfair coin with 9:1 odds of turning up heads, you can never estimate the a priori odds from the outcome of a single trial. Is it a fair coin, with 1:1 odds or an unfair coin? If you have only one trial, you can never tell. When the event crystallizes, the probabilities vanish. If we could somehow run the same election 500 times, then we could know the probabilities to within 3% or so, but we only get a single outcome.
- roidubouloi
November 2, 2012 at 10:06pm
Also, because Obama is ahead, the wobble to Romney would have to be bigger, which carries a lower probability. Think of each state as a little bell curve located at Nate Silvers predicted vote. If the mean, the expectation, is +1.5% Obama, then some portion of the bell curve will lie over the line in Romney territory. But more of it, roughly 2/3, will be in Obama territory. This is approximately why Silver has the odds he does in each state. The question is how he aggregates the state-by-state odds into a probability for the compound events that result in wins or losses for each -- for example Obama loses OH, VA, and FL, but wins NH, IA, NV, and CO, which is still a win for him. It is in this area that I sense that Silver is too conservative. How can this be? Why don't the numbers dictate the outcome? Because one can make an assumption of statistical independence amongst the swing states, that all the wobbles occur without any relationship to one another -- which would give Romney very, very low odds -- or you can assume that there are forces that affect all of the swing states in the same direction, that their wobbles are at least partially correlated. If the wobbles are partially correlated, it raises the likelihood that enough of them could simultaneously wobble to Romney to give him the election. The things that Silver writes make clear that his model does not treat the swing states as statistically independent, but we have no idea how he links them. That is invisible inside his black box. It is merely my feeling, based on the fact that the demographics of the swing states are so different, that Silver is treating them as too highly correlated, giving him a relatively conservative overall set of probabilities, currently 81% for Obama. It is also in his interest to do this because it hedges his position and he avoids appearing too wrong if Romney wins. If he "takes no prisoners," like Wang, and says 99% and Romney wins, he is WRONG. If he leaves a reasonably high percentage for Romney, he cannot be falsified. 17% left for Romney, 83% for Obama, seems pretty good for Obama, but the 17% is about your risk of losing in a single round of Russian roulette with a six-chambered pistol. Would you want to play Russian roulette with a six-chambered pistol? Put that way, 17% doesn't seem nearly low enough. If Romney wins and Silver can say, well, I only had Obama winning 5 out of 6 times, it is tough to say Silver was wrong. My point is that Silver has an incentive to write a conservative model. Wang has nothing much on the line, no book, no job, and so can afford to be bold.
- roidubouloi
November 2, 2012 at 10:23pm
I should have added that if Silver says 83% and Obama wins, it looks like Silver called it. (If Romney wins, he gets to say that he predicted Romney 1 in 6.)
- roidubouloi
November 2, 2012 at 10:25pm
I am not saying that Silver cooks his books, just that he has a model that appears conservative in the way in which he aggregates the state-by-state probabilities and that a somewhat conservative model is in his personal interest as a prognosticator who wants to have a following after the election is over. This is the opposite of the accusations made by the Republicans that Silver is overstating Obama's odds. I think Silver is understating them.
- roidubouloi
November 2, 2012 at 10:28pm
This is fun. Just looked at 538. Silver has Obama's probabilities ticking up just as I suggested. But I also realized exactly why I think he is being conservative. He has the odds of an Ohio win, a virtual lock on victory for Obama, at 82%, and the odds overall at 82.7%. But Obama has multiple paths to 270 while Romney does not. Effectively, Silver is saying these are all so correlated with Ohio that they barely increase the probability of Obama victory (there are scenarios that cut both ways, but that is the gist of it). I don't think it is rational to have states from NH to VA to IA to NV treated as so highly correlated with Ohio in their outcomes. Now, since I cannot do this in a rigorous way, that is just may sense of it, but my sense is that Obama's overall probability should be at least 5% higher than his Ohio probability.
- roidubouloi
November 2, 2012 at 11:05pm
Silver's column today backs up what I have been saying. But he reports that the specific event that his model incorporates as a highly correlated move by all the swing states is the possibility that the polls have all been systematically biased against Romney. He has done the work, as I have not, but I find his 1 in 6 estimate for that possibility too high. I infer that Wang does not consider that and hence treats the current probabilities for the battleground states as being largely independent. That is why he comes up with an extremely small probability that Obama loses. As the very soul of moderation, I am even more convinced that the correct answer lies approximately in the middle. As Silver today gives Obama a probability of 82.7% and Wang is at 99%, 91% seems about right. On the other hand, I said add 5% to Silver, which would be 89%. Compromising with myself and my two different seat of the pants methodologies, I conclude that the correct probability today for an Obama win is 90%. On Monday, if there is no change in the tenor of the race, I will raise that to 93%, by application of my own "secret sauce." The 7% is the probability I assign to the risk that the polls are systematically biased against Romney and that a true sample of public opinion would should him in the lead -- reduced by the chance that even if public opinion favors Romney slightly, he loses anyway due to random wobble. Bottom line, I assign 10% to the risk of a systematic polling error that has favored Obama and a 67% chance that that eventuality would result in a Romney win. Together, that is 7%. Hence, 93% is the highest probability that I, based on the sensations I have in my rear-end when I put on my pants, will assign to Obama on the eve of the election, barring any surprises between now and then. If the polls had Obama up by more, say 5%, I would be inclined to go with Wang's 99%, and I imagine Silver would too.
- roidubouloi
November 3, 2012 at 2:58pm
Roi, the next step, for 2016, is to start your own blog, called roithirtyeight.com. Then, by 2020, you'll also be sucked in by the NYT, and raking in mucho dinero. Of course, I don't know what you do today, so that may actually be a step down for you :-)
- austinous
November 4, 2012 at 10:31pm
Nico writes: "Obviously, you can't. You would have to flip the coin a large number of iterations until you had a statistically significant sample, enough to see if heads is running 70% on average." Not true. if you believe that heads will appear with 70% certainty, then you'd be willing me to pay me 2:1 odds for a single bet IF tails comes up. This is how you detect if someone is giving fair odds: You ask them to take EITHER SIDE with odds. Similarly, Silverman is favoring Obama 3:1. This means that if he bets $1000 that Obama wins, then he'd pay out $3000 if Romney wins. Note that Silverman offered Scarborough 1:1 odds. Thus, when it came time to bet his own money, he didn't seem to see much of an advantage for Obama. But it also means Silverman should also be happy taking Romney for $1000, paying $400 if Obama wins. In fact, that is a better bet for him to take. If the person laying odds will only take one side of the bet, then he's not laying honest odds. Odds are determined precisely to make the bet fair.
- seattleeng
November 4, 2012 at 10:52pm
Right now, statistical arbitrage, austinous. More glory for Nate Silver. More money for me. ___________________ Even without casinos taking their cut, only a fool makes fair bets (or someone doing it for the fun of it, a friendly bet on a sporting even let's say), because the marginal utility of what you stand to lose is less than the marginal utility of what you stand to gain. That makes your expected marginal utility on a fair bet negative. If you don't think you have a statistical edge (which by definition you don't with a fair bet), there is no point. I make a living by having a very small statistical edge in the market. Only when the odds in your favor are sufficient to overcome this expected loss of utility (meaning the odds in the bet are sufficiently better than what you take to be the "real" odds), do you bet. This is exactly what Silver offered. He's no dummy. If the other guy claims Romney is going to win (meaning better than even odds), why shouldn't Silver offer him an even odds bet, the opportunity to put his money where his mouth is? Given Silver's analysis, this would be a sucker bet. The Romney fan should in turn ask for odds, but then he would be confessing that he doesn't really think Romney is favored to win.
- roidubouloi
November 5, 2012 at 12:58pm