This is the fourth in a series of blog posts for folks who are into the geeky mathematical details of how Election Graphs state polling averages have compared to the actual election results from 2008, 2012, and 2016. If this isn’t you, feel free to skip this series. Or feel free to skim forward and just look at the graphs if you don’t want or need my explanations.
In the last post I used the historical deltas between the final Election Graphs polling averages in 2008-2016 to construct a model that given a value for a poll average, would produce an average and standard deviation for what we could expect the actual election results to be. So what can we do with that?
I don't have another election year with data handy to test this model on. No 2020, no 2004, no 2000, no earlier cycles either. So I'm going to look at 2016, even though I shouldn't.
Just as examples, lets look at what the odds this model would have given to the states Election Graphs got wrong in 2016… This technically isn't something you should do, since we are using a model on data that was used to construct the model, which isn't cool, but this is just to get a rough idea, so…
The only one that is really surprising is Wisconsin, just as it was on Election night in 2016. Every other state was clearly a close race, where nobody should have been shocked about it going either way.
Wisconsin though? It was OK to be surprised on that one.
OK, and maybe the margin in ME-CD2, but not that Trump won it.
Doing some Monte Carlo
Let's go a bit farther than this though. One thing Election Graphs has never done is calculate odds. The site has provided a range of likely electoral college results, but never a "Candidate has X% chance of winning". But with the model we developed in the last post, we now have a way to generate the chance each candidate has of winning a state based on the margin in the poll average, and with that, you can run a Monte Carlo simulation on the 50 states, DC, and five congressional districts.
Now, once again, it is kind of bogus to do this for 2016 since 2016 data was used to construct the model, but we're just trying to get an idea here, and we'll just recognize this isn't quite a legitimate analysis.
So, here is a one off running the simulation 10,000 times to generate some odds. I'd probably want a bit larger number of trials if I was doing this "for real". I might also smooth the win chances curve in the last post to get rid of some of the jaggy bits before using it as the source of probabilities for the simulation. And obviously if you ran this again, you'd get slightly different results. But here is the result of that one run with 10,000 trials…
Well, that is a fun graph. It puts the win odds for Trump at 25.38%.
Now, I emphasize again that this is cheating. Because the facts of Trump's win are baked into the model. We're testing on our training data. That's not really OK. Having said that though…
How does this compare to where other folks were at the end of 2016? I looked at this in my last regular update prior to the results coming in on election night, so here is my summary from then:
So this Monte Carlo simulation using the numbers calculated as I have described would have given Trump better odds than anybody other than FiveThirtyEight. Again though, I am cheating here. A lot.
But here is the thing. Even though I would be giving Trump pretty good odds with this model, the chance of him actually winning by as much as he did (or more) is actually still tiny at 0.29%. With these odds a Trump win should not have been a surprise, but a Trump win by as much as he actually won by… that still should have been very surprising.
In this series of posts, we've been looking at a whole bunch of different ways of answering the basic question "what is a close state?". One reason I am looking at this is that the way Election Graphs has done our "range of possibilities" in the past is just to define what a close state is, and then let all of them swing either to one candidate or the other, and see what the range of electoral college results would be.
So lets see what electoral college ranges we would have gotten in 2016 with each of the methods I've gone over in the last few blog posts:
The two showing the ranges from the Monte Carlo simulation are dimmed out because they are determined by a completely different method, not swinging all close states back and forth.
It is interesting that both the 1 sided and 2 sided histogram 1σ boundaries would end up with the exact same boundaries as my current 5% bounds. But as you can see there are a ton of different ways to define "too close to call" which result in a huge variation on how the range of possibilities gets described.
So what to do for 2020? How will I define close states?
You'll have to wait a little longer for that.
Before I get to that, it is also worth looking at the national race as opposed to just states. On Election Graphs I have used the "tipping point" to measure that. What tipping point values should be considered "too close to call"?
This is the third in a series of blog posts for folks who are into the geeky mathematical details of how Election Graphs state polling averages have compared to the actual election results from 2008, 2012, and 2016. If this isn’t you, feel free to skip this series. Or feel free to skim forward and just look at the graphs if you don’t want or need my explanations.
In the last post I ended by mentioning that assuming the error on poll averages was independent of the value of the poll average might not be valid. There are at least some reasonable stories you could tell that would imply a relationship. So we should check.
I've actually looked at this before for 2012. That analysis showed the error on the polls DID vary based on the margin of the poll average. But it wasn't "close states are more accurate". But maybe that pattern was unique to that year.
So I looked at this relationship again now with all the data I have for 2008, 2012, and 2016:
That is just a blob right? Not a scatterplot we can actually see much in? Wrong. There is a bottom left to upper right trend hiding in there.
Interpreting the shape of the blob
Before going further, let's talk a bit about what this chart shows, and how to interpret it. Here are some shapes this distribution could have taken:
Pattern A would indicate the errors did not favor either Republicans or Democrats, and the amount of error we should expect did not change depending on who was leading in the poll average or how much.
Pattern B would show that Republicans consistently beat the poll averages… so the poll averages showed Democrats doing better than they really were, and the error didn't change substantially based on who was ahead or by how much.
Pattern C would show the opposite, that Democrats consistently beat the poll averages, or the poll averages were biased toward the Republicans. The error once again didn't depend on who was ahead or by how much.
Pattern D shows no systematic bias in the poll averages toward either Republicans or Democrats, but the polls were better (more likely to be close to the actual result) in the close races, and more likely to be wildly off the mark in races that weren't close anyway.
Pattern E would show that when Democrats were leading in the polls, Republicans did better than expected, and when Republicans were leading in the polls, Democrats did better than expected. In other words, whoever was leading, the race was CLOSER than the polls would have you believe.
Finally, Pattern F would show that when the polls show the Democrats ahead, they are actually even further ahead than the polls indicate, and when the Republicans are ahead, they are also further ahead than the polls indicate. In other words, whoever is leading, the race is NOT AS CLOSE as the polls would indicate.
In all of these cases the WIDTH of the band the points fall in also matters. If you have a really wide band, the impact of the shape may be less, because the variance overwhelms it. But as long as the band isn't TOO wide the shape matters.
Also, like everything in this analysis, remember this is about the shape of errors on the individual states, NOT on the national picture.
Glancing at the chart above, you can determine which of these is at play. But lets be systematic and drop some linear regressions on there…
2008 and 2012 were similar.
2016 had a steeper slope and is shifted to the left (indicating that Republicans started outperforming their polls not near 0%, but for polls the Democrats led by less than about 11%). But even 2016 has the same bottom left to top right shape.
I haven't put a line on there for a combination of the three election cycles, but it would be in between the 2008/2012 lines and the 2016 line.
Of the general classes of shapes I laid out above, Pattern F is closest.
Capturing the shape of the blob
But drawing a line through these points doesn't capture the shape here. We can do better. There are a number of techniques that could be used here to get insight into the shape of this distribution.
The one I chose is as follows:
At each value for the polling average (at 0.1% intervals), collect all of the 163 data points that are within 5% of the value under consideration. For instance, if I am looking at a 3% Democratic lead, I look at all data points that were between an 8% Democratic lead and a 2% Republican lead (inclusive).
If there are less than 5 data points, don't calculate anything. The data is too sparse to reach any useful conclusions.
If there are 5 or more points, calculate the average and standard deviation, and use those to define boundaries for the shape.
Here is what you get:
This is a more complex shape than any of the examples I described. Because it is real life messy data. But it looks more like Pattern F than anything else.
It does flatten out a bit as you get to large polling leads, even reversing a bit, with the width increasing like Pattern D, and there some flatter parts too. But roughly, it is Pattern F with a pretty wide band.
Fundamentally, it looks like there IS a tendency within the state level polling averages for states to look closer than they really are.
Is this just 3P and undecided voters?
All of my margins are just "Republican minus Democrat". Out of everybody, including people who say they are undecided or support 3P candidates. But those undecideds eventually pick someone. And many people who support 3rd parties in polls end up voting for the major parties in the end. Could this explain the pattern?
As an example assume the poll average had D's at 40%, R's at 50%, and 10% undecided, that's a 10% R margin… then split the undecideds at the same ratio as the R/D results to simulate a final result where you can't vote "undecided", and you would end up with D's at 44.4% and R's at 55.6% which is an 11.1% margin… making the actual margin larger than the margin in the poll average, just as happens in Pattern F.
Would representing all of this based on share of the 2-party results make this pattern go away?
To check this, I repeated the entire analysis using 2-party margins.
Here, animated for comparison, is the same chart using straight margins and two party margins.
While the pattern is dampened, it does not go away.
It may still be the case that if we were looking at more than 3 election cycles, this would disappear. I guess we'll find out once 2020 is over. But it doesn't seem to be an illusion caused simply by the existence of undecided and 3P voters.
Does this mean anything?
Now why might there be a tendency that persists in three different election cycles for polls to show results closer than they really are? Maybe close races are more interesting than blowouts so pollsters subconsciously nudge things in that direction? Maybe people indicate a preference for the underdog in polls, but then vote for the person they think is winning in the end? I don't know. I don't have anything other than pure speculation at the moment. I'd love to hear some insights on this front from others.
Of course, this is all based on only 3 elections and 163 data points. It would be nice to have more data and more cycles to determine how persistent this patten is, vs how much may just be seeing patterns in noise and/or something specific to these three election cycles. After all, 2016 DID look noticeably different than 2008 and 2012, but I'm just smushing it all together.
It is quite possible that the patterns from previous cycles are not good indicators of how things will go in future cycles. After all, won't pollsters try to learn from their errors and compensate? And in the process introduce different errors? Quite possibly.
But for now, I'm willing to run with this as an interesting pattern that is worth paying some attention to.
Election Result vs Final Margin
Before determining what to do with this information, lets look at this another way. After all, while the amount and direction of the error is interesting, in terms of projecting election results, we only really care if the error gives us a good chance of getting the wrong answer.
Above is the actual vote margins vs the final Election Graph margins, with means and standard deviations for the deltas calculated earlier plotted as well. Essentially, the first graph is this new second graph with the y=x line (which I have added in light green) subtracted out.
The first view makes the deviation from "fair" more obvious by making an unbiased result horizontal instead of diagonal, but this view makes it easier to see when this bias may actually make a difference.
Lets zoom in on the center area, since that is the zone of interest.
Out of the 163 poll averages, there were only actually EIGHT that got the wrong result. Those are the data points in the upper left and lower right quadrants on the chart above. That's an accuracy rate of 155/163 ≈ 95.09%. Not bad for my little poll averages overall.
The polls that got the final result wrong range from a 7.06% Democratic lead in the polls (Wisconsin in 2016) to a Republican lead of 3.40% (Indiana in 2008).
For curiosity's sake, here is how those those errors were distributed:
D's lead poll avg but R's win
R's lead poll avg but D's win
2 (NC, IN)
4 (PA, MI, WI, ME-CD2)
So, less than 5% wrong out of all the poll averages in three cycles, but at least in 2016, some of the states that were wrong were critical. Oops.
Anyway, once we have averages and standard deviations for election results vs poll averages, if we assume a normal distribution based on those parameters at each 0.1% for the poll average, we can produce a chart of the chances of each party winning given the poll average.
Here is what you get:
Alternately, we could recolor the graph and express this in terms of the odds the polls have picked the right winner:
You can see that the odds of "getting it wrong" get non-trivially over 50% for small Democratic leads. The crossover point is a 0.36% Democratic lead. With a Democratic lead less than that, it is more likely that the Republican will win. (If, of course, this analysis is actually predictive.)
You can also work out how big a lead each party would need to have to be 1σ or 2σ sure they were actually ahead:
68.27% (1σ) win chance
95.45% (2σ) win chance
Margin > 1.11%
Margin > 4.87%
Margin > 2.32%
Margin > 6.42%
Margin > 1.72%
Margin > 5.64%
Democrats again need a larger lead than Republicans to be sure they are winning.
These bounds are the narrowest from the various methods we have looked at though.
Can we do anything to try to understand what this would mean for analyzing a new race? We obviously don't have 2020 data yet, and I don't have 2004 or earlier data lying around to look at either. So what is left?
Using the results of an analysis like this to look at a year that provided data for that analysis is not actually legitimate. You are testing on your training data. It is self-referential in a way that isn't really OK. You'll match the results better than you would looking at a new data set. I know this.
But it may still give an idea of what kind of conclusions you might be able to draw from this sort of data.
So in the next post we'll take the win odds calculated above and apply them to the 2016 race, and see what looks interesting…
This is the second in a series of blog posts for folks who are into the geeky mathematical details of how Election Graphs state polling averages have compared to the actual election results from 2008, 2012, and 2016. If this isn't you, feel free to skip this series. Or feel free to skim forward and just look at the graphs if you don't want or need my explanations.
Last time we looked at some basic histograms showing the distributions for how far off the actual election results were from the state polling averages, but pointed out at the end that we don't just care about how far off the average is, we care about whether it will actually make a difference to who wins.
For instance if we knew the poll average overestimated Democrats by 5%, this means something very different depending on the value of the poll average:
If the Democrat was ahead by 15% the overestimation wouldn't matter, because it wouldn't be enough to change the outcome. The Democrat would just win by a smaller margin.
If the poll average showed the Democrat ahead by 3% the overestimation would mean the Republican is actually ahead. This is the case where the overestimation would actually make a difference.
If the poll showed the Republicans ahead the overestimation of the Democrats wouldn't change the outcome, it would just mean that the Republicans would win by a bigger margin.
Two sided by individual results
So lets look at this same data we did in the last post, but in a different way to try to take this into account… Instead of bundling up the polling deltas into a histogram, we consider all 163 results, and try to figure out at each possible margin, how many poll results had a big enough error that they could have changed the result.
As an example, if you look at all 163 data points for cases where the Democrats beat the poll average by more than 15%, you only find 2 cases out of the 163. (For the record that would be DC in 2008 and 2016.) That lets you infer that if the Republicans have a 15% lead, you can estimate the Democratic chances of winning given previous polling errors is about 2/163 ≈ 1.23%, which of course means in those cases Republicans have a 98.77% chance of winning.
Here is the chart you get when you repeatedly do this calculation:
As you would expect, as the polls move toward Republican leads, the Democratic chance of winning diminishes, and the Republican chance of winning increases. The break even point is almost exactly at the 0% margin point. (It is actually at an approximately 0.05% Republican lead based on my numbers, but that is close enough to zero for these purposes.)
This is good, because it means even if there are some differences in the shape of the distribution on the two sides, at least the crossover point is basically centered.
Taking the exact same graph, but coloring it differently, we can look at not which party wins based on the polling average at a certain place, but instead at the chances that the polling average is RIGHT or WRONG in terms of picking the winner.
For instance, at the same "Republicans lead by 15% in the polling average" scenario used above, there is a 98.77% chance the polling average has picked the right winner, and a 1.23% change the polling average is picking the wrong side.
Here is that chart:
Looking at it this way, and again looking at 1σ being getting things right about 68.27% of the time, and 2σ being getting things right about 95.45% of the time we can construct the table below. With the asymmetry, it is different for Republicans and Democrats:
68.27% (1σ) win chance
95.45% (2σ) win chance
Margin > 1.76%
Margin > 8.26%
Margin > 3.01%
Margin > 12.56%
Margin > 2.38%
Margin > 10.41%
Basically, given the results of the last three election cycles, Democrats need a bit larger lead to have the same level of confidence that they are really ahead.
Now, doing something for Election Graphs based on this asymmetry is tempting as it has now showed up in two different ways of looking at this data, but…
A) It is certainly possible that this asymmetry is something that just happens to show up this way after these three elections, and it would be improper to generalize. 163 data points really is not very much compared to what you would really want, and it is very possible that this pattern in an illusion caused by limited data and/or there are changes over time that will swamp the patterns seen here.
B) A big part of the appeal of Election Graphs has always been having a really simple easy to understand model… including having nice symmetric bounds… "a close race is one where the margin is less than X%"… without that being different depending on which party is ahead… is a big part of that, even if it is a massive oversimplification.
So lets look at this in a one sided way again…
One sided by individual results
Once again we we calculate a "chance of being right" number, as we did earlier, but now just looking at the absolute error. We will assume we only know the magnitude of the current margin and the previous errors, not the directions, and that errors have an equal chance of going in either direction.
Running through an example:
At the 5% mark, there were 107 poll averages out of 163 that were off by less than 5%. These 107 would all give a correct winner no matter which direction the error was in.
The remaining 56 polls had an error of more than 5%, so could have resulted in getting the wrong winner. But since we are assuming a symmetric distribution of the errors now, we would only expect half of these errors to be in the direction that would change the winner. So another 28.
107+28 = 135. So we would expect at the 5% mark the poll averages would be right 135/163 ≈ 82.82% of the time, and wrong 17.18% of the time.
Repeat this over and over again, and you get the following graph:
So if you are looking to be 68.27% (1σ) confident that a state poll average will be indicating the right winner, the leader needs to be ahead by at least 2.49%. To be 95.45% (2σ) confident though, you need an 11.36% margin.
These last two ways of looking at things have the 68.27% level considerably narrower than the 5% that is the current first boundary on Election Graphs. If we are thinking of this as the boundary for "really close state that could easily go either way" this seems counter intuitive.
If we kept the same "Weak/Strong/Solid" names for the categorizations, then in the final state of the 2016 poll averages Michigan would get reclassified as "Strong Clinton" instead of "Weak Clinton", while Ohio and Georgia would move from "Weak Trump" to "Strong Trump". Given that Michigan ended up actually won by Trump, this seems like it might not be a good move.
Or maybe it would just be even more important to be clear that "Strong" states are actually states that have a non-trivial chance of flipping. The "Solid" category was intended to be the states that really should not be expected to go the other way. "Strong" was originally intended to indicate a significant lead, but not that a state was completely out of play. "Weak" was supposed to be states that really were so close enough you shouldn't count on the lead being real.
If we changed the categories in a way that moved the first boundary inward, it would be important to make this very clear, perhaps by changing the names.
If, on the other hand, we moved the "close state boundary" outward to the 95.45% (2σ) level, it just seems way too wide. A state where one candidate is ahead by 11.36% just isn't a close state. Maybe it is true that there is a 4.55% chance that the poll average is picking the wrong winner. This seems to imply that. But even so, it seems misleading to say that big a lead is still a close race.
There is something else to think about as well. The analysis above assumes that the difference between the election result and the final poll average is not dependent on the value of the poll average itself.
But is that reasonable?
One might think (for instance) that maybe poll averages in the close states would be more accurate than polls in the states where nobody expects a real contest. The theory here would be that because close states get more frequent polling the average can catch last minute moves better than in less competitive states that are more sparsely polled. (At least this logic might make sense for a poll average like the Election Graphs average that uses the "last X polls", other ways of calculating a poll average may differ.)
Or maybe there is some other factor at play that makes it so we can say more about how far off a poll may be if we take into account what that poll average is in the first place.
And that's what we will look into in the next post…