New Charts for the Probabilistic View

A couple of months ago, Election Graphs added charts showing how the odds of candidates winning each state evolved. Since then we have referred to those odds quite a bit, and have also discussed how I can combine those individual state by state odds through a Monte Carlo simulation.

I started doing those simulations offline and occasionally reporting results based on that here on the blog. But these were still only manual simulations I was doing offline. Nothing on the ElectionGraphs.com pages for Election 2020 showed this.

Well, a couple of weekends ago, I fixed that, and have done a bit of debugging since, so it is ready to talk about here. I have started with the comparison page where you can look at how various candidate pairs stack up against each other.

Here is the key chart:

This chart shows the evolution over time of the odds of the Democrats winning as new state polls have come in. The comparison page also shows graphs for the odds of a Republican win, if you prefer looking at things from that point of view. Those two don't add up to 100% because there is of course also a chance of a 269-269 electoral college tie, and there is also a chart of that. Together the three will add to 100%.

The charts are automatically updated as I add new polls to my database.

The summary block for each candidate pair on the comparison page has also been updated to include the win odds information:

For the moment this is only on the comparison page, not on the individual candidate pages. This summary also contains more detail than is available in the graphs at this point. I will be adding more charts to close that gap when I get a chance.

I've used the Harris vs. Trump summary as the example here because it (along with O'Rourke vs. Trump) contains something curious that requires a closer look. Namely, you'll notice that the "Expected" scenario (where every candidate wins all the states where they lead in the poll average) shows a different winner than the "Median" scenario (the "center" of the Monte Carlo simulations when sorted by outcome).

When you look at the charts for the expected case vs. the median case, it is evident that the median in the Monte Carlo simulations does not precisely track the expected case. In fact, in some instances, the trends don't even move in the same direction. So what is going on here?

It would take some detailed digging to understand specific cases, but as an example, a quick look at the spectrum of the states for Harris vs. Trump can get some insights.

Now, I don't currently have a version of this spectrum showing win odds instead of the margin, but without that, you can still immediately see why even though Trump leads by six electoral votes "if everybody wins the states they lead", Harris might win in the median case in a simulation that looks at the situation more deeply.

The key is the margins in the swing states. With only a six electoral vote margin, it only takes three electoral votes flipping to make a 269-269 tie, and 4 to switch the winner.

Fundamentally, there are four "barely Trump" states that have a good chance of ending up going to Harris, but only one "barely Harris" jurisdiction that has a decent chance of going to Trump.

Looking at the details:

Trump's lead in Virginia's (13 EV) poll average is only 0.1%, which translates into a 44.9% chance of a Harris win.

Trump's lead in Florida's (29 EV) poll average is only 0.5%, which translates into a 40.2% chance of a Harris win.

Trump's lead in Ohio's (18 EV) poll average is only 1.2%, which translates into a 30.9% chance of a Harris win.

Trump's lead in Iowa's (6 EV) poll average is only 1.5%, which translates into a 28.4% chance of a Harris win.

Those are all the states with a Trump lead where Harris has more than a 25% chance of winning the state. Harris only needs to win ONE of those states to end up winning nationwide. Doing the math, if the odds of winning are independent (which is not strictly true, but is probably a decent first approximation), there is an 83.7% chance that Harris will win at least one of these four states.

Now, there is one Harris state where Trump has a greater than 25% chance of winning. That would be Colorado, where Harris leads by 1.2%, which translates into a 41.6% chance of a Trump win. So that compensates a bit.

But in the end, with this mix of swing states, Harris wins more often than she loses in the simulations (62.4% of the time), and the median case is a narrow 16 EV Harris win.

The straight-up "if everybody wins all the states they are ahead in" expected case metric is a decent way of looking at things as far as it goes. Election Graphs has used it, along with the tipping point, as the two primary methods of looking at how elections are trending in the analysis here from 2008 to 2016. And it has done pretty well. In those three elections, 155/163 ≈ 95.09% of races did indeed go to the candidates who were ahead in the poll average. That view has the advantage of simplicity.

But the Monte Carlo simulations (using state win probabilities based on Election Graph's previous results) give a way of quantifying how often the underdog wins states based on the margin, and how that rolls up into the national results. It can catch subtleties that are out of reach if you only look at who is ahead.

So from now on, Election Graphs will be looking at things both ways. The site will still have the expected case, tipping point, and "best cases" gotten from simply classifying who is leading and which states are close. But we'll also be looking at the probabilistic view. We may be looking at things the new way a bit more. But they will both be here.

Right now that information is on the national comparison page, the state detail pages, the state comparison pages, and the blog sidebar. There is still nothing about the probabilistic view on the candidate pages. That is next on the list once I get some time to put some things together.

469.6 days until polls start to close.

Stay tuned.

For more information:

This post is an update based on the data on the Election Graphs Electoral College 2020 page. Election Graphs tracks a poll-based estimate of the Electoral College. The charts, graphs, and maps in the post above are all as of the time of this post. Click through on any image to go to a page with the current interactive versions of that chart, along with additional details.

Follow @ElectionGraphs on Twitter or Election Graphs on Facebook to see announcements of updates. For those interested in individual poll updates, follow @ElecCollPolls on Twitter for all the polls as I add them. If you find the information in these posts informative or useful, please consider visiting the donation page.

New Charts for State Odds

There were new polls in Florida since the last update, but they didn't result in any category changes for the state, so instead I'll talk about some new features I added to the site a few days ago.

Back on January 29th, I discussed a way of taking the historical performance of state-level Election Graphs averages vs. actual election results and using that to infer the odds of the Republican or Democratic candidate winning based on the current Election Graphs average.

Now, to be clear, since this analysis compares the FINAL average before the election to the election results… it did not look at how those averages varied over time in the leadup to the election… this is looking at the odds "if the election was today." There is no factoring in the likelihood of changes over those intervening months as some more complicated models might.

But it still gives a snapshot I think is interesting, and EVERYTHING on Election Graphs is "if the election was today," so it fits in well.

In my May 8th post, I mentioned that I had added a display of these state-level win odds to the state detail pages and state comparison pages. I was only displaying the numbers, not any visualizations. As of this week, I am now displaying charts of how these numbers change over time as well.

To illustrate, I'll show examples of the new charts and how they relate to the older charts.

The above is the standard graph for an individual candidate combination and state that has been on Election Graphs since the 2016 cycle. It shows dots for the specific polls and a red line for the Election Graphs average. While this is only a static image in this blog post, on the actual detail page, you can hover over elements of the chart and get more details.

This new view is the graph that I added to the page. It translates the poll average into the chances of each candidate winning the state based on the methodology detailed in that January blog post.

So, in this example, as of right now, Biden has a 7.1% lead in the poll average, which translates into a 98.8% chance of Biden winning the state (or a 1.2% chance of Trump winning). I show the axis labels for the Democrat's chances on the left, but if you prefer, the axis labels on the right show the Republican's chances.

While the first chart does a great job at showing in an absolute way where the polls are, this second chart gives a better idea as to what this means for who is probably going to win and shows how much changes in the poll average do or do not change those odds.

When looking at the state detail page, these two charts are side by side for easy comparison:

Looking at this example makes clear that the "Weak" category is still pretty broad! That 3.8% Trump lead in Texas translates into a 91.4% chance of Trump winning!

Remember though the following important caveats:

  • As mentioned above, this is "if the election was today." It does not take into account how polls may move in the time between now and the election. Until we get right up to the election, this is very important. Poll averages can and do move quickly. A few weeks can make a huge difference (as shown by the last few weeks before the 2016 election). In the over 500 days we have left at the moment, the world could change completely!
  • I base the odds estimates on the aggregated performance of the Election Graphs averages in 2008, 2012, and 2016. It is possible that those three elections will not be representative or predictive of 2020. As they say in the investment world, "past performance is not a guarantee of future results."
  • For the moment, Michigan is the only state where the Election Graphs average is based only on 2020 polls. For the rest, I'm still "priming" the numbers with election results from 2000 to 2016. Only 13 states have any 2020 polling at all at this early stage, and most of them have three or less. So we still have pretty sparse data.

Of course, in addition to the state detail pages for individual candidate matchups, there are also the charts on the comparison page:

Above is the traditional poll view.

And then the odds based view. The idea is the same as the view for the individual candidate pairs, but of course, you see all five of the best-polled candidate pairs and can compare how they are doing.

Now, all of the new graphs are on state-level views. What about national? How does this roll up into an overall picture of the election?

Well, it is coming but isn't ready yet. As I described in my January 30th post, you can use these state-level probabilities as part of a Monte Carlo simulation to generate some information on the national picture.

I don't have any of that automated and live yet on the site yet, but I have started to build some of the elements. So here is a preview of the kinds of information this will produce.

First, looking at the odds of winning for the five best-polled candidate pairs (with all the caveats I mentioned above) based on the current Election Graphs averages and 1,000,001 Monte Carlo trials each:

  • Biden 87.3% to Trump 11.9% (0.8% tie)
  • Sanders 74.9% to Trump 23.7% (1.5% tie)
  • Warren 66.1% to Trump 32.0% (1.9% tie)
  • Harris 58.9% to Trump 39.0% (2.0% tie)
  • O'Rourke 48.6% to Trump 49.7% (1.7% tie)

These stats differ a little bit from simply looking at the "expected result" where each candidate wins every state they lead in, or looking at the tipping point metric, as these also look at how likely it is that the various close states end up flipping and going the other way. So this should provide a bit better view of what might happen than those simpler ways of looking at things. But of course, that comes at the cost of complexity and being a bit harder to understand.

Another kind of view that will come out of this is looking at the range of possibilities in a bit more sophisticated way than the "envelopes" already shown on the site. Looking at Biden vs. Trump as an example:

  • Median Result: Biden by 52 electoral votes
  • Central 1σ (68.3% chance): Biden by 106 EV to Biden by 6 EV
  • Central 2σ (95.4% chance): Biden by 158 EV to Trump by 30 EV
  • Central 3σ (99.7% chance): Biden by 218 EV to Trump by 66 EV

So, sometime in the next few weeks, I'll probably get these textual stats added to the live site and automatically updated when I add new polls. After that, I'll try to get some visualizations of both the current state and how that evolves up on the site, but that will take longer.

Anyway. Coming soon.

522.8 days until polls start to close!

For more information:

This post is an update based on the data on the Election Graphs Electoral College 2020 page. Election Graphs tracks a poll-based estimate of the Electoral College. The charts, graphs, and maps in the post above are all as of the time of this post. Click through on any image to go to a page with the current interactive versions of that chart, along with additional details.

Follow @ElectionGraphs on Twitter or Election Graphs on Facebook to see announcements of updates. For those interested in individual poll updates, follow @ElecCollPolls on Twitter for all the polls as I add them. If you find the information in these posts informative or useful, please consider visiting the donation page.

Clearing things out for 2020

It isn't quite time to get everything launched properly for the 2020 version of Election Graphs… but 2020 is getting closer and closer. Here at Election Graphs HQ, I've been occupying myself with other things for a while, like launching the Wiki of the Day podcast a little over a year ago, and continuing with my weekly current events podcast Curmudgeon's Corner, but it is well past time to start getting things ready for 2020.

Behind the scenes I've done some additional analysis of the 2008 through 2016 election results that will inform what I do for 2016. I'll post a bit about that soon.

But first just to note the immediate changes to the site itself. The 2016 charts and graphs have been moved off the front page of Election Graphs in favor of a blog format where the analysis posts and such will live. In the last cycle, these had been posted on my personal blog, but now they will live natively on Election Graphs proper.

I haven't built out the new detail pages for 2020 yet. Those will be coming over the next few months. My target is to launch fully right after the 2018 general elections are over.

The archival material is still there of course, just tucked away a bit. For those looking for that:

Thanks again to everybody who followed our analysis in 2016. I'm looking forward to doing it all again for 2020.

Stay tuned.