Comparing Nate Silver's popular vote/electoral college predictions with mine

 So, Nate Silver put out a tweet earlier this month claiming that in order for Biden to have more than a 50% chance of winning the electoral college, he would need to win the popular vote by greater than 3 points. I just want to compare my percentages with his given my recent electoral college data. His predictions are as follows:

Biden +0-1% - 6% chance of EC win

1-2 points- 22%

2-3 points- 46%

3-4 points- 74%

4-5 points- 89%

5-6 points- 98%

6-7 points- 99%

Currently, as I stated in my previous post, Biden is up 7.4% 7.1% in a 2 way race. Since most other data for the general election on a statewide basis is a 2 way race, I will use that figure. 

To regurgitate my chart from last time (note this is old data, the updated chart changes some things around but has minimal impact on the purpose of this specific exercise): 

States	Winner/Margin	SD	% Biden Win	% Trump Win	Electoral Votes if Biden Wins	Electoral Votes if Trump Wins
New Hampshire	Biden +8.0%	-2.00	98%	2%	216	326
Minnesota	Biden +6.4%	-1.60	94%	6%	226	322
Wisconsin	Biden +6.3%	-1.58	94%	6%	236	312
Nevada	Biden +6.0%	-1.50	93%	7%	242	302
Arizona	Biden +5.6%	-1.40	92%	8%	253	296
Pennsylvania	Biden +4.3%	-1.08	86%	14%	273	285
Michigan	Biden +4.2%	-1.05	85%	15%	289	265
Ohio	Biden +2.4%	-0.60	74%	27%	307	249
Florida	Biden +1.2%	-0.30	62%	38%	336	231
North Carolina	Biden +0.8%	-0.20	58%	42%	351	202
Maine CD2	Unknown (0.0%)	0.00	50%	50%	352	187
Nebraska CD2	Unknown (0.0%)	0.00	50%	50%	353	186
Georgia	Trump +1.3%	+0.33	37%	62%	369	185
Iowa	Trump 1.7%	+0.43	33%	67%	375	169
Texas	Trump +3.5%	+0.88	19%	81%	413	163
Missouri	Trump +7.7%	+1.93	3%	97%	423	125

And my conclusion is that the ultimate swing state that decides the election is Pennsylvania at +4.3%. Assuming a 4% margin of error, that gives Biden a roughly 86% chance of winning the state. That said, I give him a roughly 86% chance of winning the election. Because if Pennsylvania falls, I assume all swing states with lower margins also fall such as Michigan, Ohio, and Florida, while states with higher margins might hold. In reality things might be more messy as in 2016, but I don't really want to worry about bumps in the data introduced by chaos theory. That's way above my pay grade. 

As it stands, with Biden at a 7.1% popular vote lead, by Nate's model, he has Biden at a 99% chance of a win. I have Biden at a 86% chance, more in line 4.3% lead. That is what he has in PA, but we're talking the national vote here. If we got rid of 4.3 points of Biden's lead, he would be down to 2.8% in the national popular vote. So roughly 3% is the 50% mark for Biden. 2-3% is also where Silver predicts a 46% chance of a win, so that's not far off. His data seems to coalesce with mine.

 That said, let's start off as the baseline. Say Biden and Trump are tied in the popular vote and there's a 7.1% shift toward Trump. Well, at that point, the entire slew of swing states goes red outside of New Hampshire and Trump wins 322-216. Pennsylvania, the tipping point, will go Trump by a total of 2.8%. At that point, by my model, Trump has a 76% chance of winning the presidency, with Biden a 24%. That's much higher than what Silver holds. As a matter of fact, I'm going to run over the entire spectrum of possibilities to give you an idea:

Popular Vote Lead	Pennsylvania Lead	Z score	Percent Biden Win	Percent Trump Win
Trump +6	Trump +8.8	-2.20	1%	99%
Trump +5	Trump +7.8	-1.95	3%	97%
Trump +4	Trump +6.8	-1.70	4%	96%
Trump +3	Trump +5.8	-1.45	7%	93%
Trump +2	Trump +4.8	-1.20	12%	88%
Trump +1	Trump +3.8	-0.95	17%	83%
Tie	Trump +2.8	-0.70	24%	76%
Biden +1	Trump +1.8	-0.45	33%	67%
Biden +2	Trump +0.8	-0.20	42%	58%
Biden +3	Biden +0.2	+0.05	52%	48%
Biden +4	Biden +1.2	+0.30	62%	38%
Biden +5	Biden +2.2	+0.55	71%	29%
Biden +6	Biden +3.2	+0.80	79%	21%
Biden +7	Biden +4.2	+1.05	85%	15%
Biden +8	Biden +5.2	+1.30	90%	10%
Biden +9	Biden +6.2	+1.55	94%	6%
Biden +10	Biden +7.2	+1.80	96%	4%
Biden +11	Biden +8.2	+2.05	98%	2%
Biden +12	Biden +9.2	+2.30	99%	1%

So, my results don't really align with Nat/se very well in the details. My spectrum of probabilities is far more broad. I suspect this is because I use a 4 point margin of error leading to the Z scores being more spread out. With my model, I'm not calling you in safe territory with a 98% chance of a win until you're 8 points ahead. I do this to be cautious, and understanding not all polls are equal. It is an estimate on my part and I admit it might be a bit strict at times. Many polls do have margins of error closer to 3. But just to compare directly with Nate:

Popular vote total	My prediction	Nate’s prediction	Nate’s estimated Z score
Biden +1	33%	6%	-1.75
Biden +2	42%	22%	-0.77
Biden +3	52%	46%	-0.10
Biden +4	62%	74%	+0.70
Biden +5	71%	89%	+1.23
Biden +6	79%	98%	+2.05
Biden +7	85%	99%	+2.33

Nate definitely has a far more aggressive bell curve going on with a much tighter margin of error. I'm estimating about 2.5-3 points? He might have different assumptions than I do. As I said, I'm far more conservative in my outlook, especially after 2016. I mean, I saw states swing a good 7-10 points, so I don't want to give false hope saying "oh yeah there's no way this will go red/blue."

Regardless, there are similarities, and despite the difference levels of aggression in terms of certainty in our models, we do come to the same overall conclusion: Biden needs to stay around 3 points ahead in the popular vote to win the electoral college. If the popular vote is a tie, I would expect most swing states to go Trump like in 2016. Even if we had an HRC type 2.1 point lead in the electoral college, that's a Trump +5 scenario vs what we have now. That's game over. Trump wins again. He gets anything from Pennsylvania on down on my chart and he might even win over a couple extra outliers like in 2016 (looking at you, Wisconsin). He would have 285+ electoral votes and while it would be a narrow victory, it would be a victory. And looking at the vote totals in 2016 by state, Trump won Michigan and Wisconsin by a point or less, and Pennsylvania and Florida by slightly more than a point. So one point can make a difference when you're talking 2 vs 3. In my own model, a 3 point popular vote lead for Biden would mean narrowly taking Pennsylvania and Michigan, and those two states would swing the election. That said, at their core, my predictions are similar to Nate's, I just assume a wider bell curve of possibilities.

Now, I know some people assume this means the electoral college leans republican. And I guess relative to the popular vote, it does. While democrats can win big in California and New York, if they aren't 3 points ahead nation wide, they lose the electoral college. That isn't really fair. The electoral college is a trash system. 

At the same time though, I will say that the electoral college generally does favor the democrats under current conditions. Democrats are more popular than republicans overall. Republicans take advantage of the flaws of our system which sometimes gives power to people based on land area than population and get overrepresented. However, republicans are declining in popularity overall and have been for a few election cycles now. From 1992 on, democrats hold the edge. When they lose, they lose narrowly, when they win, they win big. Republicans haven't had a truly decisive win since the 1980s. 2004 is their only outright popular vote win. Otherwise they get in this weird territory of winning the popular vote but losing the electoral college. And I would personally argue most losses happen simply because they run uninspiring candidates and republicans gain support by default. That said I think democrats are ultimately poised to shift the map more and more in their favor as long as they dont screw it up. But they kind of do. Which is one of the reasons I rip them so bad on this blog. It's embarrassing to lose to republicans in the electoral college, but I digress. 

But yeah, I just wanted to see how my predictions line up with Nate Silver's in this respect. Same results, but with different levels of confidence. It's interesting to see how our two models contrast but have similar conclusions.