THREAD: I've been reading about Texas' #SCOTUS filing to overturn the election results in PA, MI, WI, GA. The suit claims there was a "one-in-a-quadrillion" chance Biden could possibly have won even one of these states.

I decided to look into how they arrived at that figure. 1/
On the face of it this figure seems absurd, but even so there are Trump supporters who look at it as statistical proof Biden could not have won fairly. 2/
Luckily if you look in the appendix of the Texas filing you can find where their expert witness (A USC Econ professor) showed his work: 3/
I can translate:
"I tested the hypothesis..." = I wanted to know if the pool of Democratic voters in 2020 was identical to the pool of Democratic voters in 2016, after adjusting for turnout (hot tip: of course it wasn't) 4/
translation (continued):
"I estimate the variance by..." = Well, it is pointless to estimate the variance in this analysis. But here the witness is basically claiming here that voting is a random process with each vote having a certain *uncorrelated* D/R probability. Uh...no 5/
To understand what *uncorrelated* means, imagine there is an infinite pool of voters with a known ratio of D/R, and holding an election is equivalent to randomly selecting a few million voters from this pool.

It does not work that way, obviously. 6/
Alternatively, you can imagine that each voter is a person who randomly choses who to vote for, and has a certain probability of choosing D or R. Lets say, by flipping a weighted coin.

Again...no

7/
Translation (cont):
"I use the Z-score to obtain to p-value..." = I found out how likely it would be for the same group of random voters -- flipping the same weighted coins they used for Clinton (who lost) -- to elect Biden by an equal or greater margin than they just did. 8/
In other words, if we re-ran the 2016 election again *In 2016* how likely would it have been for Clinton to have suddenly won PA by 1.2% instead of losing it by 0.7%?

Not likely! 9/
So, a few major flaws:
1. Voting is not an random process. Everyone decides who they will vote for months if not years ahead of time. It is absurd to model it this way.

10/
2. Votes are not uncorrelated. If one person in a state swings their vote to D, others likely will too.

Also since there are a finite number of voters, with fixed ratio of R/D, then if the early vote leans R, the late vote will lean D. This is another way votes correlate. 11/
3. The one-in-a-quadrillion figure is not even the odds that Biden could have won. *It is the odds he could have won with Clinton's constituency*.

12/
If your argument was "I'll bet Biden didn't win over a single person that wasn't already a Clinton supporter" you could maybe point to these 1-in-a-quadrillion odds. Maybe by chance millions of those supporters got sick or missed the bus in 2016 and not 2020 13/
But he did win over new people. That is why he won. If he had not done so, he indeed would have had a very small chance of winning by the margin he did. I wouldn't say 1-in-a-quadrillion b/c of the other fallacies I mentioned. 14/
That being said, I put the odds of the Texas v Pennsylvania #SCOTUS decision coming down in Texas' favor at one in a magical unicorn wish. 15/
Hopefully the few people that read this will be reassured that the maniacs attacking our democracy, though they may have fancy degrees, are truly awful at statistics.

Please retweet. 16/
PS: I've noticed a *lot* of people are incorrectly explaining this figure as "The odds of Biden winning given Trump's early lead" -- As I've explained the figure has nothing to do with early/late votes. It is the odds of a counterfactual Clinton landslide https://twitter.com/thejimjams/status/1336439528404369408?s=20
PPS: Here is a link to the filing in case you want to check my math:
https://www.supremecourt.gov/DocketPDF/22/22O155/163048/20201208132827887_TX-v-State-ExpedMot%202020-12-07%20FINAL.pdf
I just found this tweet which just about sums it up better than I could have done: https://twitter.com/markcc/status/1336415410011377668?s=21 https://twitter.com/MarkCC/status/1336415410011377668
PPPS: @PressSec has now gone on TV saying the odds of Biden winning all four states is 1-in-a-quadriilion-to-the-4th-power. This is would only be true if states were not correlated (ie if a Biden win in MI did not generally improve his odds of winning WI and PA)
Which is absurd of course — if you win one blue wall state by a lot then odds-makers would give you a good chance of winning the others too.
If you want to check his math you can find the z-score using this free excel worksheet: https://vwo.com/blog/ab-test-duration-calculator/ like I did here. Note that I got a much lower z-score (90) than Cicchetti did BECAUSE HE FORGOT TO ADJUST FOR TURNOUT.
In conclusion: https://twitter.com/trevir3/status/1336598056809205760?s=20
Here is a link to a thread explaining how to do conduct your own GOP election fraud analysis using a free online tool: https://twitter.com/usbtypewriter/status/1336860578204295170?s=20
You can follow @usbtypewriter.
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