President Trump has moved all of his electoral eggs into a new basket.

Now, his efforts to undermine the will of the electorate and seize a second consecutive term in office hinges upon a lawsuit filed by Texas Attorney General Ken Paxton, a lawsuit that essentially argues that Texas is harmed by the election results in four states that flipped from red to blue last month. It is a lawsuit that people with much more legal expertise than myself have dismissed out-of-hand as ridiculous given the legal case being made. But it is also a lawsuit that makes statistical claims that are so bizarre, it falls well within my area of expertise to point out that on that rhetoric alone, it’s a disaster.

The lawsuit’s statistical case comes down to this question: How many zeros will it take for you to be sufficiently impressed that you’ll ignore basic logic? The author of the lawsuit appears to have settled on the number 15.

“The probability of former Vice President Biden winning the popular vote in the four Defendant States — Georgia, Michigan, Pennsylvania, and Wisconsin — independently given President Trump’s early lead in those States as of 3 a.m. on November 4, 2020, is less than one in a quadrillion, or 1 in 1,000,000,000,000,000,” it reads at one point. “For former Vice President Biden to win these four States collectively, the odds of that event happening decrease to less than one in a quadrillion to the fourth power.”

After citing the individual credited for this interesting math, it continues.

“The same less than one in a quadrillion statistical improbability of Mr. Biden winning the popular vote in the four Defendant States — Georgia, Michigan, Pennsylvania, and Wisconsin — independently exists when Mr. Biden’s performance in each of those Defendant States is compared to former Secretary of State Hilary [sic] Clinton’s performance in the 2016 general election and President Trump’s performance in the 2016 and 2020 general elections,” it reads. “Again, the statistical improbability of Mr. Biden winning the popular vote in these four States collectively is 1 in 1,000,000,000,000,000.”

Just complete nonsense.

Let’s start with the second claim. It holds that the odds of President-elect Joe Biden winning Georgia, Michigan, Pennsylvania, and Wisconsin are 1-in-1 quadrillion because ... well, because of [imagine me waving a sparkly magic wand] statistics.

It’s unclear in the lawsuit where this number comes from, particularly since Biden’s improvements over the 2016 Democratic nominee, Hillary Clinton, were fairly modest in those four states. Clinton lost to Trump by about 290,000 votes across the four; Biden won them by about 270,000. That’s a swing of about a third of a percentage point relative to all of the votes cast in 2020. Yes, Biden got more votes than Clinton, averaging about 23 percent more votes across the four states. But Trump added an average of 16 percent more votes.

These were close states, ones that fell into the category of toss-up for at least part of the year. If the odds of Biden winning each were 1-in-2, the odds of winning all four were 1-in-16 (1-in-2 to the fourth power). If, for some reason, we wanted to assume that Biden’s odds in each state were 1-in-1,000, we’re still talking about only 1-in-1 trillion odds of a sweep. But obviously Biden’s odds were far better than that, particularly given that the dynamics of the 2020 race were different than 2016, with a more popular Democratic candidate and a more polarized electorate.

The lawsuit’s first claim is no better.

It asserts that the swing from a Trump lead to a Biden won that occurred in the hours after polls closed was similarly unlikely. It seems to think of vote-counting as being similar to flipping a coin, and that the odds of a large flurry of Biden votes late in the process would be like, say, getting tails 50 times in a row.

But this isn’t how voting works. States aren’t homogeneous entities with one Democrat and one Republican in each square meter of space. Counties aren’t all the same size and don’t all count ballots at the same time. Nor do people all vote at the same time.

All of that came into play last month. Perhaps the best way to show it was in Wisconsin.

Coming into Election Day, we knew a number of things about how voting was likely to unfold in the state.

• We knew that polling showed that people who planned to vote by mail preferred Biden over Trump by about 47 points and that people who planned to vote in person preferred Trump by about 21 points.
• We knew that nearly 2 million votes were cast by mail or in-person absentee.
• And we knew that the process of counting mail votes was subject to two constraints: counting wouldn’t begin until polls opened and that the results of the mail-in vote wouldn’t be announced until all of the mail ballots were counted.

Those are substantial qualifiers! Imagine a heavily Democratic city with a lot of support for Biden where hundreds of thousands of people chose to vote by mail, given the coronavirus pandemic. The effect would be that the first results in the city might show a narrow race or favor Trump, since they included only day-of voters. Then, if the city could only tally a few thousand ballots an hour, it could take some time for the mail ballots to be counted. It would only report its results hours later.

Now imagine that city is called, say, “Milwaukee.”

We’ve been over this particular scenario before. Trump and his allies like to claim that a large surge of votes in the early morning hours in Wisconsin are somehow suspicious. But they aren’t: They’re the final tally of mail ballots in Milwaukee being added to the total. And since Milwaukee is both heavily Democratic and constituted 14 percent of all votes cast in the state, it put Biden over the top.

But, here. Let’s put a fine point on it.

Here’s an interactive which uses the actual results from Wisconsin and the number of absentee ballots cast to simulate vote-counting in the state. We left some variables up to you: how fast mail ballots are counted and how big the split in mail-versus-day-of voting was. We added some randomness to it (including the pace of day-of ballot-counting) and rounding means that the final numbers won’t land exactly where the vote totals in the state did, but you’ll get the point.

Mail ballot counting speed: Normal
Mail/in-person split: 20 points

Unless you set the absentee count to be instantaneous, at some point the votes from Milwaukee and Dane counties will suddenly pop up, giving Biden a big vote advantage. Just as they did on the night of the election. The interactive is inelegant, yes, but it mirrors the actual results in that specific way.

The other states had other rules that guided their vote-counting, but similar dynamics were at play. Places with lots of people had lots of mail ballots and those ballots couldn’t be counted until Election Day itself. That meant a slow shift to the vote totals — a shift that was both predictable and predicted. There were about 19,000 mentions of “blue shift” in the month before the election, according to Google, a function of the media explaining that results would shift to benefit Biden given the density of his support among voters planning to vote by mail. The odds were not only 1-in-1 quadrillion that this would happen, they were 1-in-1.

Paxton’s lawsuit fails in other ways, such as its insistence that there is utility to the sheafs of affidavits obtained by the Trump campaign, none of which have been proved to show any credible evidence of fraud and a large portion of which have already been rejected by the courts. It’s a dubious effort, though one which will endear him to Trump — a potentially useful alliance for Paxton to build.

If this suit is Trump’s last, best hope to eke out a victory from his 2020 defeat — in a tweet, Trump called it “the big one” — it seems clear where this is all headed: To Joe Biden being sworn in as president on Jan. 20, 2021.

Update: A reader found the actual analysis cited by Paxton. It’s from a gentleman named Charles J. Cicchetti who lives in California.

Here’s how he describes his effort in the document:

“I compared and tested the significance of the change in tabulated ballots earlier in the reporting to subsequent tabulations. For both comparisons I determined the likelihood that the samples of the outcomes for the two Democrat candidates and two tabulation periods were similar and randomly drawn from the same population.”

He determined, in other words, the likelihood that the votes tallied earlier — day-of voteswere similar to and randomly drawn from the same pool as votes tallied later — mail-in ballots. Looking specifically at Georgia, he notes that “the reported tabulations in the early and subsequent periods could not remotely plausibly be random samples from the same population of all Georgia ballots tabulated.”

Yeah. They aren't.

At another point, again discussing Georgia, he marvels that “the increase of Biden over Clinton is statistically incredible if the outcomes were based on similar populations of voters supporting the two Democrat candidates.” Well, what if Biden is a more popular candidate than Clinton? What then?

Cicchetti’s analysis is based on assumptions that are obviously incorrect and should be treated accordingly.