Why do Biden's votes not follow Benford's Law?

My book is cheap at Waterstones and signed at Maths Gear:

Check out Steve Mould's Numberphile video about Benford's Law.

Buy a signed copy of "How Many Socks Make a Pair?" by Rob Eastaway.

There’s more on Mark Nigrini’s work here:

"Benford's Law and the Detection of Election Fraud" 2011 paper.

And here is a paper by the same author specifically about the 2020 US election results:

Get your Chicago Board of Election Commissioners data here!

Yep, 2069 precincts. Some would say that's too many.

If you must, here are links to people using Benford's Law to suggest the Biden votes were fraudulent. Please do no harass or brigade anyone.

CORRECTIONS
- Hello loyal viewer. If you are reading this you most likely regularly watch my videos and know that I put corrections here. But the comment section on this video has been, to put it lightly, "wild". I don't think anyone is checking the corrections here! So I'm going to break with tradition and put the corrections in a pinned comment. But in short:
- I should have said I used the Chicago data (instead of a swing state, let's say) because that is what people claiming election fraud were using. I didn't pick it myself to make a point.
- Foolishly I cut a bit of the video where I talk about how Trump's data is also a bad Benford fit but that massive spike of 1s makes it look like a good match. Check out how low 3, 4 and 5 are.
- There has been specific criticism of aspects of that paper I read from, but only the usual back-and-forth of academics. Everyone agrees with the idea that Benford is not a magic tool to detect election fraud (nor is any statistical tool really; they all require careful interpretation).
- As always, let me know if you spot any other mistakes.

Thanks to my Patreon supporters who mean I can spend TWO DAYS trawling through election stats and making plots. I'm meant to be writing a new book you know. So, thanks a lot.

As always: thanks to Jane Street who support my channel. They're amazing.

Filming and editing by Matt Parker
Music by Howard Carter
Design by Simon Wright and Adam Robinson

MATT PARKER: Stand-up Mathematician

[berserkerciaran]

Not to get political, but what the hell is a number?

[deept]

If you write the numbers in binary, apparently almost all the numbers start with a 1

[Eloquence]

Im sure the comments will be all perfectly reasonable and coherent discussion on the complete video.

[claireumstead]

I love how you pointed out the importance of context in interpreting data! It's so often overlooked.

[Yiazamat]

The way I see it, these things are like metal detectors. They're great at finding points of interest, but you have to start digging to see if it's a coin or a bottlecap.

[SehnsuchtYT]

Let's look at the comments section to see what the experts think

[tomseiple]

Fellow data geek here, this was a TEXTBOOK example of how an analyst approaches their work. Bravo, well done!

[MatthewLiuCube]

1:58 Let's not get distracted that there are 1000π counties in the US

[Cscuile]

Getting some insight behind the votes from a mathematician is refreshing.

[forgetfulHaWk]

They need to start bringing out maths experts on election coverage, its not like they don't have huge amounts of time.

[wj]

The takeaway: if you discover an anomoly, you actually have to investigate the source of said anomoly before you can accurately say you know its cause.

[ericpenrose]

These kinds of misunderstandings are, I think, a subset of a larger problem of people getting 'evidence' confused with 'indicators.' One is often the other, but not necessarily so. The indicator should cause you to look closer, but if you look closer and find no evidence you shouldn't continue to tout the indicator.

[ButzPunk]

"AND ELECT ION DATA"
To be honest, if there were someone named "Ion Data" running for any position, I'd be very tempted to elect them based on the name alone.

[Chaos]

More people need to understand how statistics can mislead you, and how misleading people can make statistics lie to you

[xcvwarmane]

Compared to Bidens normal distribution, Trumps vote counts are best described by a Poisson distribution, which is a pretty sophistacated roundabout way of saying, that Trump just ain't popular in Chigago.

[nmd]

I really like that you compared side by side the digit pairs of pi with the last two digits of Biden votes. A very clever way to impartially show the expected variation at that sample size. Without that comparison, people surely would be looking for patterns in the noise, which as we know is a dangerous thing.

[rokevh]

This guy's agenda is nothing political: he's peddling his fantastic book!

[ForensicAnalytics]

Thanks for mentioning my name and my work starting at 3:56 :) I did an analysis of the Maricopa County election results and got pretty much the same patterns. Here's an interesting tidbit... At 2:00 you talk about the populations of the 3, 141 counties and Benford's Law. At 13:25 you talk about the digits in pi, .... and, of, course, the first four digits of pi are 3141 :) You went full circle or 2πr.

[rugbychampion]

Guy makes complex statistical analysis look like algebra for beginners

[justfrankjustdank]

the only thing i really learned was use a random number gen for filing false tax returns :)