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Number 1 and Benford's Law - Numberphile

815 736 views | 20 Jan. 2013

Why number 1 is the

Why number 1 is the "leading digit" more often than you may expect?

More links & stuff in full description below ↓↓↓

See us test the law using Brady's YouTube viewing figures at: http://youtu.be/VbtNy54ya9A

Blog about all this at: http://bit.ly/benfordslaw

Brown Paper from this video on ebay: http://bit.ly/brownpapers

This video features Steve Mould: http://www.stevemould.com/ and http://twitter.com/moulds


Website: http://www.numberphile.com/

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Tons of people here using this to try and confirm Democrat voter fraud. While Benford's law can detect some forms of fraud and on the surface seems applicable to the election, Standupmaths has a great video explaining why it is problematic to imply voter fraud specifically based on Benford's Law

Tony Chintz

Why when I type "benfords la" into the youtube search bar does it not auto fill to find "benfords law" for me? Weird. Must be an error in youtube algorithims.....


Who’s here because Tim Pool said something about this?

Cy2k Cy2k

Just wondering - is the cameraman having a seizure or something ? It's really hard to watch the shakycam!

H. H.

5:37 ?


Who's here from "Why do Biden's votes not follow Benford's Law?" video?

Erik Knudsen

This video is about to be banned by the communist regime of youtube.

j.kenneth fraac

get some sleep steve mould

Jocelyn Freeze

Ironic, posted Jan 20


Here before mathematics is cancelled for spreading disinformation.

Rizzo 919

There is no system of outcome. If you flip a coin and it lands on tales 5 times in a row, the chance of it landing on heads is still 50 percent. You cannot will a result with probabilities.
Sorry ; )


Trump 2020: Interesting

H Acc

The odds benfords law is broken decreases the higher the numbers. 74,000,000 biden votes would suggest that it looks shady. Benfords law doesn't apply 100% of the time but it sure requires investigation.

Holy Crap Thats A Lot of Ketchup

imagine being the guy that figured this out, must of have so much free time


What age and demographic (employed, in school, retired, unemployed, etc?) are most youtuber commenters I wonder. There seems to be a disproportional Trump lean. Is it kids? Judging by comments, there seems to be lots of kids. Elders? Unemployed bloke?

kevin a

Despite all the recent talk online it doesn't look like Benford's law really proves fraud in the 2020 election.. as Matt Parker explained in his new video, voting precincts are basically designed to have similar population sizes, i.e. the data won't span multiple orders of magnitude so Benford's Law shouldn't really apply

Mark Miller

We need you to testify before congress sir.?

Steven Jones

Most intuitive way to think about it for me is that the ten 9s of the 90s are glued to one hundred 1s of the 100s, the one hundred 9s of the 900s are glued to one thousand 1s of the 1000s, etc. So the 9s are always linking arms with 1s that are ten times as many.

Kai R.

WTF is going on here? Numberphile used to attract intelligent people mostly and now I see "fraud" and "Trump" in most of the comments? Usually you don't care about science at all, why now all of a sudden? It doesn't even apply to the election numbers at all...
Guess you take every straw that you can, even if you don't understand a thing.

A fine addition to my collection


Yuki Hotta

It makes sense once it's explained


I don’t find this surprising at all.

Phillip Mosness

Likes and dislikes both start with "1".

Jakub Skowron

Wow, why this video looks like it was filmed in the late 90's, early 2000's?


I see all the mathematically illiterate idiots came to post "muh voter fraud" comments.

Richard Wicks

Everybody enjoying the latest US coup attempt?

ItzThe Poyratz

See you in 2024!!!

Justice Sportsman

Seeing this video for a second time makes me feel old. 7 years ago didn't feel that log ago, the video quality says differently.


So if you applied this law to...ooh, I don’t know, *the US election*, I wonder would it would show... ???

Hemant NavKumar

It is High time that Benford's law should be part of school curriculum across the globe..!

Ned Kelly

Democrats obviously didn't watch this.

Alan Forster

The algorithm led me to this video... interesting how stand up maths is trying to explain why should ignore this for Biden's vote count.

Strangely Brown

I’ve watched Numberphile once and there is a diminishing chance of me watching more... :-)

Ghazanfar Ali

Nice video

percy de vries

So biden. Explain


Wow Steve Mould


Probability of a second term: 100%


It has been fun watching trumpists go at great lengths to obtain their copium.

Ze Rubenator

Gotta love the droves of morons that have taken over the comment section with their "hurr durr Biden fraud," yet I'm willing to bet not a single one of them actually watched the video, understand the math or know how it does and does not apply to detecting election fraud. Not a single mathematician or statistician worth their salt would claim that Benford's law on its own can be used to detect election fraud, including Steve Mould who features in this video.

Byron Watkins

You neglected to point out that the base of the logarithm that you use MUST MATCH the base of the number system used for counting... If we count in base ten, then we MUST use the base ten logarithm and if we count in binary, then we MUST use the base two logarithm, etc.

Tabby Lorentz

If you're here because you've listened to Radiolab, then you'll enjoy Secretly Incredibly Fascinating - Random Numbers.


I wasn't running into this with my Minecraft ender pearl testing experiment where at numbers 4, 9, 6, and 8 (rarely 8) after over 800 test, I ran into this repeating result. 1 NEVER came up. Is this normal? Did I not run enough tests? 1 didn't come up at all. Even the ratio of dropping ender pearl percentage I ran across was 4%!!! 4 is not 1, again am I just doing something wrong?


Here to read comments by Libtards furiously trying to debunk mathematics as a conspiracy theory.

Stadler Planck

So many republican tears, it brings me such life. Idiots.

Darth KEK

Seven years later: "but obviously this doesn't apply to election fraud"


Democrat thugs don't follow science.

Mobius Trip

Why did this obscure video pop up?


Incoming coping republicans feebly attempting to falsely apply this law to their fantastic voter fraud claims.


Once again people are incabable of understanding math and think this supports the idea of an election fraud when in fact it debunks it completely

John Swiecki

That’s just the craziest thing I’ve ever heard. I’m really having a little trouble getting over it.


Why is every second comment about politics? It’s a math video. Please stop.

Aonoymous Andy

Isn't it sad that a party like the democRATS is so rotten that they have to commit voter fraud to win elections? No It's pathetic!

Philip Dennis

President XI and the CCP already have in hand a preliminary analysis they will finalize and present to Biden at their first meeting as he explains the meaning of the word "IMPOSTER".

Matt C

7:18 "It's a clue that you MIGHT be cheating". This part is key and what a lot of folks on here claiming that Benford's Law is "PROOF" that Biden cheated fail to understand. There is a whole slew of other reasons why applying Benford's law to our recent election results is faulty. The simple fact is that Benford's Law alone does not prove anything.

BS DaoKee

Biden forced me to learn Benford's law

Andrew Baxter

I just spotted the number 1 in the title frame of "Benford's 1aw" - triggered


Decimal system makes this law valid.

Viktor B

Q of love

Natan Sandle

2:03 and 2:30 to all my overnight mathematicians.
The reason those graphs of Biden votes don't follow Benford's law is because all the data points are on the same order of magnitude.
98.7% of the precincts in Chicago had a vote total between 100 and 1000
The bar graph shows that the highest share of precincts had 300 + something votes for Biden
Absolutely not proof of fraud

Same goes for all the other areas where these discrepancies could be found.
Precincts (or whatever divisions they have for voting) are purposefully made to be similar in population

Varun Negi

Kamla is a fraud

Massimo Zanetti

That book with all numbered tickets... tear one ticket off and... book is useless for later use :D

YouTube Censors

Wikipedia's entry for Benford's Law had a whole section about how it's reliably used to detect election fraud. Until last week, when that passage was suddenly deleted. Last week... We're in 1984 people.

El Bicho

Thanks for explaining how the Democrats tried to steal the 2020 elections.

Nikita Kucherov

This is just awesome!

David Jackson

What do you think about using Benford's Law to look for signs of Covi19 numbers "being cooked"?


3:12 Why is Biden There?
Not a Coincidence.


in this comment section: people who first heard of benford's law because they were told it was "proof" that their cult leader is infallible

Sen Perez

Cool! I'm in the minority that thought this was common sense

Jason Song

I beg you to take a look at the judicial audit of the Voting machines in Antrim County.

Deepanker Joshi

why do i see a 10 written on right side of his forehead. have i become so much numberphile.


YouTube 2020 algorithm: "this is important for you to know after the election."

Chad Sanborn

So a distribution of votes should follow Benfords Law as well and when it doesn't, its an indicator of cheating .. like on taxes



Muttakin Mufti

Here from Matt

RJ Bush

Rename it Biden’s paradox


2:04 So, if for instance Biden received roughly similar sized votes from every county in Chicago, then Benford's Law doesn't tell you anything.

Ryland Chase

Just to be clear for everyone who doesn't understand the law properly. This law only works when you data is over many different orders of magnitude. Because precincts are all relatively the same size, it does not apply.

The Outsider

Message to all conservitards:

Benford's Law applies very poorly to elections and no election in history has ever followed Benford's Law cleanly. Typical conservatives completely misunderstanding math and science, what a shock.

Phil Lee

Who’s this guy doing explanation?


And fk Biden I guess.

Elementalism :D

So can anyone explain to me how these numbers "prove" biden was cheating?

Because this video seems to suggest to me quiet the opposite.

Meu Nome

Trump winning in 2016, also didn't follow benford's law

UEG Productions

Im only here because I'm supposed to explain why the number 1 is so common.

Doctor Pepe

Nice this proves voter fraud & biden rigged the election

Jonathan Kierkegaard

Did you see they edited Wikipedia regarding Benford's Law, saying it's misleading and wrong? Because of the election. What do you make of that?

Joel Ross

Can you apply it to base2 ?


Biden goofed a few million votes. Oops


For the election data gathered by county, you have to realize that most counties are cut up into roughly equally populated zones. So immediately that's problematic for Benford's law, because you need a very wide distribution of numbers, and counties are PURPOSEFULLY made to be roughly equal in population size.

The election returns for Biden by county weren't orders of magnitudes different from each other, they're within 100-1000. A wider distribution is REQUIRED to trigger Benford's Law. Keep in mind, the law only works, because "leading 1s" return every time you hit a new order of magnitude. It was not triggered for Biden because his performance was consistently within a single order of magnitude. Since this condition is not satisfied, you have to look at the last digit of the county returns, which should be evenly distributed 1-9, and indeed they are for Biden.

Donald Trump's returns do follow Benford's law, because his range of performance was larger by county–10s-1000s–spanning two orders of magnitude. This is why his results DO satisfy Benford's law.

EDIT: I said counties when I meant districts

Scott R. Hardie

This s a handsome guy


! The math is disputed

Ghazanfar Ali

Wtf, i can't understand the full context

Possibility of 1 maximum in leading digits, is that all or something else also.

Tell me please !!!

Aonoymous Andy

Trump's voter data follows benfords law, but Biden's data does not, therefore biden committed voter fraud and he should be arrested

Peter Bollen

To all those people thinking this video proves election fraud: this video only explains the law. It says nothing about its power to prove election fraud. All mathematical experts have already debunked that this law is applicable to the elections the way lots of republicans are trying to claim. Go check out the recent podcast Radiolab (an excellent scientific podcast) to understand why this law can not be used in this case. They even explain to you how the law should be used (on the second digit, not the leading digit!) and then come to the conclusion that there was no irregularity at all, that the results actually follow the predictions made by Benford's law. It's only 30 minutes of your time to understand how it really works. Better than just repeating whatever uninformed people tell you. There are more expert mathematicians in YouTube explaining why the results don't follow the law. Go find them.


Here because of the election and Biden’s votes not following the law

Matthew Meyers

very interesting.

Ghl Scitel

Benford's law is in a similar way a law like Moore's law or Murphy's law.
All 3 are not laws but RULES depending on certain boundary conditions.
Therefore, the use on voting systems is error prone and lead to fallacious results.


7:45 THANK YOU for this explanation! It makes so much sense when you think about it that way

Give me Marw

Maybe someone could clarify why this would highlight tax/account fraud? I would've thought a business or a person wouldn't have daily/weekly/monthly/yearly intake or returns of several magnitudes so according to this information, we wouldn't expect it to follow Bedford's law. Do auditors look at something else (such as the log of the data) or is there a bit of information I am missing?

Rick Medina

"You don't hang around the 9's" seems to be the best explanation to me


For things growing exponentially, like population, going from “1” to “2” takes log10(2) time, which is 0.3.