The "Book-Cooking" Index Soars To All Time Highs

Tyler Durden's picture

Everyone has heard of the Big Mac Index, the Misery Index, even the Shoe Thrower Index. But the Book Cooking Index? This latest addition to the compendium of oddly named yet extremely fascinating "indices" is based around the statistical irregularity known as Benford's law, according to which within sets of numbers that span orders of magnitude, the distribution of first digits is strikingly regular: numbers beginning in 1 occur about 30% of the time, those beginning in 2 about 18% of the time, falling to roughly 5% of the time for the number 9. Specifically, as noted by the keenly observant Jialan Wang of Washington University in St. Louis, "there are more numbers in the universe that begin with the digit 1 than 2, or 3, or 4, or 5, or 6, or 7, or 8, or 9.  And more numbers that begin with 2 than 3, or 4, and so on.  This relationship holds for the lengths of rivers, the populations of cities, molecular weights of chemicals, and any number of other categories." The most curious application of this law resides in the field of corporate fraud, "because deviations from the law can indicate that a company's books have been manipulated." Here is where things get interesting for fraudulent corporate America: the inquisitive Wang "downloaded quarterly accounting data for all firms in Compustat, the most widely-used dataset in corporate finance that contains data on over 20,000 firms from SEC filings" and "used a standard set of 43 variables that comprise the basic components of corporate balance sheets and income statements." Her results were, in a word, startling.

As she observes, "here are the distribution of first digits vs. Benford's law's prediction for total assets and total revenues."

In other words, corporate numbers behaving precisely as predicted by a purely statistical law!

But here is where it gets truly strange. In her words, "Deviations from Benford's law have increased substantially over time, such that today the empirical distribution of each digit is about 3 percentage points off from what Benford's law would predict.  The deviation increased sharply between 1982-1986 before leveling off, then zoomed up again from 1998 to 2002.  Notably, the deviation from Benford dropped off very slightly in 2003-2004 after the enactment of Sarbanes-Oxley accounting reform act in 2002, but this was very tiny and the deviation resumed its increase up to an all-time peak in 2009."

Said otherwise, the chronological change in this parameter allows some starting conclusions. As the Economist notes, "This regularity has been used to identify cases of fraud in public documents. Someone cooking books is likely to choose numbers somewhat randomly, generating a distribution of digits far more uniform than Benford's law would predict. Any divergence that shows up sets off alarm bells in those looking for funny business."

Visually presented, it looks as follows:

Yes, book-cooking, in the purest statistical "correlation does not imply causation" has hit an all time high! Granted we doubt any regulator, least of all the corrupt criminal SEC, whose own Benford's law chart would look like a lie detector test hooked up to Jamie Dimon during a conference all, would admit this evidence in a court of law, but deluded investors who believe that corporation are being always truthful with data and reporting should probably be aware that that is certainly not the case. Per the Economist: "As Ms Wang notes, this isn't decisive proof of misbehaviour. It is suggestive, however, of the possibility that systematic number-fudging has been on the upswing in recent decades. Moreover, it's an excellent use of clever statistical analysis to provide a new perspective on an economic question."

Considering the surge in white collar criminality over the past 3 decades, especially among financial firms, and the fact that this "index" is now at all time highs, we would hardly be as politically correct about the issue as the Economist.

But that's us.

As for next steps, "What types of firms, and what kind of executives drive the greatest deviations from Benford's law?  Does this measure do well in predicting known instances of fraud?  How much of these deviations are driven by government deregulation, changes in accounting standards, and traditional measures of corporate governance?" All these are fascinating questions that Wang will answer in the immediate future and we will advise readers when she does.

For now, the take home message is this: if it appears that "they" are lying to you, "they" probably are. Just run a numerical regression analysis to prove it.

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Josh Randall's picture

Sauteed books B!tchez!

Oracle of Kypseli's picture

In other news, gold is hovering around $1666/oz. Is someone telling us we control everything? don't dare buy? the devil is in control?

Your thoughts!

Arkadaba's picture

He he - I have no idea which way metals and certain currencies are going. There are just too many variables in the game right now. 

tekhneek's picture

I see two immmediate variables:

Paper and Money.

I'll take Money for $1 trillion Trebek.

Unprepared's picture

The researcher is wrong.

This is nothing other than 'only $-.99' pricing strategy applied to corporate paper sales.

Happy Chrismess.

Ahmeexnal's picture

Time to analyze the blowjob index?

Cynical Sidney's picture

wang heh, i just can't get behind wang's fraud index; "limitations of Benford's law: it can only be applied to data that are distributed across multiple orders of magnitude." there's your problem right there, for example hardly anyone or anything can go beyond the 100 billion dollar threshold, a fact which diminishes the prevalence of 100,000,000,000. desirdavenir cite ur sources plz

i have my doubts at this moment; but maybe it is true, maybe it's telling us there are more off-balance shells than ever before; i'd have to check with a biostatistician.

Storch's picture

There arent more numbers that start w 1, they just come earlier when counting something so you are more likely to stop on them when counting. There are more MEASURMENTS in yhis universe that start w 1. That is a scary important distinction that wang needs to be semantically correct about. I can assure you i can prove there are just as many numbers that start w 9 if you never stop counting.

AbelCatalyst's picture

Are you saying this may be more of an inflation indicator? Does it indicate that the numbers in the sample set are increasing over time? That would seem to make sense.... If it actually tracked fraud I think it would have more of a hockey stick look to it - begin moderately then shoot to the moon the past 10 years...

Raymond K Hessel's picture

This is a statistical law, not real number theory, so you are mixing apples and oranges.


I have never been introduced to Benford's law before this so I would do research into it.  From what I've seen thus far on Wikipedia, it seems plausible.  As with any encylcopedia, that would be a jumping off point for research, not the final read.


If it works, I would guess this is how the SEC uses these anomalies in trading data to find insider trading, porn-surfing permitting.

mediaprizm's picture

In a perfect world all of us would could spend hours meandering around the local farmers' market, hand-selecting ingredients for a gorgeous meal. Then we'd leisurely make our way back to our well appointed kitchens to prepare said meal, giving no thought to time constraints.Tecfrigo - Mercatus

desirdavenir's picture

the Benford laws also applies well to prices in a supermarket. This is odd, but true. Also, funnily, it applies also when you convert the prices in another money (e.g., Franc to Euro)... One can find a mathematical justification for it (using a natural measure on numbers which is not a probability distribution), but the fact that this justification is correct is odd...

Taint Boil's picture



Well ‘Smear my ears with jam and tie me to an ant hill’ now I have heard everything. Very, very interesting and probably spot on.

11b40's picture

''s just 19.99 turned updide down.  Inflation drove that 9.99 pizza all the way to 19.99

Hearst's picture

Couple years ago Gold hovered at $666 for a few.  I wouldn't worry because now it's a larger and more appreciated number.  As for the devil?  Read Matthew 4 starting at verse 8 to understand that the devil is the house and all the world gambles at his tables.  All it took was for the most righteous Man ever to put the devil in his place.  

Strike Back's picture

Yeah, uh, I got it off of reddit.

IQ 101's picture

"If you do not have a sword,sell your robes and get one"

Where did I read that?

Hephasteus's picture

So you're saying your reading an instruction manual that's 2000 years old and never worked?

God is evil. Not regular evil. Lawful evil. He lives as lawful evil but dies as chaotic stupid.

Mentaliusanything's picture


Hope the moon stays where its been for a millennia

Hope the tide rises to meet you exactly as planned

Hope the Sun rises just where it has, at the time it has for......  ever

Hope season show you who is in control

Hope the stars that have stood since man could looked up from the ground continue to shine and show us our insignificance.

Hope that you understand that the existence of something very stationary and very powerful is evident in nature.

Be wise and Fear what a man and his mind cannot contain. 

Spoken by someone who was like you... and much like Paul of Tarsus

Apologies to the others but it deserved a recant based of visual undeniable facts.

Now back to Guns Gold Grub and a little Banker Hatin 


Josh Randall's picture

I wouldn't doubt it - all these Power Brokers are into numerology, symbolism, and intimidation. The biggest gag of all is a Presidential candidate named Cain (as opposed to Abel) with a 666...errr..999 plan whom was a Director of the Fed (the most wicked entity there is) --- if people can't wake the hell up and see that these aren't coincidences, then they derseve what they get.


scatterbrains's picture

11/11/11 bitches with a full moon passing on the evening of the 10th.

Lord Blankcheck's picture

Gold is the Anti-Dollar not the Anti-Christ

jus_lite_reading's picture

The amount of cooking going on in the home building industry (especially with Troll Bros) would make Rachel Ray jealous...


Game over!


And Happy Kwanaza BITCHES!!! I am BAAAACK!!

Finance Addict's picture

Yes, excellent work by Jialang. We noticed it here earlier today on Finance Addict, as well:

decon's picture

I'd be willing to bet that some categories of financial data would not conform to Benfords distribution.  An example would be an analysis of item pricing data.  The most common numeral used in pricing is "9".

CrazyCooter's picture

I think you are correct (not that I have any omnipotence about such things). On that note, I would observe it doesn't explain the multi-decade trend.




SelfGov's picture

I bet it would look fudged beyond belief which prices almost always are.

zhandax's picture

As I understand it, Benford's distribution predicts how often a number begins with a particular digit.  Although 9 seems most common in pricing, it is also most commonly used in the last digits.

desirdavenir's picture

Benford's law is on the first digit

CompassionateFascist's picture

The smallish (7 employees, 30 indep contractors) Co. I work with is "solvent"....provided you don't count the $100,000 maxed-out corporate credit card. As to where that money went, don't ask. There hasn't been an audit in many years...just like the Fed/Fort Knox.

alien-IQ's picture

sounds like a pink sheet about to go on a 50,000% run.

arm50's picture

Would love to see the distribution of our Govt supplied numbers

CrazyCooter's picture

Just wait til they are all "zero" ... that will do a number on that chart!



alien-IQ's picture

I'm gonna need a bigger calculator....

Caggge's picture

Original movie: Wall Street reams main street with their wangs.

Sequel : The Wang strikes back

maxw3st's picture

Nice to see there is statistical evidence backing something I strongly suspected when reviewing corporate financials. I spent several years as a broker and did a lot of 10Q reading. It ultimately led to my exiting the business as it became obvious it was a rigged game. Rigged against the small investors I was supposed to be serving that is.

Belarus's picture

Broker's reading 10Q's? I thought brokers just sold the the lipstick on the pigs?

maxw3st's picture

Any body for checking GOP campaign financing?

CompassionateFascist's picture

Prolly a lot like Democrat campaign finance. Check out Solyndra, you stupid f^^^k.

Caggge's picture

For that matter, when Hillary ran up her campaign bills, I think she was bailed out by the DNC. Living within a persons means should start at the top.

Belarus's picture

I wonder how badly the Fed's balance sheet has been book cooked? I'm guessing it has been fairly well fried since a couple doofus' we all know well took the chairman's seat.