[HN Gopher] Using Benford's Law to Detect Bitcoin Manipulation
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       Using Benford's Law to Detect Bitcoin Manipulation
        
       Author : luu
       Score  : 126 points
       Date   : 2021-07-25 08:46 UTC (14 hours ago)
        
 (HTM) web link (statmodeling.stat.columbia.edu)
 (TXT) w3m dump (statmodeling.stat.columbia.edu)
        
       | mrfredward wrote:
       | Benfords law is used to find evidence that the numbers came from
       | a person, not a measurement or mathematical process, right? So
       | anyone who knows what a limit order is should not be surprised to
       | find evidence that humans are involved in picking the prices,
       | right?
       | 
       | It should be obvious that violating Benfords law isn't evidence
       | of fraud or manipulation or even fomo, just evidence that the
       | price is impacted by the people typing in the orders having to
       | pick what number to type in.
       | 
       | Edit: I've softened the language in my comment a bit, but I stand
       | by the fact that this only shows humans are affecting prices,
       | this analysis can't distinguish between fraud and psychological
       | effects around "key" prices, like $10,000.
        
         | UncleMeat wrote:
         | Benfords law is a perfect example of something that is cool and
         | compelling and then gets applied inappropriately all over the
         | place by people who don't know better. Voting, for example.
        
           | abaga129 wrote:
           | Or by people who do know better and have malicious intent.
        
         | [deleted]
        
         | iratewizard wrote:
         | This is exactly it. If you look at price changes as bitcoin
         | approaches round numbers, you can see that a significant number
         | of people have their limit price set to something like $10,000.
         | When it would approach those round numbers, it would be stuck
         | just under that number for a while. If the price cracked the
         | round number, meaning all those limits got sold, the price
         | would then slingshot much higher.
        
         | JumpCrisscross wrote:
         | > _If the author had spent 5 seconds thinking about how markets
         | work_
         | 
         | The author has spent a career thinking about this, and has
         | written a good fraction of the textbooks on statistics in
         | market contexts.
        
           | mrfredward wrote:
           | I guess we need to make a distinction between the blog post
           | and the Gary Smith post it links to here.
           | 
           | Gary smith (the person I think you're referring to having
           | spent a career in this) says this:
           | 
           | >The market manipulation, the irrational price gyrations, and
           | the enthusiasm of so many investors for investing in bitcoin
           | (and other cryptocurrencies) is ample evidence that market
           | prices are not invariably equal to intrinsic values.
           | 
           | I entirely agree. A perfectly efficient market should follow
           | Benford's law given enough data.
           | 
           | It's the blog post by Andrew that I think totally misses the
           | point. He leaps from inefficiency which could be market
           | manipulation to this:
           | 
           | >I saw this and I was like, well, yeah, isn't all bitcoin use
           | either crime or manipulation? But then I realized, no, that's
           | not all of it. Some bitcoin playas are motivated by politics,
           | some by fomo, some are doing anti-virtue signaling...
           | 
           | And never considers the fact that the world is full of people
           | who feel very different paying $100.00 vs $99.99
        
             | JumpCrisscross wrote:
             | > _the world is full of people who feel very different
             | paying $100.00 vs $99.99_
             | 
             | Agree, though that effect is not constrained to Bitcoin.
             | Retail orders, for instance, follow Benford's law. This is
             | despite well-documented psychological biases towards _e.g._
             | certain digits, whole numbers, round numbers, _et cetera_
             | [1]. Benford 's law [2] derives from deeper mechanics.
             | 
             | As you point out, however, a better control would have been
             | _not_ all prices in public stocks, but retail orders.
             | 
             | [1] https://mro.massey.ac.nz/bitstream/handle/10179/2695/02
             | _whol...
             | 
             | [2] https://en.wikipedia.org/wiki/Benford's_law#Krieger-
             | Kafri_en...
        
               | mrfredward wrote:
               | Liquid retail stocks follow Benford's law because there
               | is a notion of intrinsic value from the company and an
               | army of quant traders trying to exploit any price
               | inefficiency caused by the retail traders.
               | 
               | With cryptocurrency, the market is less mature and the
               | intrinsic value largely comes from people believing in
               | its value. So really, it would be surprising if we didn't
               | see some Benford's law anomalies associated with people
               | picking numbers.
               | 
               | Anyway, thanks for the discussion; the links above have
               | given me stuff to chew on and calmed the red mist after I
               | got so many drive-by downvotes.
        
               | [deleted]
        
           | brighton36 wrote:
           | Yet The author assumes theres' a moral/legitimate transaction
           | vs an immoral/illegitimate transaction. I don't believe there
           | is an economic distinction of faith...
        
         | [deleted]
        
       | nobrains wrote:
       | Why do some people keep trying to prove Bitcoin as a pump and
       | dump scheme? Yes it has pumps and dumps, but if you zoom out,
       | those pumps and dumps get smoothed out and you see a digital
       | asset which keeps increasing in value because people see it as a
       | hedge against USD and other currencies inflation. The increase in
       | value is not infinite, and that can also be seen in the price
       | increase curve (log). The price increase is slowing. Why is it
       | difficult to come to the conclusion that initially Bitcoin price
       | increase will be volatile and eventually it will come to parity,
       | decreasing the volatility. From that point onwards, the price
       | will be more closely related to actual inflation (world over).
       | 
       | (The above purposefully ignores the other debate about
       | electricity, usage, etc. to keep the discussion simplified.)
        
         | acover wrote:
         | Gold isn't even an inflation hedge in the scale of one's
         | lifetime, why will Bitcoin be different?
        
           | nobrains wrote:
           | Gold is an inflation hedge in many, many countries.
        
             | acover wrote:
             | I'm not an expert, I am referring to the following. Am I
             | misunderstandibg something?
             | 
             | > due to its real-price volatility, gold had not been a
             | good inflation hedge over the short- or long-term.
             | 
             | They did find that, going back to the era of Emperor
             | Augustus who reigned from 27 BC-14 AD, gold had been a
             | pretty good hedge for inflation measured by military pay.
             | So, if you have a liability due in 2,000 years, gold might
             | be a good way to maintain your purchasing power.
             | 
             | https://www.pwlcapital.com/will-gold-save-the-day/
        
             | bhaak wrote:
             | Is the USD a worse inflation hedge in those countries?
        
             | [deleted]
        
         | johnny_b_g wrote:
         | > _Why do some people keep trying to prove Bitcoin as a pump
         | and dump scheme?_
         | 
         | And why do all the Bitcoin bros get instantly butthurt the
         | moment anyone shows any skepticism about it (but they feel
         | totally entitled to have skepticism about any/all other
         | currencies)
        
       | louwrentius wrote:
       | Frankly, I can't judge the merits of this article because I lack
       | the knowledge required.
       | 
       | But I think at this point we know that all cryptocurrencies are
       | 'greater fool' "investments". [1]
       | 
       | They are in every way totally irrelevant and detrimental to
       | society. Governments are unfortunately slow to crack down on the
       | exchanges, although progress is being made.
       | 
       | And that effort is essential to battle the cancer that is the
       | ransomware epidemic.
       | 
       | Anyone who follows the Lock Picking Lawyer on YouTube knows that
       | with time, resources and dedication virtually all locks can be
       | defeated and cryptocurrencies make 'expensive' attacks worthwhile
       | on IT infrastructure.
       | 
       | Frankly it hurts to see how cryptocurrencies have been
       | 'legitimized' by HN & ycombinator's coinbase. Because so many
       | people will be hurt.
       | 
       | [1]:
       | https://twitter.com/smdiehl/status/1384055017003311106?lang=...
        
         | MichaelBurge wrote:
         | I tend to agree, but this rant has nothing to do with using
         | Benford's law to detect Bitcoin manipulation.
        
         | Joeboy wrote:
         | > But I think at this point we know that all cryptocurrencies
         | are 'greater fool' "investments"
         | 
         | It seems to me to be very apparent that we do not all know
         | that. It is in fact a point of significant controversy.
        
           | louwrentius wrote:
           | I don't think so.
           | 
           | It's quite simple: where do the profits come from?
           | 
           | Other people, who by definition will lose money because
           | crypto doesn't create value.
           | 
           | A large amount of people will hold the bags of worthless
           | currencies while a few laugh their asses off in their
           | lambo's.
        
             | xiphias2 wrote:
             | El Salvador's Bitcoin Beach project is a great example of
             | people profiting from a debit based value network instead
             | of a credit based financial system: even though both US and
             | El Salvador had USD as the legal tender, it took $10 to
             | remit $50 through the western union network.
             | 
             | Lightning network (which is using Bitcoin as a settlement
             | network) is both dramatically lowering the fees and
             | provides instant debit transfer from an El Salvadorian
             | living in US remitting money to his/her parents in their
             | village (or directly paying the rent / gas bills) instead
             | of the parents needing to travel hours by bus to the city.
        
               | nootropicat wrote:
               | LN isn't actually used - the way it actually works is:
               | Strike holds dollars for the user. The user wants to send
               | dollars to someone. Strike buys btc using dollars (from
               | itself), sends btc via ln - to itself - and then sells
               | btc for the same amount of dollars, again to itself, and
               | credits the receiver. What's actually happening is that
               | Strike is a normal payment provider like Paypal, Venmo,
               | Revolut that fakes the btc transfer process because
               | pretending to be only a btc wallet means less regulation
               | than a full payment provider.
               | 
               | They don't actually spell it as directly - they just
               | claim an absurdity that buying btc and then selling btc
               | is somehow cheaper than a direct transfer, which of
               | course is impossible because it means taking the ask and
               | then selling into the bid, and the actual spread on most
               | liquid btc markets can be observed on biggest exchanges
               | like Coinbase or Binance, and that's ignoring the fact
               | that one part of the exchange is supposed to happen in a
               | local illiquid market in El Salvador.
               | 
               | The whole thing would be less convoluted if stablecoin
               | tokens were sent directly using a payment channel without
               | a fake trade step - using btc is a completely pointless
               | for anything but marketing (Strike to btc holders and
               | marketing btc itself).
        
               | xiphias2 wrote:
               | You are totally right in each step, but there's 1 thing
               | that makes it different from most exchanges: you can
               | already transfer money in/out of it using LN, which makes
               | it much more practical than using a Coinbase exchange
               | account.
               | 
               | Also, while Coinbase Pro has a 0.1-0.3% fee for market
               | order, if you want guaranteed execution, Coinbase and its
               | competitors take 3-4%.
               | 
               | If you listened to talks from Jack Mallers, he was
               | tracking lnd head instead of waiting for the full
               | releases, and picking and testing pull requests by hand,
               | fixing bugs that come up in practice (or giving feedback
               | to lightning devs), that's one of Strike's advantages
               | over other exchanges.
               | 
               | Also the ,,less regulation'' is just not true generally,
               | people have to go through KYC to link with bank accounts,
               | they are communicating with regulators:
               | https://jimmymow.medium.com/announcing-strike-public-
               | beta-32...
        
               | SV_BubbleTime wrote:
               | I read that twice and now it makes less sense. What is
               | the purpose of the fake transfer steps?
        
               | axiosgunnar wrote:
               | > because pretending to be only a btc wallet means less
               | regulation than a full payment provider.
        
             | echopurity wrote:
             | >where do the profits come from?
             | 
             | Every heard a money printer go brrr?
        
             | Joeboy wrote:
             | > I don't think so
             | 
             | But the fact you don't disagree with yourself doesn't mean
             | other people don't disagree with you.
        
         | casi wrote:
         | I equally find it strange that people continue to come to
         | hackernews- the Silicon Valley VC startup land - and can't
         | grasp that the infrastructure for programmable money might have
         | some value. And write off p2p communication and coordination
         | tools as zero-sum/ fraudulent games. And then wish for the
         | government to ban other people's jobs and hobby's and
         | communities because they don't like it.
         | 
         | Blows my mind that people might spend their day coding, and
         | night playing mmorpgs, and still not understand crypto. I guess
         | we need better UX and storytellers.
        
           | Hokusai wrote:
           | > the infrastructure for programmable money might have some
           | value
           | 
           | And it has, Central Banks are creating their own digital
           | currencies for digital wallets. They aware based on real
           | needs for speed, volume, security, trazability, etc.
           | 
           | > the infrastructure for programmable money might have some
           | value
           | 
           | I think that people understand cryptocurrencies quite well,
           | and from that knowledge comes the skepticism.
           | 
           | > wish for the government to ban other people's jobs and
           | hobby's and communities because they don't like it
           | 
           | I want it banned because people with unsofisticated knowledge
           | of economics and technology are being scammed out of their
           | money by snake oil salesmen. But, that is not needed. As soon
           | as normal accounting guaratees are required it probably will
           | call by its own weight.
           | 
           | I know people working hard jobs putting hard earned money
           | into this scam trying too get money to better their lives. It
           | breaks my heart to thing that they are being lied in such a
           | way, this study suggests is all manipulation, and that is my
           | experience with everything related to cryptocurrencies. The
           | sooner it gets regulated the better.
        
           | z3c0 wrote:
           | To give the original commenter some credit, they did warn us
           | that they lack knowledge on the subject.
        
           | FabHK wrote:
           | You can easily (!) and efficiently (!) do "programmable
           | money" without crypto[1]/blockchain/consensus (ie whatever
           | Bitcoin and its descendants brought to the table), and guess
           | what, people do.
           | 
           | > Blows my mind that people might spend their day coding, and
           | night playing mmorpgs, and still not understand crypto.
           | 
           | Let's agree that you can lambast cryptocurrencies even
           | despite understanding them, ok?
           | 
           | [1] with good old cryptography, of course, but without
           | "crypto"
        
           | Jasper_ wrote:
           | Nobody has been able to tell me a single thing that this
           | "programmable money" can do, despite having 12 years of
           | gestation to think on it. Everyone just seems excited about
           | the concept and assumes that because it's "natively
           | programmable", it's somehow more useful than what we have
           | right now, which is that we write programs which move around
           | money.
           | 
           | And please don't reply with DeFi, that's not taking advantage
           | of the inherent programmability of Bitcoin, it's just a
           | marketplace based on failed economics.
        
         | [deleted]
        
         | SamPatt wrote:
         | "at this point we all know..."
         | 
         | Sorry that's an appeal to majority.
         | 
         | You're wrong. Bitcoin is useful.
        
         | bouncycastle wrote:
         | Attacks on IT infrastructure have other motives besides ransom
         | too.
         | 
         | For example. IP theft such as stealing the secret recepcie to
         | the KFC herbs and spices, or stealing the soure code to a
         | competitors product, or the user database. Moreover, attacks to
         | ravage the target without the motive of ransom are common, see
         | the Sony hack for example.
         | 
         | The only solution against attacks is better security.
        
         | Geee wrote:
         | Once you learn the externalities of fiat monetary systems, you
         | will understand why we need Bitcoin. And you will realize that
         | it is the most important innovation of our lifetime.
        
       | hhjj wrote:
       | Maybe he should try with prices in yen...
        
         | fungizid wrote:
         | With a fixed exchange rate, the choice of currency does not
         | matter for Benford's law.
         | 
         | Benfords's law states that for many real-life numbers x, log(x)
         | is uniform.
         | 
         | Converting to another currency using exchange rate E, so that y
         | = E*x, yields log(y) = log(E) + log(x). This corresponds to a
         | shift of the distribution of log(x) and does not change how
         | uniform the distribution is.
         | 
         | However, if the exchange rate varies with prices, then it will
         | matter.
        
         | zeckalpha wrote:
         | There are other problems with the article but currency exchange
         | shouldn't substantially affect the distribution.
        
         | Gys wrote:
         | The currency against which BTC is exchanged the most is very
         | likely the one that shows the best fit (most perfect market).
         | Assuming that currency is the USD I expect any other currency
         | would result is an even worst fit
        
           | Metacelsus wrote:
           | Presumably yen, being a smaller unit of money, would have the
           | prices spread out over more logs. So Benford's law might be a
           | better fit.
        
             | malf wrote:
             | That's not how logarithms work
        
             | alisonkisk wrote:
             | A yen is nearly the same as a penny. Does BTC trade in
             | small fractions of yen?
        
       | echopurity wrote:
       | >Since bitcoins generate no income, their intrinsic value is zero
       | 
       | Embarrassingly bad.
        
         | Geee wrote:
         | Yeah, it's like dollars or gold, their value is zero too. There
         | is no such thing as 'intrinsic value'. Value is always
         | subjective.
        
           | Etheryte wrote:
           | Intrinsic value is a specific term in finance [0] and it is
           | by definition an estimation/approximation. Saying there's no
           | such thing as intrinsic value because value is subjective is
           | like saying there's no variables that are undefined because
           | undefined variables have a defined value of undefined.
           | 
           | [0] https://www.investopedia.com/terms/i/intrinsicvalue.asp
        
             | Geee wrote:
             | It makes sense for something that produces cash flow, but
             | saying that bitcoin doesn't have intrinsic value and
             | therefore no value is just stupid.
        
       | dannyw wrote:
       | What is the statistical likelihood of this appearing by chance?
       | Note that 2014 to today isn't actually that long of a timeframe,
       | as prices in a time-series are highly linked to the previous data
       | point.
       | 
       | Berkshire Hathaway has been trading for several decades; so
       | that's 40 years of data; as compared to 7 years of data. yet the
       | author, by using the same charts, seems to falsely imply that
       | these are remotely comparable.
       | 
       | This article seems to have as much logic as the whole "Benford's
       | law proves the elections were rigged!!!" claims by QAnon, who
       | tried to apply Benford's Law on a county level, found that it
       | generally fits a vast majority of the time, but cherry-picked the
       | counties where it didn't fit (which generally tended to be
       | smaller and hence less data points). Well, duh, it's statistics:
       | outliers are to be expected.
       | 
       | Pretty poor take from an author at
       | "statmodeling.stat.columbia.edu".
        
         | alisonkisk wrote:
         | It always amazes me how people will confidently broadcast their
         | arrogant ignorance in comments like like this.
        
         | lend000 wrote:
         | The market is simply too young compared to the "baseline," and
         | he's only testing one ticker. This might make more sense, even
         | with the limited age of data around today, if he took the 20 or
         | so most prominent cryptocurrencies to have a better sample
         | size, since they are all correlated anyways.
         | 
         | The progression of charts correlating with Benford is exactly
         | what you would expect if the titles "NYSE, Berkshire Hathaway,
         | Bitcoin" were replaced with "2800 tickers over 40 years, 1
         | ticker over 40 years, 1 ticker over 7 years."
        
         | contravariant wrote:
         | Benford's law doesn't give much of a guarantee except in highly
         | specific scenarios. You can however show it's pretty accurate
         | if you've got a 'smooth' probability distribution spanning
         | multiple orders of magnitude (how much of a guarantee you can
         | give depends on how specific you define what it means to be
         | 'smooth').
         | 
         | The rigged elections example you gave was, I believe, mostly
         | explained by the fact that the number of votes they were
         | looking at were all roughly the same order of magnitude [1].
         | 
         | [1]: https://www.youtube.com/watch?v=etx0k1nLn78
        
         | mumblemumble wrote:
         | The author at statsmodeling.stat.columbia.edu is the person who
         | wrote several of the books on things like this. I don't think
         | he can be finger-wagged away quite so easily as that.
         | 
         | There's a huge difference between this and the election one,
         | which is that this one is working with data that satisfies the
         | key statistical assumptions needed to properly apply Benford's
         | Law, and the QAnon elections rigged claims didn't. (Or at least
         | the ones I know about offhand - I don't use Benford's Law at
         | work, so this is not really my area of expertise.)
         | 
         | The big one you need to look for is that the variable spans
         | multiple orders of magnitude.
         | 
         | Berkshire Hathaway going back to 1980 spans three orders of
         | magnitude, so we're good there. Note that we could not use
         | Benford's Law to look at BRK going back only 7 years, but that
         | is _not_ because it 's not enough data. It's because that would
         | cover only 1/4 of an order of magnitude.
         | 
         | BTC going back 7 years is also decent. It's not quite as good -
         | only spanning two orders of magnitude - but it's enough that we
         | would expect Benford's Law to apply better than it does in this
         | graph.
         | 
         | By contrast, a lot of the cases where people thought they were
         | using Benford's Law to uncover electoral fraud, the data only
         | covered a small fraction of an order of magnitude. It's just
         | silly to expect 1 to be the most common leading digit in a set
         | of data that's constrained to the range [300, 600].
         | 
         | I don't know that this is compelling evidence of fraud or
         | manipulation in BTC, but it at least seems like clear evidence
         | that BTC doesn't behave like other securities. There's
         | something unusual going on that merits further investigation.
         | Perhaps it is just a shortcoming in the statistical model being
         | used. But, since this isn't a big data conference, it's not
         | sufficient to just keep hitting the "need more data" number
         | until you finally get the number you want.
        
           | alisonkisk wrote:
           | I don't think you are correctly using "orders of magnitude"
           | in benford's law in this analysis. The orders of magnitude
           | are in percent change over a few days, which is similar for
           | both BTC and BRK.
        
           | CrazyStat wrote:
           | The time series spanning 3 orders of magnitude over a course
           | if years is not sufficient condition for Benford's law to
           | apply. As a trivial example, a stock whose price started at
           | $1 and increased by $1 every day for 30 years would span 4
           | orders of magnitude over that time period, but would not
           | follow Benford's law.
           | 
           | A formal justification for applying Benford's law to a time
           | series like that would depend on some kind of ergodicity
           | argument which has not been made either by Gelman or the
           | original author of the post he's talking about. I'm _rather_
           | skeptical.
           | 
           | As a first step into deciding whether it's reasonable I would
           | do something like the plot for Berkshire Hathaway for each of
           | a large collection of companies, and collect some measure of
           | disagreement between the model (Benford's law) and the
           | observed distribution for each stock. I'm guessing many of
           | these stocks would follow Benford's law no better than
           | Bitcoin.
        
             | TomSwirly wrote:
             | > As a trivial example, a stock whose price started at $1
             | and increased by $1 every day for 30 years would span 4
             | orders of magnitude over that time period, but would not
             | follow Benford's law.
             | 
             | You would expect if you deliberately created a security
             | whose growth rate monotonically tends to zero over time
             | that you would get anomalous results in any statistical
             | point, but I don't quite see why you bring up this
             | pathological example?
        
               | CrazyStat wrote:
               | Because the claim was made that spanning several orders
               | of magnitude is sufficient to allow application of
               | Benford's law:
               | 
               | > The big one you need to look for is that the variable
               | spans multiple orders of magnitude.
               | 
               | > Berkshire Hathaway going back to 1980 spans three
               | orders of magnitude, so we're good there.
               | 
               | > BTC going back 7 years is also decent. It's not quite
               | as good - only spanning two orders of magnitude - but
               | it's enough that we would expect Benford's Law to apply
               | better than it does in this graph.
               | 
               | This claim is false. I provided a counterexample to
               | demonstrate as much. Whether or not it's "pathological"
               | is both subjective and irrelevant.
        
               | FabHK wrote:
               | If it were to grow by 9 bp (0.09%) every day, it would
               | obey Benford's law. Question is how pathological that
               | would be, but yes, arguably less.
        
             | mumblemumble wrote:
             | > As a trivial example, a stock whose price started at $1
             | and increased by $1 every day for 30 years would span 4
             | orders of magnitude over that time period, but would not
             | follow Benford's law.
             | 
             | That's actually a great illustration of the kind of thing
             | we'd expect Benford's Law to raise red flags about. Your
             | hypothetical posits the kind of behavior that we would not
             | expect to naturally come out of the kind of process that
             | governs stock prices over time. Stocks simply don't have
             | their price go up by exactly one dollar a day, every day,
             | for thirty years.
             | 
             | (This is briefly covered in the the article, which
             | describes how the other big assumption of Benford's Law is
             | that you're working with a system where things tend to
             | change by percentages rather than absolute values. So yeah,
             | it's true, covering orders of magnitude is not sufficient.
             | Nor did I claim that it is, mind. I was just pointing out
             | the assumption that I thought he original poster was
             | missing.)
             | 
             | So, if we saw the kinds of initial digits that your
             | hypothetical produces, we would be _correct_ to guess that
             | this stock is behaving in an unusual way. And it would be a
             | correct application of Benford 's Law, because we can
             | reasonably expect that its key assumptions apply.
             | 
             | By contrast, if we hypothesize a stock whose price goes up
             | by exactly 0.0001% every day for 30 years, its record of
             | daily closing prices would obey Benford's Law. In fact, it
             | would match it so well that we would also (correctly)
             | consider it to be suspicious.
             | 
             | No, it's not a formal justification in any case. It is just
             | a red flag. It turns out that red flags are useful even
             | when they're not admissible in court, because they provide
             | an easy heuristic that you can use to help direct your
             | search for more compelling evidence.
        
           | [deleted]
        
         | conformist wrote:
         | Isn't Andrew Gelman's take more like "Look what they did,
         | that's kind of interesting, what do you think?" rather than
         | "look at this article, it is true"? See also the comment
         | section.
        
           | FabHK wrote:
           | Yes indeed. Most of the article is quoted from Smith, and
           | Gelman (the prolific author of the worthwhile blog at
           | columbia.edu) only really adds a few inconclusive sentences
           | at the end. ("... There's a lot going on, and people have
           | lots of reasons for doing things.")
        
         | TomSwirly wrote:
         | > prices in a time-series are highly linked to the previous
         | data point.
         | 
         | And how many data points are there in seven years of BTC?
         | 
         | > seems to falsely imply that these are remotely comparable.
         | 
         | Why is it "false" that they are "remotely comparable" if we are
         | looking at time series of security prices?
         | 
         | You are long on the insults and short on the reasoning. Given
         | the author is a well-known statistician and you are some
         | anonymous individual, I'm going with them.
        
         | FabHK wrote:
         | Given that Benford's law tends to apply when the numbers span
         | many orders of magnitudes, I would have expected more emphasis
         | on that. Berkshire Hathaway (low 200, high 450,000) covers
         | about 3.4 orders of magnitude (and much more time, ie
         | opportunities to wander up and down), BTC (low 200, high
         | 60,000) covers about about 2.5 orders of magnitude.
         | 
         | So, we should expect BTC to have a worse fit than Berkshire.
         | How much worse would require some more sophisticated analysis
         | than looking at the graphs, it seems.
        
         | tedunangst wrote:
         | Like what does the graph look like for TSLA? Or GOOG?
        
       | arcticbull wrote:
       | I mean, we need only remember that in late 2016 two wash trading
       | bots at Coinbase accounted for 99% of all global trading volume
       | in Litecoin. (Likely Charlie Lee, btw) [1] And that Tether
       | continues to exist after this devastating NYAG settlement. [2]
       | 
       | It's clearly manipulated. And it's manipulated because its
       | roughly speaking globally unregulated, and tracks globally via
       | cross-exchange arbitrage bots.
       | 
       | If the author found anything different I'd eat my ...hat, and if
       | you believe the trading patterns are as pure and organic as the
       | driven snow I've got an NFT of the Brooklyn bridge to sell you.
       | 
       | [1] https://www.cftc.gov/PressRoom/PressReleases/8369-21
       | 
       | [2]
       | https://ag.ny.gov/sites/default/files/2021.02.17_-_settlemen...
        
       | hatware wrote:
       | Show me you don't understand statistics without showing me you
       | don't understand statistics...
        
       | saivan wrote:
       | Sorry for the shameless plug. I made a video about Benford's law
       | a while ago for anybody wondering how we get these values
       | https://www.youtube.com/watch?v=9hY43XpVr1I&ab_channel=Treen...
        
         | randunel wrote:
         | I suspect your "shameless plug" message is trying to draw
         | attention away from the fact that you've added an adblock
         | whitelisting query param to the url, presumably whitelisting
         | ads from certain providers. This is more unethical than sharing
         | tracking links in here.
        
           | dmurray wrote:
           | Good spot, but I think this happens by accident rather than
           | by design. If you have AdBlock Plus, and chose some option to
           | allow YouTube ads on certain channels, it edits URLs to
           | include this [0]. So @saivan may have just copied it from his
           | browser's URL bar.
           | 
           | [0] https://support.google.com/youtube/thread/69037368/url-
           | chang...
        
           | alisonkisk wrote:
           | "shameless plug" draws attention to, not against.
           | 
           | Anyway, it's not a big deal, ads aren't worse than tracking,
           | and anyone who uses a real blocker uBlock Origin isn't
           | affected by ab_channel.
        
       | Animats wrote:
       | Huh?
       | 
       | The NYSE looks that way because of a stock market rule that if
       | the price falls below US$1 for 30 days, it becomes a "penny
       | stock" and will be de-listed. There's also a tradition that when
       | a stock gets well over $100, it splits. (Berkshire Hathaway
       | refuses to go along with this, but everybody else does.) So
       | issuers tend to split and reverse split to stay in the
       | traditional trading range.
       | 
       | Commodity prices and foreign exchange rates don't behave like
       | that. They don't split or reverse split. Also, their price is
       | different depending on which currency you view it in.
        
       | qPM9l3XJrF wrote:
       | I don't buy it. My intuition here is that Benford's law is a
       | thing because for pretty much any statistical distribution, large
       | numbers are less likely than small numbers, and small numbers are
       | more likely to start with 1. But I'd only expect this effect to
       | show up when aggregating across many different statistical
       | distributions (e.g. looking at all stocks in the S&P 500 at once)
       | rather than looking at individual distributions (i.e. I think
       | maybe he just got lucky choosing Berkshire, and other S&P 500
       | stocks might not show Benfordness in their price even if they're
       | not manipulated).
       | 
       | Plus, even if Bitcoin's price is mainly a product of manipulation
       | -- speculators trying to make the price rise or fall relative to
       | where it is right now -- there's no reason we can't think of that
       | as also being a random process which produces some statistical
       | distribution.
       | 
       | Benford's law works for detecting fraud because the process that
       | humans use to choose random numbers -- just write down a bunch of
       | random digits -- results in a statistical distribution that is
       | unusual relative to what would be produced by a natural process.
       | But it seems quite unlikely to me that Bitcoin price manipulation
       | takes the form of a whale saying "OK, I just wrote down a bunch
       | of random digits, this is our BTC price target for Wednesday".
        
         | [deleted]
        
         | fluidcruft wrote:
         | I don't really know anything about this but every time I read
         | these analyses using Benford's Law I don't understand why
         | anyone would expect Bitcoin's exchange rate to begin with the
         | digit "1" ~30% of the time. Once you're not talking about
         | human-guestimated numbers, it seems more like a question of
         | scale factors. If bitcoin's value fluctuates between 30k and
         | 70k it's never going to start with a "1". Or if its value
         | fluctuates between 120k and 180k then it's always going to
         | start with "1". That's where I struggle trying to understand
         | how Benford's Law is supposed to provide any insight.
        
           | FabHK wrote:
           | Benford's law tends to fit better when:
           | 
           | * the numbers span many orders of magnitude
           | 
           | * the numbers are produced by multiplication (where log(x) is
           | normal-ish), not addition (where x is normal-ish)
           | 
           | Your examples span half an order of magnitude, so it
           | definitely doesn't apply (as you say).
        
           | [deleted]
        
           | x4e wrote:
           | I believe it's about which numbers it ends with, not starts
           | with
        
           | y04nn wrote:
           | Yes, I don't know if the prices should have a better
           | Benford's Law fit when the price is around and 10k or 100k
           | but then a lesser fit when the price is between 5/50k and
           | 9k/99k if you have not enough data. But if there is enough
           | data, maybe it should better fit the Benford's Law, and this
           | may be a proof that arround 10k/20k the price was rigged and
           | should have stay around it longer but manipulation put it
           | around 30k/50k.
        
         | dannyw wrote:
         | Correct. I've been in the bitcoin space for a decade now, and
         | there were only brief moments* where it was difficult to buy or
         | sell at the price quoted by major exchanges.
         | 
         | * DDoS attacks, exchange illiquidity, etc.
        
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