[HN Gopher] Using Benford's Law to Detect Bitcoin Manipulation
___________________________________________________________________
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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