In March 2019, an anonymous person under the pseudonym “PlanB” stunned investors when he published “Modeling Bitcoin Value with Scarcity” and introduced his now famous Stock-to-Flow (S2F) model. The model predicted exponential growth in the bitcoin market value, using what claimed sound scientific methods. A year later, he introduced the Stock-to-Flow Cross Asset (S2FX) model, which includes data on gold, silver, diamond and real estate. As we will see below, PlanB’s models are scientifically invalid and do not have the confidence level it claims to have. According to its website, PlanB is “a former institutional investor with 25 years of experience in financial markets. He has a legal and quantitative finance background and has always been fascinated with modeling risk and return.” Note that he does not claim to have expertise in risk and return modeling. This will soon become important, as we will soon see that the S2F/S2FX models cannot have been formulated by anyone with deep knowledge of statistical modeling. According to PlanB’s March 2019 article: “The linear regression function: ln(market value) = 3.3 * ln(SF)+14.6.. can be written as a power law function: market value = exp(14.6) * SF ^ 3.3The possibility of a power law with 95% R2 across 8 orders of magnitude, adds confidence that the key driver of bitcoin value is being captured correctly with SF.” Impressive as that may sound, PlanB made a recovery mistake here. Notice how the function says that “market value” equals a function of Stock-to-Flow? This is a model misspec with tautological logic and therefore statistically invalid, for the simple reason that “market value” breaks down into “stock * price” while “stock / flow” is on the other side of the equation. In layman’s terms, PlanB essentially claims that “Inventory is a function of Inventory.” A tautology is a trivial statement that is true under all circumstances. It is like saying that a banana is a type of banana. Of course stock is a function of stock. Therefore the data fits, but is scientifically worthless. Tautologies are true, but tell us nothing useful. Rather, they are true because of the meaning of the terms. The other problem is that the model autocorrelates, where the results of today’s value are a function of yesterday’s value. If you correct for that, the R-Square (R2) value is zero. So scientifically Stock-to-Flow is nonsensical and cannot be used to model price.” It shows a high correlation [because] it uses the same term in every axis (stock), and if you take the log of two terms with the same variable, you ADD it. When a (stock) is much more volatile, it dominates. The model is autocorrelated. Doesn’t need S2F at all. Just price versus time.”—Cory Klippsten In addition, the architecture of his models shows a lack of understanding of statistical modeling, let alone that the model doesn’t even take demand into account. PlanB could avoid the tautology by only having price on one side of the equation and maybe build a regression of price on flow or stock to flow, but the fit would be different without changing the parameters. In addition, he should be slowing down the time series. Their innovations, the minor inconsistencies, should contain information about the other side of the equation. Without detrending you will get false results. Simply putting two oblique lines against each other creates a semblance of correlation that simply isn’t there. PlanB’s Stock-to-Flow Cross Asset (S2FX) model suffers from the same basic flaw and has additional problems. PlanB claims that the S2FX model allows time for bitcoin, but this is false because its Bitcoin phases are a function of time. The clusters are equal to half-lives and on the X-axis all the following phases can be drawn. The other assets are cherry-picked and even the values for those assets are cherry-picked. For a more detailed look at PlanB’s bad math, read btconometrics’ Bitcoin and Stock to Flow critique, where he shows the misleading statistics behind PlanB’s models and illustrates the fallacy of scam statistics. This is argumentum verbosium – otherwise known as evidence by verbosity or evidence by intimidation. “In this article I’ll show you why stock to flow is nothing but a flight of fantasy – a fairy tale or a fantasy supported by emotional support from irrational actors, a lack of broad mathematical knowledge and proof through verbosity.” (btconometrics)PlanB has rejected valid criticisms saying that the model can be fitted to price using completely different parameters that avoid the tautology.However, these alternative parameters are just random numbers that it changes from time to time. why this is a problem we can compare it to the famous Bitcoin Rainbow Chart.The Rainbow Chart was created by Über Holger and has a very visible disclaimer that says: “The color bands follow a logarithmic regression (introduced by Bitcointalk User trolololo in 2014) , but are otherwise completely arbitrary and without any scientific basis. However, we never change them. In other words, it will only make sense until one day it is no more.” Holger is completely honest and transparent about the Rainbow Chart. It is not intended to be anything more than a wild guess. It does not pretend to be scientific. Unlike PlanB, which has gone out of its way to falsely provide a scientific basis for it. models in his writings and on dozens of podcast shows, these shows he claims to welcome criticism, but his Twitter account tells a different story: anyone pointing out a bug, a potential problem, a valid question, or even a valid investigation “Like” the validity of his claims is blocked. PlanB says he blocks people for “noise control” but assures his followers that he welcomes valid debate and criticism. However, his actions on Twitter suggest a different motivation. criticizing PlanB’s models in good faith will be blocked by PlanB Inquiring why S2FX phases are aligned with halvings, and therefore appearing as if they are a time series quickly results in a blockage. PlanB blocks those who express opposing views. He blocks people who “like” tweets with sincere criticism. Followers have been blocked for privately sending him a serious question. He’s even blocked people from jokingly changing their Twitter name to PlanC. This is not the behavior you would expect from someone with real expertise in quantitative finance or who has respect for the scientific method. If PlanB wants to honestly claim that its models have scientific R2 value in the high 90s, then it can’t block and censor valid criticism that shows otherwise. What it means to be a “useful” model PlanB often echoes George Box’s claim that, “All models are wrong, but some are useful.” He misused the quote. Box referred to scientific models that provide testable hypotheses, not tautologies.In an article on the subject of Nature, Alexander J. Stewart explains: “But the purpose of a model is always to clarify our understanding of what we study. That sounds simple, but it isn’t, because clarity of understanding can only be assessed retrospectively. A model should help us formulate testable hypotheses in a way that advances a field, perhaps pointing us to a new idea that empirically finds support, by enabling us to discard an old idea, or by making a more accurate quantitative forecast. […] Bad models are not wrong, they are tautological.” The ardent followers of PlanB often reply: “But Einstein and Newton made mistakes! His model will work until it stops working.” This misses the point and is offensive to scientists like Einstein and Newton. Yes, it is true that Newton and Einstein were fallible, but as adherents of the scientific method, they welcomed criticism and admitted their mistakes. PlanB avoids both. Einstein and Newton’s revolutionary models were groundbreaking hypotheses that clarified our understanding of the universe. Neither is known for postulating tautologies. Newton said that forces act on matter. Einstein said that matter is energy and energy is matter. PlanB made the nonsensical claim that inventory is a function of inventory. That is not a useful hypothesis or model. Bitcoiners who claim to fight against the sale of snake oil and shitcoinery should demand better. Tell me the good news Now that we know that the S2F/S2FX models are just lines on a graph with no scientific basis, we can put those models aside and move on and focus our energies on better hypotheses to be tested and possibly how we think about bitcoin is changing. We don’t have to tie our expectations to PlanB’s arbitrary pricing schedule. Those who fell for PlanB’s argumentum verbosium can go further and gain real conviction in Bitcoin by learning about its properties, network effects and what sets it apart from all other projects. Bitcoin has a bright future and the sooner we move away from bad models, the sooner we can understand it. This is a guest post from Level39. The opinions expressed are entirely their own and do not necessarily reflect those of BTC Inc or Bitcoin Magazine.