What’s Up With S2F? — A Look At The Popular Bitcoin Model

One of the most fascinating aspects of bitcoin is its historical meteoric price rise. Is bitcoin going to continue on this historical path or is growth going to slow, or even halt?

The stock-to-flow (S2F) model, put forward by PlanB, suggests that bitcoin’s future price can be forecast quite precisely and that the price will continue a steady and impressive path upwards, with approximately tenfold returns every four years. The S2F model has attracted a lot of attention, and PlanB has amassed an impressive number of followers (1.7 million at the time of writing).

harshly-worded recent article published in Bitcoin Magazine. Also, in July 2020, Eric Wall put together a collection of criticisms.

It appears that most people find themselves in either of two camps: the “pro” S2F and the “con” S2F camps. How should we position ourselves?

Before I go on: I have written negatively about the S2F model since 2019, when I predicted that the S2F model’s predictions would prove too bullish. I have also exchanged with PlanB both publicly on Twitter (e.g. here), and privately. I have coauthored a more mathematical article together with InTheLoop, clarifying why we both think the S2F model is too bullish. It might therefore come as no surprise that I am not exactly in the S2F camp. However, I have also noticed that some of the criticisms towards the S2F are invalid. Other criticisms purport to deal a death blow to the S2F model, whereas in fact, they do not. I therefore hope to add some clarity. It is important to be right for the right reasons, because correct principles are our only chance of being right in the future.


What’s wrong with this model? Let’s look at some arguments that are put forward to discredit the model:

Tautological Specification

In their recent Bitcoin Magazine article, Level39 had this to say regarding the S2F model:

“Notice how the function says ‘market value’ equals a function of Stock-to-flow? This is a model misspecification with tautological logic and therefore statistically invalid, for the simple reason that ‘market value’ decomposes to ‘stock / price’ while ‘stock / flow’ is on the other side of the equation. In layman’s terms PlanB is essentially asserting that ‘stock is a function of stock.’ A tautology is a trivial statement that is true under any circumstances. It’s like saying a banana is a kind of banana. Of course stock is a function of stock. This is why the data fits, but is scientifically worthless. Tautologies are true but do not tell us anything useful. Rather, they are true because of the meanings of the terms.”

here), and have not been blocked. We have exchanged privately and I cannot characterize PlanB’s behavior as anything other than very friendly.

I have heard of events when people were blocked by PlanB, but I am not surprised by this: He has to manage an audience of 1.7 million people, which cannot be easy. In any event the ad hominem argument says nothing about the validity of the S2F model and should be disregarded.

long debate regarding whether a certain property known as cointegration (pronounced co-integration, not coin-tegration) exists between stock-to-flow and the price of bitcoin. Cointegration is supposed to hint at a causal relation between the two variables. When it ultimately came out that the cointegration property does not exist between stock-to-flow and price, this was interpreted as meaning that a change in stock-to-flow cannot possibly cause a change in price. A death blow to the S2F model! But is that really the case?

I had never heard of cointegration prior to 2019, when studying the stock-to-flow model. It is a concept that is widely used in econometrics, but not in any other fields (as far as I am aware). For example, in March 2020 Judea Pearl, the de facto inventor of causal statistics and author of “The Book of Why” had not heard of cointegration either! He gave two clarifying statements that cointegration might give an indication that there is causal relation, but that it by no means implies a causal relation. In 2022, Pearl again lamented that no one was able to satisfactorily explain the concept of cointegration to him.

The fact that the inventor of causal statistics did not know about the concept of cointegration is telling: The importance of cointegration seems overblown. The lack of cointegration might perhaps hint at trouble for the S2F model, but it should not be considered a death blow.

power-law corridor of growth which relies on the observation (which I owe to Giovanni Santostasi’s reddit post) that bitcoin’s price follows a straight line when plotted using an x-axis that is scaled logarithmically.

published the below plot in an article at the end of 2019. Various people have made predictions apparently based on the assumption of nondiminishing growth (roughly represented by the green line). I predicted that these forecasts would prove to be too bullish, and that the price would more closely follow the orange line, which is governed by diminishing returns.

same article I explained that S2F forecasts nondiminishing growth, and that I therefore also expect it to be too bullish, similarly to the forecasts made by the individuals above. Below is the plot that I published:

in an article I coauthored with InTheLoop which explains in more detail how the shape of the S2F price curve does not match the actual price data well.

The popular Twitter handle s2fmultiple tracks how the price is performing compared to the S2F forecasts. The metric is referred to as the S2F multiple. A multiple greater than 0 means that the price is higher than the S2F multiple, and vice versa.

The history of the S2F multiple so far looks like the below plot. There have often been high values before 2015, but not so much after that. This is a hint that the price is not quite catching up to the S2F model forecasts (and also that the shape of the S2F price curve does not match actual price data well).


By comparing my own power-law corridor of growth forecasts to the S2F model, I am able to compute the trendline of how I expect the S2F multiple to evolve in the future:

original article I have forecast a price of $100,000 per bitcoin no earlier than 2021 and no later than 2028, and $1,000,000 per bitcoin no earlier than 2028 and no later than 2037. I still expect these forecasts to come true.

This is a guest post by Christopher Burger. Opinions expressed are entirely their own and do not necessarily reflect those of BTC Inc or Bitcoin Magazine.