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Bitcoin Stock-To-Flow: The Model of S2F and S2FX Explained and PlanB

Anyone who had said in 2009 that Bitcoin would be worth a $47,000 per Bitcoin in 2021 would  have been laughed out. At the same time, predictions of $20,000, $15,000, $10,000 or even $1,000 per Bitcoin would also raise eyebrows.

Afterwards it is always easy to look back and to determine why a price has risen or fallen so strongly in a certain period of time. Therefore there is a lot of speculation from many more ‘specialists’ or ‘experts’ who all predict different prices for Bitcoin in the coming years.

Where the local fanboy talks about a price of $100,000 or $250,000, the more pessimistic critic speaks of prices between $100 and $1,000. On the one hand, predicting prices always feels a bit like watching coffee grounds. Estimating the development of prices is what distinction successful traders from less successful traders.

In the case of Bitcoin, there is a model that, based on historical data and a formula between stock and production capacity, seems to say all kinds of things about Bitcoin’s financial development in the coming years.

In any case, this is a good reason for us to take a deep dive into this and see what exactly the model entails, what the model predicts and what the positive and negative reactions to the model entail. In addition, we are not only looking at the original Stock-To-Flow (S2F) model, but also at the so-called upgrade of the model, the Stock-To-Flow Cross Asset, or S2FX.

Make sure you are well rested before you read on, it is a relatively technical article, but nevertheless very interesting and we think the model definitely contains a grain of truth and a scientific logical basis that will help Bitcoin’s price for the coming years. could become comprehensible.

Note: This article is not intended as financial advice and is for educational intent only. Buying cryptocurrency is your choice and yours alone.

Scarcity and its correlation with price

Nice word, huh, correlation? By this we mean the link between scarcity and price. As a current example, let’s take a look at mouth caps. In the past, when the world was still normal, you bought a box of 100 mouth caps for € 7.50. Today you can easily put down €50 for exactly the same box. Why? Because there is scarcity.

The whole essence of price development is incredibly simple. There is a demand side (buyers) and a supply side (sellers). When there are many more products than there is demand for, the price decreases. If there are far fewer products than there is demand for them, the price will rise.

So far it’s not all that complex. It should be clear that when a product is very popular, the seller can raise the price considerably because there are enough people who want to buy the product.

Scarcity means that little of a product is available or can be made. This can be caused by a huge sudden increase on the demand side (for example toilet paper or face masks during the pandemic) or by a sharp decrease on the production side, because machines break down or raw materials run out.

One of the products that has a certain degree of scarcity and is also regarded as a means of payment, are the raw materials gold and silver. Bitcoin is now also increasingly becoming a valid means of payment. And Bitcoin also has scarcity. We will of course come back to this in detail shortly.

First, let’s take a look at the Stock-To-Flow model and its ratio.

Stock-To-Flow (S2F) ratios

The Stock-To-Flow ratio is a mathematical calculation between the ‘stock’ and the ‘flow’. Here the stock is the total stock that is available and the flow is the new production quantity of the product or raw material.

In short, the Stock-To-Flow ratio is therefore S2F ratio = Stock / Flow.

The image below shows a historical development of the S2F ratio of the commodity gold. One year more gold is mined than the other year and one year there is more gold in stock than the other year. As a result, the S2F ratio is constantly changing.

Image 1: Gold’s S2F ratio over the past 120 years. Source

On average, the S2F ratio of gold is a factor of 66. That means that in general there is 66x more gold in stock than is added annually. This also shows that when there is a large amount of gold in stock, its price falls. Because prices are falling, it is less interesting to mine a lot of gold, so that the flow decreases.

As a result, there is less gold in stock, causing prices to rise again. This makes it more interesting to mine more gold, causing the stock to increase again and prices to fall again. Both the price development and the stock development (and therefore also the S2F ratio) are inextricably linked and have a very strong influence on each other.

That’s all great, of course, but what about Bitcoin? Does it work the same there? No, not quite. And why? We are happy to explain that to you.

Bitcoin mining and the Bitcoin halving

It was probably not completely premeditated when the term ‘mining’ came up from the Bitcoin corner, but it comes in handy for this article. Because just as gold and silver cannot be counterfeited and you have to mine it, the same goes for Bitcoin.

Yet there is an important difference between mining (or mining) Bitcoin and that of gold and silver. The main difference is that the total flow of Bitcoin is pre-programmed. So you can estimate fairly accurately on the month how much Bitcoin will be added.

This is much less the case with gold and silver. The more expensive the raw materials are, the more energy will be put into mining them. With Bitcoin, Bitcoin miners were paid a fee of 50 Bitcoin for each successfully mined block. This fee is halved every 210,000 blocks. This phenomenon is also known as Bitcoin halving.

We have now had a Bitcoin halving in 2012, one in 2016 and one in 2020. During the first Bitcoin halving, the fee was reduced from 50 to 25 Bitcoin. After the Bitcoin halving of 2016, there was only 12.5 Bitcoin per block to be earned and earlier this year that amount was again halved to 6.25 Bitcoin per block as a fee.

Image 2: Bitcoin’s stock in the blue line, versus Bitcoin’s inflation rate in the orange line. Source

If we go back to the Stock To Flow model again, hopefully you will understand that every time there is a Bitcoin halving (i.e. about every 4 years), Bitcoin’s S2F ratio doubles. On the flow side, suddenly only half as much Bitcoin can be produced.

Unlike with gold, you can’t suddenly send twenty extra teams into the mines to make sure that a little more comes in than would normally come in. The amount of Bitcoin that can be produced is determined in Bitcoin’s software or design. So it’s a given that about every four years, Bitcoin’s S2F ratio will double.

In short, this would have the plausible effect that every 4 years the scarcity of Bitcoin will only increase more and more, unless the demand side decreases so much and prices still fall. In any other scenario, this development could only mean that if the quantity remains the same or increases on the demand side, the price of Bitcoin will rise sharply in the next 120 years in which the Bitcoin halvings will still take place.

Of course, only the ‘supply side’ is certain and the mysterious question of how Bitcoin’s ‘demand side’ will develop remains. However, we notice that as Bitcoin is in the news more and more often and the global adoption increases, there is a significant chance that Bitcoin will also become more and more in demand.

So there are now two different S2F models in circulation for Bitcoin. The first Bitcoin S2F model and the second Bitcoin S2F model, which is called S2FX. We will of course first explain the first Bitcoin S2F model for you.

The first Bitcoin S2F model

The first Bitcoin S2F model was conceived or designed by someone who calls himself Plan B. Plan B is a pseudonym and a Dutch investor and econometrician who chooses to remain anonymous.

The model was published in the article “Modeling Bitcoin Value with Scarcity” and the article described how Bitcoin is the world’s first digital object to have a certain scarcity. It is precisely this scarcity that makes Bitcoin a monetary object (it represents value) that can increase in value over the coming years.

Let’s take a closer look at the model via the graph below:

Image 3: The chart associated with the first Bitcoin S2F model. Source

What you see on the graph is the combination of different data points. On the left you can see the development in the price of Bitcoin. Each step up is a multiplication of 10. So 10 dollars doesn’t become 20 dollars and then 30, but becomes 100 and then 1000 dollars.

On the right you see the amount of blocks that are produced per month. The spheres themselves are placed on the axis of the value, the color of the spheres is then determined by the amount of the number of blocks that are mined.

There is also a black line in the graph. This black line represents the stock-to-flow model. In other words, according to Bitcoin’s S2F model, how much would Bitcoin be worth at any given time? For this, the model uses the formula 0.4 x Stock-To-Flow-Ratio ^3. It may seem arbitrary, but as you can see the formula of the model is frighteningly close to reality. There is a confidence level of 95% when looking back at the past 10 years. According to Plan B, the model works so well that it can be safely assumed that this will continue to be the case in the coming period.

The First S2F Model: The Forecast for Bitcoin

With a certainty of 95%, Plan B says it can predict the future price of Bitcoin using the first S2F model. The model quickly became known. Still, there is a good chance that a major factor in this success was a fairly favorable prediction of the Bitcoin price.

People like it when something they’ve bought goes in the right direction in predictions. According to the first S2F model, after the third Bitcoin halving (yes, that of 2020) the price would slowly rise to $55,000.

Because the supply side of Bitcoin is thus fixed both now and in the future, the S2F ratio becomes an interesting speculation especially on the demand side. In order not to create too hysterical expectations, Plan B has flattened the parameters somewhat downwards in its model. Still, he predicted a price of $55,000 at a time when the price had fallen to a meager $4,000 USD at that time.

All in all, a decent ‘bold statement’, but now that we have seen the price of Bitcoin suddenly rise to a record-breaking All Time High of more than $24,000 in December, doubling to 50K suddenly doesn’t sound so crazy anymore. However, there is also more than enough criticism of the plan. We briefly explain the most frequently heard counter-arguments.

The first S2F model: the critique of the model

Just like you always have pros and cons with everything, so is the S2F model of Plan B. So there are always fanboys and there are always haters. In this case, the proverbial haters have worked hard to refute Plan B’s model of the Stock To Flow.

The easiest, of course, is to criticize something by stating that it’s all too good to be true and that the correlation is apparently related, when in fact it’s just a coincidence.

In the past, there have been much more demonstrable statistics in which it strongly seems as if there was a causal relationship between the two values, while in practice this has absolutely nothing to do with each other. Hater #1’s criticism is therefore completely in line with this claim. The 95% relational variance achieved is so high that it seems too good to be true.

As an example, this traditional example of the number of divorces and the number of people who bought a tub of margarine at the supermarket was juxtaposed in the image below.

Image 4: The number of divorces and the number of tubs of margarine purchased in the US state of Maine. (Bron)

As you can see in the image, there seems to be a strong relationship between the two lines. Nevertheless, the chance that there is a strong relationship between the amount of separations and the number of tubs of butter purchased does not seem very great. Even non-divorced people seem to buy butter.

The question that naturally arises is whether the S2F model represents a relationship in a similar way between two variables that in practice have nothing to do with each other.

Another critical note came from an Australian statistician, Nick Emblow. Emblow produced an article he called “The Drunken Value of Bitcoin”. In the article, Emblow focused not so much on the validity of the model, but on the relationship between the variables mentioned.

Instead of questioning the entire model, Emblow came up with a fork on the model and chose a direction that is in line with the S2F, but that is slightly different. The term he often uses is ‘Cointegration’.

Cointegration in this context, according to Emblow, is like a drunk who walks his dog with a leash. As a result, the article has also been called “The Drunken Value of Bitcoin”. In this metaphor the drunkard wanders aimlessly criss-cross, while the dog is dragged along on a leash by the drunkard.

Although both the dog and the drunk can move without any direction, they always stay together thanks to the leash. So they always move together, even if they may not have the same end goal. The question is therefore whether the Bitcoin S2F ratio and the price are co-integrated according to this metaphor and therefore not based on complete coincidence, as emerged in the first point of criticism.

Whether there is a grain of truth in the criticism or in the first S2F model in itself is certainly interesting, but it may have been overtaken by the second S2F model, the S2FX. The new model is therefore called the Stock To Flow Cross Asset in full. Let’s quickly move on to this new model and see how it works!

The second Bitcoin S2F model (S2FX)

Before the biggest discussion about the first Bitcoin S2F model broke out, Plan B was already one step further. He was already working on the new Bitcoin S2FX model at that time. His biggest challenge has been to make comparisons with other monetary assets that have a similar structure so that they can be included in the model.

There are quite a few figures available for both gold and silver, so a whole range of S2F ratios can easily be determined on that basis. At the same time, it soon stops there. Other similar assets (think of diamonds or platinum) an S2F ratio is much more difficult to calculate because there is less data. For example, if you look at oil, an S2F ratio is easy to calculate, but you cannot pay with oil and is therefore not a comparable asset. That’s why Plan B comes with a Plan B (haha) for its earlier S2F model, the S2FX.

Instead of building on the first model in which there is not enough relevant data available, Plan B has changed course somewhat and has started investigating to what extent Bitcoin as a currency is going through different phases.

Bitcoin is of course still Bitcoin, but where Bitcoin was once conceived as the very first crypto project without any fame, today it is a widely recognized and recognized e-currency, just to name one example.

Another example – and perhaps a little clearer – is the example of ice. No chocolate, strawberries or pistachio, just that from a lump. Water (or ice) can be in different phases and pass from one phase to another.

Depending on its temperature, water is in solid, liquid, gas or ionized form.

Image 5: The different transition phases of water or ice.

For the S2FX model, Plan B therefore examined the different transition phases of Bitcoin. He argues that the US dollar has also gone through several phases of transition, namely:

  • The gold dollar coin
  • The silver dollar coin
  • The paper dollar bills until 1970 (backed by gold through Central Bank)
  • The paper dollar bills after 1970 (no longer backed by gold)

In line with this, Plan B has also defined a number of different transition phases for Bitcoin.

Bitcoin’s transition phases within the S2FX model

Following the same line of thought, Plan B once took a critical look at Bitcoin’s development. Even though Bitcoin is still the same in terms of code and software, things have certainly changed about the phases Bitcoin has been in.

Plan B has defined and used the following transition phases in the Bitcoin S2FX model:

  • E-cash proof of concept (from white paper)
  • Payments (from when payments could be made)
  • E-gold (when Bitcoin was worth 1 ounce of gold)
  • Financial asset (the moment Bitcoin became accepted on a global scale after the 2nd halving)

As you can see in Figure 3, the different points lay neatly along the rising trendline of the S2F ratio. According to Plan B, however, it is more sensible and correct to speak of different clusters. He has plotted the data from the S2F model in another overview.

Image 6: The S2F ratio and price in one overview. (Source)

The Bitcoin clusters within the S2FX model

If you look at image 6, with a bit of good will you can easily make 4 clusters out of it. The second, third and fourth cluster in particular are relatively clear in terms of points.

Plan B then came up with the idea of ​​using a generic algorithm to determine exactly where the epicenter of Bitcoin’s four transition phases would be. As you probably guessed, they actually fall pretty neatly into the clusters:

Image 7: The four different Bitcoin clusters plotted in the grid model of S2FX. (Source)

To reinforce the four points that are now defined as clusters within the S2FX model, Plan B has chosen to also add the points of both gold and silver to the diagram. As you can see in the image below, they are also beautifully aligned with the S2F ratio. And suddenly the Bitcoin S2F Cross Asset Model (S2FX model) was born:

Image 8: The four Bitcoin clusters expanded with gold and silver data points. (Source)

In the last diagram, a regression test is also applied based on the S2F ratios of gold and silver, bringing the total number of data points of the S2FX model to six points.

Again, critics wonder whether the amount of data is conclusive enough to be able to say with certainty that this model corresponds to reality. At the same time, there are a number of historical points where reality matched the model very closely.

According to Plan B itself, the probability that 6 random data points will fall on a line exactly this way is less than 99.7%, he said on Twitter.


As mentioned, there are always fans and opponents of a wide variety of subjects, and the Stock-To-Flow principle is no exception. There is also more than enough to say about the Stock To Flow Cross Asset model. In particular, the only six data points ensure that the haters have more than enough material to express their displeasure with.

However, it is not all hot air. On the contrary. Many data points have already been established at individual moments that are completely in line with the S2F ratios. And of course it is very good news for many of us if the S2FX model turns out to be correct. The prediction is that in a relatively short period of about 4 years the price of Bitcoin can grow to $228,000.

And let’s face it, a price of $228,000 per Bitcoin that can only make everyone’s mouth water today. Of course, a lot can also change on the demand side. Lawsuits, the massive rejection of crypto as a means of payment, the legal closing of crypto exchanges and countless other reasons can be argued why Bitcoin can also die a silent death in the future despite all its potential.

But one thing is now certain: Bitcoin has more name recognition today than ever before. And additionally: After today only more and more people will come into contact with Bitcoin. Whatever the future holds and whatever role the S2F model or the S2Fx model plays in Bitcoin price predictions, we can all agree that Bitcoin’s journey is one in a million!

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