You don’t need S2F to value Bitcoin

In 2019, PlanB published his Stock-to-Flow model for the Bitcoin price. This model essentially takes the following inputs:

  • The Bitcoin supply, which overall is fixed, but is componentized into “stock”, the existing mined supply, and “flow”, the supply yet to be mined.
  • The Bitcoin block reward schedule, which halves every four years, and dictates the future mining rate of Bitcoin for the next century.
  • The prior Bitcoin price, in the years since its public release in 2009.

Using these inputs, S2F uses a linear regression to model the future price of Bitcoin. In a nutshell, the model essentially says:

As the supply of Bitcoin diminishes over time, if Bitcoin’s price follows a similar trajectory to prior years, that price will increase in a way that is directly correlated to the diminishing newly mined supply.

The primary argument for the veracity of this model is that since it was created in 2019, it has been very accurate in predicting the price trend of Bitcoin.

I do believe Bitcoin will increase in value — but not as a direct result of the halving schedule. I believe its price will reflect its ever-increasing levels of adoption. A such, I think S2F doesn’t provide a lot of value in terms of explanatory or predictive power. Here’s why.

Demand is variable

The first, obvious argument is: how can you possibly predict the price of an asset using only the available supply (and future available supply) as a variable, but not treating demand as a variable?

The price of anything: stocks, equities, bonds, real estate, Pokémon cards are based on both supply and demand.

If the demand drops to zero the price will drop, as more and more people try to sell but find no buyers. If the supply increases to infinity, the price will drop, as buyers have a huge market to choose from.

Let’s say tomorrow, one of these two things happens:

  1. The US and EU proclaim “we will introduce legislation to ban bitcoin”, or
  2. The US and EU proclaim “we will start buying bitcoin as a treasury reserve asset”

The first would potentially dramatically reduce the demand for Bitcoin. The second would dramatically increase the demand. Either event would probably move the price of Bitcoin outside of the predictions made by the S2F model.

These are black swan events

In fairness, the likelihood of the US or EU banning or adopting Bitcoin in the short term is slim, and of course no model can be designed to take these kinds of events into account, so it’s fair to say that is too high a standard to hold the S2F model to.

That notwithstanding: it is clear that without increased adoption and demand, it is not possible for any asset to increase in price, including Bitcoin.

What this means is, even though demand is not an explicit variable in the S2F model, the model has no choice but to implicitly assume a consistent increase in demand over future years. Without this increased demand, the Bitcoin price inevitably either flattens off, or trends towards zero.

So it is probably more fair to define S2F as predicting the following:

As the supply of Bitcoin diminishes over time, if Bitcoin’s price follows a similar trajectory to prior years, and if the demand consistently increases as it has in prior years, that price will increase in a way that is correlated to the diminishing newly mined supply.

So it’s probably not fair to say “S2F ignores demand”. It implicitly assumes demand.

That said: I believe it’s a mistake to treat demand as implicit. Demand for Bitcoin will continue be an extremely variable factor; as it is for other assets, and as it has been for Bitcoin, demonstrated by its volatility so far.

Of course we all hope the demand for Bitcoin will continue to go up. But is there any good reason to believe the demand will increase in lockstep with the halving schedule? And what happens at the point when the demand comes into equilibrium with available supply on the market?

S2F could be causing demand!

Yes, knowing about the S2F model could be causing people to buy Bitcoin in anticipation of the predicted price, and sell when the price exceeds the S2F prediction.

However: that is circular reasoning, and does not provide evidence that the Bitcoin price is actually a function of future mined supply.

Saying “Bitcoin’s price trajectory is caused by the predictions of S2F” is entirely different than saying “Bitcoin’s price trajectory is caused by diminishing supply”, which is the actual claim made by S2F. The S2F model itself does not claim to be a model based on a self-fulfilling prophecy.

Moreover, on a more pragmatic note, if S2F itself is actually being front-run by the market, don’t you think some of those big institutional investors would have brought the model up as one of the reasons they chose to buy Bitcoin?

Ultimately, if you argue that S2F actually causes demand, you also have to acknowledge that demand is the primary driver of the price trajectory, not supply. So by making this argument, S2F proponents are arguably hoisted by their own petard.

But it’s programmed!

Yes, the supply is programmed.

You know what is typically priced in? Anything that is programmed and known ahead of time. Including supply, since the mined supply and halving schedule for Bitcoin is known to an extremely high degree of accuracy.

You know what is not typically priced in? Anything that is not known ahead of time. Including demand, since there is no way to predict ahead of time exactly how many investors and institutions will buy in to Bitcoin, and to what degree.

There is a reason the Bitcoin price spiked when Tesla made their first purchase, and that reason has nothing do to with any sudden changes in supply. It caused a sudden spike in demand that no model could predict.

This principle is known as the Efficient Market Hypothesis, and Nic Carter does a fantastic job explaining how it applies to Bitcoin.

But the market isn’t totally efficient!

PlanB has also published an article arguing that EMH does not refute the S2F model.

This article’s main thesis is that Bitcoin’s risk is vastly overestimated, which leaves room for error and inefficiency in the market. For what it’s worth: I agree with PlanB here. I think Bitcoin is a whole lot less risky than the market assumes, and that is one of the factors holding back the price. Over time, as Bitcoin proves its stability, the market’s assumptions about risk will change, and that will be reflected in the price. There is no way to prove that Bitcoin is stable and safe over time, without waiting for time to pass.

That said, I struggle to see how this risk based argument has any bearing on the S2F model. If the market overestimates risk, then it is “risk” not “supply” that is the unknown future data point, and as the market better understands that risk, the price is likely to reflect that knew knowledge and understanding.

Risk is not shown to correlate with the reward schedule, nor is there any causal argument made that “lower block reward results in lower risk”.

As such this seems to be a case of a great argument for how Bitcoin’s price will evolve, that happens to be totally orthogonal to the S2F debate, and does not refute how EMH factors in to the reward schedule.

But the market is based on emotion!

Of course, human psychology and emotion both play a large role in Bitcoin price fluctuations. There are frequent examples of investors experiencing “FOMO” and buying in, so as not to miss the boat on what they think could be a great investment, without dollar-cost-averaging or assessing the current froth in the market or other factors.

This doesn’t refute Efficient Market Hypothesis either. EMH just says “all things which are widely publicly known, are by definition priced in”.

EMH can not, of course, explain the number of people experiencing FOMO or making emotional decisions about investing or trading. By definition, that counts as “new information”, which is surfaced directly as information in the price action of any asset, or indirectly in public forums and media.

So: EMH is mainly useful for telling us the effect of existing information, it offers very little help for what effect new information will surface in future.

In the Bitcoin world, the halving schedule is still very much ‘existing information’. What is ‘new information’ is the emotional and psychological effect each halving will have. That new information is impossible to predict. If it could be accurately predicted, according to EMH it would also be priced in.

That new information (future investor psychology and emotion) is also not a function of the existing information (the halving schedule). You can make an educated guess and say “each time the Bitcoin rewards halve, people will emotionally view it as more scarce, and ape in”. But this is a big assumption, and relies on:

  • Human emotions/psychology being constant and unchanging over time.
  • Emotional retail investors being the main controlling force in the market, even as institutions role in.

These are big assumptions to make, especially when forecasting the price of an asset and making financial decisions.

Only Bitcoin can be scarce

It’s trivial to fork Bitcoin’s codebase and create a new coin. Many have done this, and many of the popular cryptocurrencies out there today are forks of Bitcoin.

You can change the rules to make these coins as scarce as you like. You could introduce a fixed cap of only 10 coins, as opposed to the Bitcoin cap of 21 million. You could halve the mineable supply every one year, rather than every four.

None of these guarantee the price of your coin will increase. The reason is, there is no guarantee that there will be any actual demand for your coin — or if there is any demand, there is no guarantee that demand will continue to grow consistently year over year.

But Bitcoin was first!

It has been argued by some that S2F works only for Bitcoin, but not other cryptocurrencies, because Bitcoin was the first and best digital asset to create decentralized scarcity.

This sounds like a semi-plausible argument, until you ask: why would Bitcoin being first or best, lock Bitcoin’s price trajectory into an unchanging function of future mined supply? What is the relationship?

On the demand side, it’s easy to argue how these two factors have a credible impact:

  • Being first enables Bitcoin’s first-mover advantage, which in turn enables higher demand. More people are familiar with the product, more people want to buy it.
  • Being best, means that more people are willing to bet on Bitcoin’s future success, by buying in and hoping for a future return as the rest of the market realizes the same fact.

On the supply side, there is a much less obvious causal link.

But Bitcoin is fundamentally better!

It can also be argued that no alt-coin matches Bitcoin in terms of its hash-rate, lack of pre-mine, lack of centralized control, and other extremely positive qualities that the market uses to assess its value.

This is arguably true. But again: these qualities are all either:

a) Known ahead of time (the lack of pre-mine, and lack of centralized control, are both immutable facts) and thus subject to efficient-market-hypothesis.

b) A function of demand (e.g. hash-rate, which usually increases as the price of Bitcoin increases), and thus is variable and unpredictable, and unlikely to follow in lock-step a model whose sole variable is supply.

S2F has been accurate since 2010

No, S2F has been accurate since 2019. All of the existing data is based on a linear regression. The trend line is literally designed to fit the existing price chart for the previous ten years.

S2F has been accurate since 2019

The price of Bitcoin since 2019 has never diverged more than one standard deviation from the S2F chart.

This sounds impressive, but in reality one standard deviation is a $40,000 wide margin. Until extremely recently, Bitcoin’s price had barely crossed that amount.

This essentially means that so long as the Bitcoin price continues to go up for any reason in the years following a halving event, the S2F model will remain reasonably accurate to within one standard deviation, in line with other “Number Go Up” models.

Two years is also a reasonably small amount of time, and it will of course be interesting to see how long this purported accuracy lasts in future. Regardless, it will be difficult for Bitcoin to break out of those huge error margins so long as the price continues to increase at any rate.

But there is a correlation

Well, sure, but as Nick Emblow argues succinctly, it is not difficult to create an even better model than S2F, with more of a statistically significant correlation. Nick also dives into the topic of ‘cointegration’ and demonstrates that it is not a valid test when applied to a static pre-determined variable like Bitcoin’s block reward schedule (which is the variable that dictates the S2F ratio).

I’m not a statistician, so I won’t try to embellish these points; Nick’s article speaks perfectly for itself.

S2F is the only accurate model

Actually the Bitcoin Rainbow Chart popularized by Eric Wall is pretty accurate too — albeit, also pretty silly.

That chart is based around the idea that the Bitcoin price follows the trajectory of a rainbow, and that the current color of the rainbow indicates whether we’re near a market bottom or a market top, with handy “HODL!” and “SELL!” labels.

Does the accuracy of this chart prove that the Bitcoin price is likely to always follow the shape of a rainbow? Probably not. Similarly, S2F being accurate, does not provide any real evidence that Bitcoin’s price trajectory must follow the diminishing supply, as we progress through each future halving schedule.

It has been argued that the Rainbow Chart, or any other “Number Go Up” style of model which follows a time series, is inherently misleading, because those models do not take supply and halving schedule into account, as the S2F model does.

In my view, this is a form of begging the question or circular reasoning, since by making this argument you are essentially arguing for the following two points:

  1. That S2F forms an accurate model, because it takes supply and halving into account, and
  2. That supply and halving should be taken into account, because S2F demonstrates that it results in an accurate model.

The first proves the second, and the second proves the first. This avoids coming up with a fundamental causal reason for either.

Isn’t it a pretty big coincidence though?

Yes, if there was a single Bitcoin price prediction model, and it happened to be accurate, we would all be scratching our heads wondering how it could be so mysteriously coincidentally accurate, without there being some truth to it.

In reality, there have been many Bitcoin price models created over the years. Survivorship Bias explains why people only tend to focus on the more recent successful models, or on the models which turned out to be accurate in the longer term.

If you’re terrible at darts, but you throw a dart at a dartboard 100 times, eventually you will hit a bullseye. It is very possible S2F achieves the same result as that winning dart, and the conclusion we are drawing is “this guy must be great at playing darts!”, analogous to “the supply and halving schedule must be the primary driver of Bitcoin’s price trajectory!”.

But the miners could be setting the price, right?

The block reward right now is 6.25 bitcoins per block. That ends up being approximately 900 bitcoins per day.

The Bitcoin trading volume has swung between 20,000 to 100,000 bitcoins per day over the last month.

Assume the volume is a conservative 20,000 bitcoins per day. That means that less than 5% of the daily trade volume could be miners selling freshly minted bitcoins.

And yet, the S2F argument implies that that 5% of daily volume must be responsible for 100% of the price trajectory of Bitcoin, and it will continue to do so for the foreseeable future no matter what tiny percentage of the trading volume can be attributed to the diminishing block reward.

In reality, the only “supply-shock” that actually has a chance of moving the market, is that caused by more and more investors and institutions hoarding and hodling their Bitcoins, and refusing to sell. That population can easily sway 95% of the daily volume and resulting price trajectory and volatility, by deciding on any given day to hold or sell.

Can supply be manipulated?

A fun hypothetical question posed by Eric Wall is this:

If the supply dictates the price, and the miners control the supply, could miners form a cabal (or agree to a soft-fork) which accelerates the halving schedule or burns a fixed percentage of all newly mined coins in each block?

Of course they could.

Would this cause the price to accelerate upwards in line with future S2F predictions, based on the future supply and halving schedule?

Obviously not: the market would tank, since investors would feel less secure about the sanctity and immutability of the rules upheld by the Bitcoin network.

In other words: changing the rules of Bitcoin would decrease the demand, which would in turn decrease the price. The change in demand would be a large factor, the change in supply would not be enough to offset that in any meaningful way.


The summary of these arguments is:

  • Demand, not supply, is the the crucial thing to consider when attempting to predict Bitcoin’s price trajectory.
  • Supply is pre-defined and static, demand is variable and unpredictable, even ignoring black-swan events.
  • If S2F is itself causing demand, that offers no proof for the validity of the underlying S2F reasoning.
  • The efficient market hypothesis dictates that anything known ahead of time, including the Bitcoin reward schedule, must be priced in.
  • Risk is something which may not be known fully by the market, and may not be priced in, but this is orthogonal to S2F
  • Emotions and psychology are also difficult to anticipate, and also can not be predicted. These are also orthogonal to S2F
  • Bitcoin is not the only asset which can be scarce, so scarcity can not be the factor which makes S2F apply to it and no other coin.
  • Being ‘first’ or ‘best’ are more likely to be drivers of price appreciation. But these have more to do with demand, than with supply.
  • Being accurate since 2010 isn’t a selling point for a model derived as a linear regression
  • Being accurate since 2019 isn’t a selling point when other models can easily achieve the same, and when the error margins are so large.
  • Survivorship bias is a real thing, and can not be discounted for S2F
  • It is unlikely miners could be setting the price based on current newly mined supply, since they make up such a small amount of the trading volume.
  • Even if you could tweak supply and make it variable or reduce it ahead of schedule, it is unlikely the Bitcoin price would follow in lockstep.

As a final word, here’s my view. You don’t need to believe the price of Bitcoin is pre-programmed, to believe that Bitcoin is awesome. Bitcoin is an incredible technology that is seeing unheard-of adoption, and will likely take over a larger chunk of the financial world than many people anticipate.

Believing that the Bitcoin price is a function of adoption is, in fact, the optimistic view: it means that the price is not going up for an arbitrary reason, but instead because Bitcoin is providing real world value to many individuals and institutions.

This is a good thing!





works for PayPal, as a lead engineer in Checkout. Opinions expressed herein belong to him and not his employer.

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Daniel Brain

Daniel Brain

works for PayPal, as a lead engineer in Checkout. Opinions expressed herein belong to him and not his employer.

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