Stock-to-flow (S2F)

What stock-to-flow is

Stock-to-flow = stock ÷ flow. Stock is everything already in existence; flow is new production per year. The inverse, flow ÷ stock, is the yearly supply growth rate, so an S2F of 100 means supply grows about 1% a year. Saifedean Ammous used the ratio in The Bitcoin Standard (2018) to explain why gold held a monetary role, and PlanB built his model on it (PlanB, 2019).

Gold and silver, as cited by PlanB: his 2019 article gives gold an S2F of 62 and silver 22. His 2020 follow-up uses figures from Jan Nieuwenhuijs instead: gold 58.3 and silver 33.3 (PlanB, 2020). The silver figure moved by half just from a different estimate of above-ground stock, which shows how uncertain metal stock numbers are. We did not find an independent primary source to update them, so we quote them only as PlanB's inputs.

The numbers from the issuance math

Bitcoin's block subsidy started at 50 BTC and halves every 210,000 blocks (GetBlockSubsidy). At 10-minute blocks a year has about 52,596 blocks, so yearly flow and the ratio one year after each halving follow directly:

These are ideal 10-minute-block figures. Real blocks have come slightly faster than 10 minutes on average while hashrate grew, so actual yearly flow runs a little higher and the measured ratio a little lower. The table ignores lost coins and the few coins that were never spendable or never claimed, which PlanB handled by dropping the first million coins from his stock.

PlanB's model (2019) and S2FX (2020)

• In March 2019 PlanB fitted monthly data from Dec 2009 to Feb 2019 (111 points) and reported ln(market value) = 3.3 × ln(SF) + 14.6, with R² of 95%. He projected a $1 trillion market value, about $55,000 per coin, after the May 2020 halving, calling it “a great out of sample test” (PlanB, 2019).
• In April 2020 he published S2FX, which drops time, groups bitcoin's history into four “phases” and adds silver and gold to fit one line across six points (R² 99.7%). It put bitcoin's next phase at about $5.5 trillion, or $288,000 per coin, and he noted it had “not yet been replicated and reviewed by others” (PlanB, 2020).

Critiques, and PlanB's response

• The 2021 projections missed. In June 2021 PlanB posted a “worst case” path of above $98,000 for the November close and above $135,000 for December. November closed near $57,000; he called it the floor model's first miss and said S2F was “on track to $100K” (Cointelegraph). Bitcoin ended 2021 well under $100,000. On Dec 24, 2021 he wrote that his earlier statement that S2F would be “invalidated” below $100,000 that December was “an ill attempt to clarify ‘$100K average this cycle’” and that the model remained intact (quoted by WazirX).
• Statistics: spurious regression and cointegration. Both log price and log S2F trend upward over time, and regressing one trending series on another can produce a high R² by coincidence. Nick (@btconometrics) set out to falsify the model in 2019 and, using an ARDL test, concluded the relationship was not spurious (Nick, 2019). Marcel Burger later withdrew his own earlier cointegration finding: once the deterministic halving steps are accounted for, S2F behaves as a stationary series while price does not, so cointegration “is impossible” and the relationship can no longer be shown to be non-spurious (Burger, 2020).
• S2F is mostly a clock. Because the ratio follows a fixed schedule, it rises with time almost no matter what happens. A 2024 peer-reviewed study found S2F estimates had an 80.6% correlation with the log of time since the genesis block, lost significance once time effects were controlled for, and had little to no out-of-sample ability to predict returns (Shelton, 2024).
• Demand is not in the model. Scarcity alone does not set a price; buyers do. PlanB agreed: “the model only accounts for scarcity/s2f-ratio, that is the only model input. All the rest, demand, macro, crypto, covid, war etc, causes deviation. The model is VERY rough” (quoted by Cointelegraph).
• Certainty is the risk. In June 2022 Vitalik Buterin wrote that models giving “a false sense of certainty” are harmful. PlanB replied that the model “certainly had a good run from Mar2019 (BTC 4K) to Mar2022 (BTC 45K)” and that “either BTC is extremely undervalued and will bounce back soon, or S2F will be less useful in the future” (Cointelegraph).
• Few data points. S2FX fits six points, four of which are clusters picked from bitcoin's own history, which PlanB acknowledged as a small sample (PlanB, 2020).

How it relates to supply and the power law

S2F is a different view of the same supply schedule: the supply page shows the new-supply rate per year, and S2F is 1 divided by that rate. The power-law model fits price against time since the genesis block. Since S2F itself tracks time so closely, both models end up describing a price trend over time, and both share the same weakness: a fit to the past is not a mechanism for the future. See also market indicators.

Disclaimer

Educational content only. Nothing here is investment, tax or legal advice, and no figure on this page is a price prediction. Models can fail at any time.