Stock-to-Flow: a useful idea and a broken model

S2F is two things — keep them separate

(a) The S2F ratio. Stock divided by new annual production. Pure math, applies to any commodity. Bitcoin's ratio is well-defined, public, and doubles every halving. Nothing wrong with it.

(b) The S2F price model. A 2019 paper by an analyst writing as PlanB fit Bitcoin's price to its S2F ratio. It looked great in 2020. It hasn't tracked since 2022 and currently predicts Bitcoin should be ~10× higher than it actually is.

Most demos teach (b) without ever flagging that it broke. We'll do (a) properly, then look at (b) honestly — alongside a different model that's still holding up. The point isn't to pick a winner. It's to learn how to evaluate models that look convincing.

Halving timeline — the math and the history, kept apart

Each row shows the S2F ratio at that halving (a math fact) and what Bitcoin's price did in that era (a history fact). They are not the same thing. Halving schedules have been public since 2009, so any halving-driven move on the announcement date itself is at most a partial surprise — the schedule is already in everyone's spreadsheet.

Two models, two fates

In March 2019, an analyst writing as PlanB fit Bitcoin's market value to its S2F ratio with a power-law regression. The fit was stunning in-sample: ln(market value) = 3.3 × ln(SF) + 14.6 with R² ≈ 95%. The model became famous and informed a generation of price predictions.

In 2019, a different researcher (Harold Burger) fit Bitcoin's price to time instead of S2F: price = 10^(-17.0159 + 5.8451 × log₁₀(d)) where d is days since the genesis block. Same kind of math (power law in log-log space), completely different independent variable.

Both fit the data through 2020. The chart below shows how each one has done since — against actual price.

Why one broke and the other (so far) hasn't

PlanB's S2F model assumes scarcity drives price. But:

• It's a one-variable model of a multi-driver system. Bitcoin's price is also moved by interest rates, ETF flows, regulatory regime, narrative cycles, and global liquidity. A single supply-side variable can't capture that.
• It was fit to ~10 years of history and projected as a law. No out-of-sample validation. When BitMEX Research reproduced it in 2020, they showed the apparent strength of the fit was driven by the shared upward trend of both variables — a known statistical pitfall (Falsifying Stock-to-Flow).
• Halving schedules have been public since 2009. Markets price in known information. Post-halving "rallies" are at most partial surprises around an expectations-resolution event, not pure scarcity-driven moves.

Burger's Power Law uses time as its only variable. That's also fragile, but:

• It allows a corridor, not a single line. Bitcoin spends roughly equal time above and below the central trend, within a factor of ~2–3.
• It survived 2022. S2F predicted ~$100k–$288k by end-2021 and didn't recover. The Power Law sat much lower and stayed inside its band.
• It still might break. The next halving cycle is its real test. The point isn't that this model is right — it's that as of today, evidence hasn't broken it.

The skill being practiced here isn't picking a winner. It's the discipline of continuing to test models against new data and stopping trust in the ones that diverge.

Comparing to other assets — six properties, no winners

"Hardness" is too vague to be useful. Below are six concrete properties of money. Different assets win on different ones; no asset wins on all of them. There's no overall verdict — that depends on what you're using money for.

Honest read: gold beats Bitcoin on durability and 5,000-year track record. Bitcoin beats gold on portability, divisibility, and verifiability. Fiat beats both on day-to-day liquidity at the cost of supply discipline. There's no asset that wins on every property — that's why money has always been a portfolio question.