Three layers
When you open the main chart, you are looking at three different things that only look comparable because they share the same axes:
- Historical BTC/USD — a time series of market prices (log scale on the vertical axis when “Log” is selected).
- Model output — median path plus σ-bands derived from the selected model (Power Law, Stock-to-Flow, etc.).
- Live spot — the latest price fetched for “now,” shown as the orange marker on the current date.
The historical line answers: what did the market actually trade at? The bands answer: where does this model think price has spent most of its time, in log space? Those are related questions, but they are not the same object.
Why the vertical axis is usually logarithmic
Bitcoin’s price has moved from cents to tens of thousands of dollars. On a linear axis, the early years collapse into the bottom edge and the chart tells you almost nothing about long-run structure. On a log axis, multiplicative moves (e.g. “doubled” or “halved”) look like equal vertical steps. That is why power-law and similar models are often discussed in log₁₀(price) space: it matches how people reason about percentage changes over many orders of magnitude.
Switch to linear scale only when you deliberately want to emphasise short-term dollar moves near the top of the range—knowing that the left side of the chart will look flat.
How to interpret the σ-bands
The coloured corridor is not a price guarantee. In typical use, it is a visualisation of dispersion around the model’s central line: the median is the model’s “best single line,” and the bands show how far price has historically wandered above and below that line in log space (when σ is assumed stationary).
If spot is near the median, the market is close to the model’s central estimate for that date. If spot is near the upper or lower band, you are looking at a regime that the model treats as more extreme relative to its own history—still not a forecast of reversal, only a measure of where you are inside the corridor.
What “actual” means in the tooltip
As you move the cursor, the tooltip shows model bands at the hovered year and an interpolated approximation of historical price along the sampled series. That is useful for eyeballing how far the market was from the model at a given time—but it is still a model vs market comparison, not a trading signal.
What this chart is not
- It is not proof that price must return to the median.
- It is not a substitute for risk management, fees, liquidity, or your own time horizon.
- It is not a single authoritative model: use the selector to compare frameworks, not to pick a favourite story and ignore uncertainty.
Practical takeaway
Use the chart to build intuition about scale, long-run structure, and how different models behave over decades. Use everything else—narrative, fundamentals, regulation, your personal situation—for decisions. The point of putting history and models on the same canvas is clarity, not certainty.