The Log Regression Band, explained

Formula

10^(a·ln t − b)

the shape of all four band lines

Bitcoin weight

11/100

in the Bitcoin Heatmeter composite

Ethereum weight

9/100

fitted to Ethereum, Ethereum Heatmeter

Fitted assets

2

Bitcoin (2009) and Ethereum (2014) only

A chart that plots an asset's price inside a channel of four fitted lines: a cycle-top pair above and a cycle-bottom pair below. Where price sits inside that channel becomes a 0–100 risk score, and a separate calculation on the same page also sorts price into one of six named valuation zones.

It's available for two assets, each fitted to its own history rather than sharing one universal curve: Bitcoin, anchored to its 2009-03-01 genesis, and Ethereum, anchored to its 2014-12-03 launch.

Every line on the chart follows the same shape: value = 10^(a·ln(t) − b), where t is the number of days since the asset launched, and a (how steeply the line climbs) and b (how high it starts) are settings fitted separately for each asset. Four lines, two pairs of settings:

For Bitcoin: the upper pair (cycle-top) uses a = 1.93 with b = 11.3 and 11.5; the lower pair (cycle-bottom) uses a = 2.5 with b = 16.9 and 17.1. For Ethereum: the upper pair uses a = 0.79 with b = 2.5 and 2.65; the lower pair uses a = 1.38 with b = 8 and 8.3.

One thing to know about the names: because the two pairs are fitted with different slopes, the lines are not guaranteed to keep their current order forever — far enough into the future, they can cross each other. That is a known limit of any model whose settings are fixed in advance.

The four band values for today's date are sorted from lowest to highest — by value, not by name, precisely because the lines can change places over time. Price at or below the lowest line scores 0. Price at or above the highest line scores 100. Anywhere in between, the score climbs smoothly, and only ever upward, as price passes each successive line.

That's an evenly divided scale, not one stretched to hug the extremes — the same design used on this platform's Rainbow Chart. A genuine cycle top can register well short of 100 rather than pinning at the ceiling, because reaching 100 requires price to be at or above the single highest fitted line, not merely "high."

The bands are fitted to cycle highs and lows that have already happened, which carries the structural risk any such model carries: a future cycle that sets a genuinely new high or low would sit outside what the current settings describe, until the fit is revisited. Ethereum's fit in particular rests on a shorter history — fewer completed cycles — than Bitcoin's.

Alongside the four fixed bands, the chart runs a completely independent calculation: one best-fit line drawn through every point in the price history, following the same shape of curve (log₁₀(price) = a·ln(days) − b) but with its two settings solved from the data rather than fixed in advance. That gives a single fair-value line, plus a measure of how far price typically strays from it — one standard deviation.

Today's distance from that fair-value line, counted in standard deviations, is the "signal sigma." It gets sorted into six named zones — Deep value, Undervalued / Accumulation, Fair value, Elevated, Overheated, and Euphoria / Cycle top — at fixed cut-points of −1.5, −0.5, 0.5, 1.5 and 2.5 standard deviations.

This is genuinely a second, independent measurement, not a relabeling of the first. The 0–100 risk score places price against the four fixed bands; the signal zone places price against a freshly fitted trend line and its own spread. The two usually agree in broad strokes, but they are not worked out from the same inputs and can diverge — and only the first one, the 0–100 risk score, is what feeds either heatmeter.

The band score asks "where does price sit inside four fixed lines?" The signal zone asks "how far is price from its own trend, by its own usual standards?" They live on the same chart and answer different questions.

Watch which zone price is in, not just the raw price. The chart also surfaces price's percentage distance to the fair-value line and the remaining upside to the cycle-top line — both derived from the same underlying fits described above, not separate calculations.

A reading near 100 has historically meant "near the cycle-top band," not "guaranteed peak." Because the scale is evenly divided across four lines rather than stretched to the extremes, the score can sit well short of 100 even during genuinely euphoric conditions.

The Log Regression Band is a weighted input to both cycle composites on this platform, not only a chart of its own. It carries a default weight of 11 / 100 in the Bitcoin Heatmeter and 9 / 100 in the Ethereum Heatmeter — among the higher weights in either 14-indicator roster — and in both cases the exact figure the composite uses is the 0–100 band-position risk score described above, not the signal zone.

On the Ethereum side it's also one of only five inputs that are Ethereum's own: measured on Ethereum's price history, rather than borrowed from Bitcoin's reading the way roughly half of that Heat Meter's other components are. We adjust those weights as the indicators are re-tested. In neither Heat Meter does this indicator alone decide the score; it's one voice, a comparatively loud one, in a panel of fourteen.

Others in price & cycle models — What price is doing relative to its own history, trend and long-run models.

• Rainbow ChartThe same long-run trend line drawn as nine coloured bands, from deep value to bubble territory.
• Golden Ratio MultiplierPrice against multiples of the 350-day moving average, a ladder that has caught intermediate cycle highs.
• 200-Week MA HeatmapHow far price sits above its 200-week average — a floor Bitcoin has only briefly traded under, at the deepest lows.
• MVRVWhat every Bitcoin is worth today against what it last changed hands for — a read on collective paper profit.
• Reserve RiskHow patient long-term holders are against the price they could sell at — cheap when they hold through a rally.

Every indicator we track — the full glossary.