Why No Two Rainbow Charts Agree

Open three Bitcoin rainbow charts and you will get three different answers. Not slightly different — different enough to disagree about which coloured band today belongs in. There is no standard rainbow chart, no published set of constants, and no authority to appeal to. Understanding why is most of what you need to read one sensibly.

The chart itself is simple. Take Bitcoin's price history, take the logarithm of both price and time, and fit a straight line through it. That line is the centre. Then draw bands at fixed offsets above and below, which is why they stay parallel on a log axis and fan out into enormous dollar ranges as the years pass. Colour them from blue at the bottom to red at the top, give them names, and you have the picture everybody screenshots.

Why no two versions agree

Every implementation makes four choices, and none of them are standardised.

What data to fit. Daily closes or monthly ones. Start at the genesis block, or at 2012, or at the first exchange price. Bitcoin's early data is sparse and wild; including or excluding 2010 visibly tilts the line.

Whether to refit. Some versions freeze their constants and leave them for years. Others recalculate on every load.

Where to put the bands. The offsets are chosen by eye. They are not derived from the data's spread, and nobody publishes a justification for them.

What to call the bands. "Fire sale", "HODL!", "Maximum bubble" are marketing, not measurements, and they were invented for one version and copied by the rest.

Blockchaincenter, where the chart originates, no longer publishes its coefficients at all. Its current version calculates the curve dynamically, fitted on daily prices since 2012, and explicitly abandons what it calls static formula snapshots. The only formula it ever published, back in 2014, was y = 2.9065·ln(x) − 19.493, which it now describes as outdated. So the canonical chart cannot be reproduced from anything it tells you, and the number most often quoted as "the rainbow formula" is one the source itself has retired.

There is no reference implementation. Every rainbow chart is somebody's fit, and almost none of them show you the fit.

The dilemma at the centre of it

The freeze-or-refit choice is not a detail. It determines what the chart can honestly claim, and both options cost you something real.

A frozen line drifts. Fitted once and left alone, it keeps climbing its own curve while price keeps arriving underneath, and the gap compounds silently. Nothing on the chart tells you it is happening. Old constants therefore tend to read too high: they promise a fair value the data stopped supporting years ago.

A live-refitted line has the opposite flaw, and it is stranger. It rewrites its own history. We tested this on Bitcoin's lowest monthly close of 2015 — $227, in May. Fitted on the 59 monthly closes that existed at that moment, the model grades that price at 0.27× the centre line: an extreme, once-in-a-cycle reading. Fitted on the full history available today, the very same close grades at 0.50× — low, but unremarkable.

Same price, same date, graded nearly twice as far apart, with nothing changing except when the curve was drawn. A continuously refitting rainbow cannot tell you what a past price meant, because its past keeps moving. That is why screenshots of rainbow charts from previous cycles rarely match what the same chart shows for those dates today.

How wide the bands really are

Here is the number almost no version of the chart shows you: the spread of the data around its own line. Fitted on 195 monthly closes, the residual standard deviation is 0.31 in log10 units.

In plain terms, the ordinary condition of this market is to sit roughly a factor of two away from the centre, in either direction. Not as an extreme — as normal. Any reading of the rainbow that treats a position two-thirds of the way up as meaningful precision is reading noise as signal.

That single statistic reframes the whole chart. It is not a price target with coloured error bars. It is a very wide distribution with a line through the middle of it.

What the band names actually contain

The labels imply rarity. The data does not agree. Measured across 195 monthly closes since July 2010:

• Buy! is the single most crowded band in Bitcoin's history, holding 22.6% of all months.
• Accumulate holds 17.4%; Still cheap 12.8%.
• The bottom three bands together account for 51% of Bitcoin's entire monthly record.
• Fire sale, named for a once-in-a-generation event, contains 11.3% — about one month in nine.
• Maximum bubble contains 4.6%.

A band describing one month in nine is not describing a fire sale. And the edges are lopsided in a way that is invisible on the picture: measured against the residual spread, the bottom edge sits at −1.03 standard deviations while the top sits at +2.75. Two edges named for opposite extremes, one of them nearly three times further out than the other.

This is what happens when band positions are chosen to look right rather than derived from the distribution. It does not make the chart useless. It does mean the names carry no statistical weight whatsoever.

What it is good for

Stripped of the colours and the slogans, the rainbow answers one question honestly: how far is price from its long-run logarithmic trend, in which direction, and how unusual is that historically? That is a genuinely useful thing to know, and hard to eyeball from a normal price chart.

What it cannot do is forecast. The model has no knowledge of halvings, ETF flows, interest rates or anything else that actually moves the price. It is a line through a scatter plot of past prices, extended forward on the assumption that the future resembles the past at the same rate. The bands are not predictions and the labels are not advice.

Three habits make it safe to use. Check whether the version you are looking at states its fit and its date — if it does not, you cannot know how stale it is. Treat a factor-of-two deviation as ordinary. And never compare a reading from one site to a reading from another, because they are different models wearing the same colours. Our live rainbow chart publishes its constants and the date they were fitted, so you can check the line rather than trust it.

Frequently asked questions

How is the Bitcoin Rainbow Chart calculated? A logarithmic regression of price against time: log10(price) = a × log10(days since the genesis block) + b. Coloured bands sit at fixed offsets in log space above and below that line, so each band is a constant multiple of the centre. The values of a and b differ between implementations, and most sites do not publish them.

Why do rainbow charts show different values? Because there is no standard. Versions differ in what data they fit, whether they refit continuously or stay frozen, and where the band edges sit. Blockchaincenter, the original, refits dynamically on daily data since 2012 and does not publish its coefficients; its 2014 formula is retired. Two charts can put the same day in different bands and both be internally consistent.

Is the Bitcoin Rainbow Chart reliable? As a measure of distance from a long-term trend, yes, within wide limits: the residual spread is 0.31 in log10 units, so being a factor of two from the centre is ordinary rather than exceptional. As a forecast or a buy signal, no. The band names imply rarity that the data does not support — the bottom three bands cover 51% of Bitcoin's monthly history.

Related reading: Are We There Yet? on a valuation model that is calibrated against its own distribution, and Bitcoin's 4-Year Cycle and the Halving on the pattern the rainbow is most often used to confirm.

Statistics computed on 21 September 2026 from 195 monthly Bitcoin closes, July 2010 onward. Band occupancy and the residual spread use the fit published on the BTCDash rainbow page (a = 5.6652, b = −16.4283); other implementations will give different figures, which is the point of the article.