Ethereum logarithmic regression bands (AUD)

Ethereum log regression historical extremes

Where does Ethereum sit on the log regression today?

ETH currently sits at +0.18 sigma above the long-run fair-value line - essentially on the regression line itself, well inside the central band (-0.5σ to +0.5σ). At A$6,769 vs a fair value of A$5,885, ETH trades about 15 percent above regression but the sigma reading is firmly neutral. For cycle-positioning context: the 2017 ETH cycle peaked at +2.74σ (January 2018), the 2021 cycle peaked around +1.7σ. ETH would need to roughly double from current levels to approach historical "overheated" zones.

How does the Ethereum regression compare to Bitcoin's?

• ETH slope: 2.38. BTC slope: 5.71. ETH's lower slope reflects later start (2015 vs 2009) and protocol-level supply changes (the Merge, EIP-1559 burn) that have flattened the long-run growth curve.
• ETH residual sigma: 0.34. BTC residual sigma: 0.25. ETH's wider residual scatter reflects shorter history and higher volatility relative to trend.
• ETH cycle alignment: ETH's cycle tops/bottoms align directionally with BTC's but with bigger sigma extremes. ETH overshoots BTC's regression bands at peaks AND at bottoms.
• Practical use: ETH log regression confirms broader crypto-cycle direction but is less precise for ETH-specific timing than BTC's regression is for BTC.

What is logarithmic regression?

Ethereum's price has appreciated by roughly four orders of magnitude since launch in mid-2015 (from cents to thousands of USD at the cycle peaks). A linear chart of this history is unreadable: the early years compress to a flat line at zero, and recent moves look like vertical spikes. The fix is the logarithmic transformation.

Transform both axes: take the log10 of price (so 10x price moves become equal vertical distances) and take the log10 of time since the Ethereum genesis (30 July 2015, the Frontier release). In this transformed space, Ethereum's long-run growth becomes nearly a straight line. That straight line is the logarithmic regression.

The mathematical interpretation is that Ethereum's price has grown according to a power law in time: price ≈ k × t^n, where t is days since the genesis block and n is the slope of the regression line. The intercept k is determined by where on the line Ethereum started. Both parameters are estimated from the fit.

Ethereum's slope is typically 2.5 to 3.5 over the full history (compared to Bitcoin's 5.5 to 6 over its longer history). The lower slope reflects Ethereum's later starting point, the decelerating growth rate of the broader crypto market post-2021, and the supply changes from the EIP-1559 fee burn and the proof-of-stake merge.

How to read the bands

Five visual elements (identical pattern to the BTC log regression chart):

• Central regression line (solid gold). The long-run fair value of Ethereum in AUD at each point in time. The slope of this line is the long-run growth rate.
• ±1σ bands (dashed yellow/green). One standard deviation above and below the central line. Roughly 68 percent of historical monthly close prices have been within this band.
• ±2σ bands (dashed red/dark green). Two standard deviations above and below. Roughly 95 percent of monthly closes are within this band. The +2σ zone is the historical overheated band; the -2σ zone is the historical undervalued band.
• Gold dots. Each dot is a monthly close. Their distribution shows where Ethereum has actually traded relative to the regression line.
• White circle. The most recent monthly close. Shows where Ethereum sits today on the regression bands.

Practical interpretation:

• Ethereum above +2σ: historically rare. The most extreme was the December 2017 to January 2018 ICO bubble, where ETH traded multiple sigmas above the regression line for a sustained period before the 90+ percent drawdown of 2018.
• Ethereum below -2σ: historically rare. Has preceded cycle bottoms (2018-2019 and 2022).
• Ethereum near the central line: historical centre of the cycle range. No strong directional bias from the model.
• The model identifies HISTORICALLY RARE ZONES, not specific peak or bottom dates.

Why the ETH regression slope differs from BTC

The Bitcoin log regression slope is typically 5.5 to 6 over the full 2009-onwards history. The Ethereum log regression slope is typically 2.5 to 3.5 over the 2015-onwards history. The two should not be directly compared in absolute terms because the time windows are different (Bitcoin has nearly twice as many years of data), but the underlying gap is real and reflects three structural differences:

• Different starting points in the adoption curve. Bitcoin's regression captures the steepest early-growth phase (2010-2014, where Bitcoin grew from cents to hundreds of dollars). Ethereum's regression starts at a later point in its own equivalent adoption phase, where the growth rate is already decelerating.
• Supply economics. Bitcoin's supply growth halves every 4 years (the halving). Ethereum's supply economics changed in 2021 with EIP-1559 (fee burn) and in 2022 with the proof-of-stake merge (no new issuance from proof of work). These changes have meaningfully altered Ethereum's net issuance, but in ways that are difficult to back-fit to a single regression slope.
• Cycle structure differences. Ethereum's 2017-2018 ICO bubble was a much larger overshoot relative to fair value than Bitcoin's equivalent peak, which produces a larger residual sigma. Ethereum's 2022 bottom drew down further than Bitcoin's. The bands are wider on the ETH chart as a result.

The practical implication: a +1σ deviation on Ethereum represents a smaller multiplier on fair value than a +1σ deviation on Bitcoin (because Ethereum's sigma is larger in absolute log terms). When comparing the two charts side by side, focus on the sigma deviation, not the slope itself.

Methodology

The regression is computed with standard ordinary least squares on the transformed coordinates:

1. For each monthly close in AUD, compute (log10(days since Ethereum genesis), log10(price in AUD)). Genesis is 30 July 2015 (Frontier release).
2. Fit a linear regression: log10(price) = slope × log10(days) + intercept.
3. Compute the residual: residual = actual log10(price) - predicted log10(price).
4. The standard deviation of the residuals is σ. The ±1σ and ±2σ bands are the central regression line offset by ±σ and ±2σ in log-price space.
5. Re-fit on every site build to incorporate the latest monthly close.

AUD price data is sourced from a public market-data endpoint, downsampled from daily to monthly closes. Build script: scripts/fetch-eth-aud-history.mjs, identical in structure to the BTC equivalent.

The current fit parameters (slope, intercept, and σ) are displayed in the meta strip directly under the chart. These update each build as the data window extends.

Where the model breaks down

Logarithmic regression is a statistical pattern-recognition tool, not a fundamental valuation framework. It has all the limitations of the BTC equivalent, plus some Ethereum-specific concerns:

• Ethereum's supply changes are not captured in the model. The 2021 EIP-1559 fee burn and the 2022 proof-of-stake merge fundamentally changed Ethereum's issuance dynamics. The log regression treats price-over-time as if Ethereum had the same monetary base structure throughout, which it does not. Out-of-sample fairness suffers as a result.
• Ethereum's product roadmap is still active. The Beacon Chain merge, sharding, danksharding, and other upcoming protocol changes can materially shift Ethereum's value proposition. The log regression is purely backward-looking.
• Shorter history than Bitcoin. Ethereum has roughly 11 years of price history versus Bitcoin's 17. Fewer cycles mean a less robust fit, and the model's identification of "historically rare zones" is less statistically powerful.
• The 2017-2018 ICO bubble is an outsized residual. The full-history fit is influenced by this single very large positive residual. Some practitioners exclude or downweight that period; the chart above uses the full unweighted history.
• Standard log-regression assumptions. All the standard caveats apply: backward-fitted, assumes stable power-law growth, statistical not causal, small-window instability, bands are descriptive not predictive.

Related tools

• Bitcoin Logarithmic Regression Bands (AUD) - the BTC equivalent. Side-by-side comparison reveals where the two assets sit in their respective cycles.
• Bitcoin Halving Countdown + Cycle Overlay - Bitcoin's deterministic supply schedule. Useful context when comparing BTC to ETH cycle structure.
• Bitcoin DCA Backtest Calculator - AUD-native DCA simulation. (ETH equivalent on the roadmap.)
• Crypto CGT Calculator - apply the ATO 50 percent discount to a specific Ethereum disposal.
• Best Crypto Exchanges Australia 2026 - AUSTRAC-registered exchanges to buy and hold Ethereum.

Frequently asked questions

About the author

Govind Satoshi

Former Institutional Trader. Founder, SatoshiMacro.

Traded allocated institutional capital at a Sydney proprietary trading firm.