Bitcoin Market Cycles and the Power-Law Debate: Rallies, Drawdowns and Evidence

A price history is a market record, not a Bitcoin consensus record

Bitcoin does not contain a dollar price. The protocol validates transactions, blocks, and issuance; prices arise on exchanges where bids and offers meet under particular custody, liquidity, and jurisdictional conditions. The series used here is Coin Metrics PriceUSD, sampled daily in UTC and reproduced in the site dataset. It is an index-style market observation rather than the closing auction of one canonical Bitcoin venue. That distinction matters most in the early years, when markets were thin, fragmented, and operationally fragile.

All prices in this dossier are nominal U.S. dollars. They are not adjusted for consumer-price inflation, and daily observations suppress intraday extremes. A date identified as a peak or trough therefore means the relevant daily observation in this dataset, not necessarily the highest or lowest trade printed anywhere in the world. Publishing the metric, time convention, retrieval date, and source checksum makes the analysis reproducible without pretending that one series exhausts every historical market.

The ascent is real, but a linear chart conceals most of the history

The dataset’s 31 December observations move from $0.30 in 2010 to $13.55 in 2012, $729.56 in 2013, $13,921.48 in 2017, $29,022.67 in 2020, and $93,389.73 in 2024. Expressed as a simple endpoint multiple, that is an exceptional long-run ascent. Expressed as a lived market path, it includes several periods in which a holder at the prior high saw more than four fifths of the quoted dollar value disappear before recovery. Both statements describe the same series.

A logarithmic price axis is normally the more honest way to show a market that spans many orders of magnitude because equal vertical distances represent equal proportional changes. It should not be used to make volatility look harmless. The companion drawdown view starts each new high at zero and measures the percentage distance below that running high. Together, log price and drawdown preserve the upward scale change while showing the severity and duration of the losses along the way.

Four completed cycles contained losses between 76.67% and 92.75%

For this dossier, a completed drawdown begins at a new daily closing all-time high, reaches the lowest later daily close, and ends on the first daily close that equals or exceeds the old peak. The 2011 decline fell 92.75% over 163 days and required 622 days from peak to first recovery. The decline from December 2013 reached 84.52%; its first recovery did not arrive until February 2017, 1,177 days after the peak.

The December 2017 peak was followed by an 83.78% loss and a 1,080-day peak-to-recovery interval. The November 2021 peak was followed by a 76.67% loss, with the old level first exceeded in March 2024 after 847 days. Calling these episodes ‘crypto winters’ is convenient market language, not an objective protocol classification. The explicit rule above makes inclusion reproducible and avoids declaring a current decline complete before a later recovery or lower trough can be observed.

Prices rose after each observed halving, but four windows cannot identify an effect

The local dataset compares the daily price on each subsidy-halving date with observations 365 calendar days before and after it. The following-year returns were approximately 8,069.11% after the 2012 halving, 284.42% after 2016, 558.92% after 2020, and 31.11% after 2024. The prior-year returns were also positive in all four windows: approximately 385.26%, 141.75%, 17.29%, and 129.75%. These calculations establish the historical paths around the selected dates, not what would have happened without a halving.

A halving changes the maximum subsidy a valid block may create. It does not command buyers, set a dollar price, or create a mechanical timetable for demand. The four episodes are not independent randomized trials: expectations can develop before the event, the same global asset appears in every observation, and liquidity, leverage, monetary conditions, regulation, custody, and investor composition changed at the same time. Event windows belong in the evidence archive, but a causal claim needs an identification strategy that a recurring annotated chart does not supply.

The power law is a descriptive log-log regression, not a protocol law

The published fit defines network age as days since 3 January 2009 and estimates ordinary least squares on positive daily observations: log10(price_usd) = alpha + beta × log10(days_since_genesis). For the 18 July 2010 through 31 December 2025 sample, alpha is −16.5405739393, beta is 5.6995933722, and log-space R² is 0.9609848770. The residual standard deviation is 0.303042 log10 units, equivalent to a descriptive multiplicative factor of about 2.009 around the fitted line.

The modern public argument is closely associated with Giovanni Santostasi’s time-based Bitcoin power-law posts. A 2026 peer-reviewed article by Şenel and Yılmaz applied a related price-versus-time model and reported evidence of long-horizon mean reversion and shorter-horizon momentum. A separate 2026 research review by Carlos Baquero emphasized that the Bitcoin price power law had not yet received the kind of formal distributional and walk-forward evaluation needed to turn an attractive historical fit into a settled forecasting result. Those records make ‘debate’ the accurate label: there is a reproducible pattern, an affirmative research case, and unresolved model-risk criticism.

The high R² says the selected curve summarizes much of the variation in these transformed historical data. It does not establish a physical scaling law, a causal mechanism, or future accuracy. Price and network age both trend; daily errors are serially correlated; the earliest observations have unusual leverage; and the origin, index, sampling interval, start date, and loss function are researcher choices. Calling the relationship a ‘law’ can obscure those modeling decisions and make an in-sample summary sound inevitable.

Changing the sample changes the curve

The site artifact reruns the same regression after progressively excluding early data. Starting in 2011 produces beta 5.55596 and R² 0.95352; starting in 2012 produces beta 5.65425 and R² 0.94244; starting in 2013 produces beta 5.32894 and R² 0.91784. Those are not catastrophic changes, but they are large enough to produce increasingly different extrapolations. A residual band calculated from the fitted sample is likewise not a confidence interval or prediction interval when the model’s errors violate ordinary independence assumptions.

The responsible use is descriptive: show the observations, publish the equation and sensitivity table, and let readers see where market cycles sit above or below the curve. This dossier deliberately supplies no future price target. It also treats Mt. Gox, regulated futures, FTX, interest-rate changes, and other events as contemporaneous context rather than arrows that ‘explain’ a drawdown by themselves. The result is less dramatic than a deterministic cycle theory and more useful to researchers who need a transparent record.