Bitcoin Halving Cycle Math: The Rival Models, Tested at the Midpoint

Bitcoin traded around $65,858 on July 22, 2026, according to Fortune’s daily price tracker, putting its market capitalization at roughly $1.33 trillion. That is a little more than half of the $126,198 all time high the asset touched on October 6, 2025, and close to where it changed hands a year earlier. For a market supposedly running on a fixed, four year mechanical clock, a surprising number of competing clocks are being read into that flat stretch.

Where the Cycle Actually Stands Right Now

The current halving epoch began on April 19, 2024, when the block subsidy fell from 6.25 BTC to 3.125 BTC. By one recent count, the network has already worked through roughly half of the blocks between that event and the next one, with about 105,000 blocks remaining before the reward is cut again to 1.5625 BTC, an event current estimates place around April 2028. Bitcoin is sitting close to the midpoint between two halvings, which is exactly the moment when every model claiming to translate the emission schedule into a price target has already said most of what it is going to say about this cycle.

That makes this a useful moment to stop repeating the halving narrative and start grading it. Three specific, named, mathematical attempts to translate Bitcoin’s fixed supply schedule into a price forecast circulate constantly across crypto media and social platforms: stock-to-flow, the power law, and a global liquidity correlation. Each has a named proponent, a specific 2026 call, and, as of today, a specific gap between that call and the number on screen. A rigorous statistical paper published this year also offers a genuine outside referee on the most mathematically ambitious of the three, rather than just another opinion added to the pile.

None of this is an argument that halving math is meaningless. The mechanism is real, the supply schedule is fixed in code, and the broad shape of four cycles each ending in a new high is a genuine pattern, not an illusion. The argument is narrower and more useful: the specific numbers attached to that pattern by its most famous interpreters have, so far, missed by very wide margins, and it is worth understanding exactly why before trusting the next one.

The Baseline: What Halving Math Alone Actually Predicts

Before grading the more elaborate models, it is worth being honest about what the halving mechanism itself guarantees, which is very little about price. Every 210,000 blocks, roughly four years, Bitcoin’s new supply issuance rate is cut in half, a fact confirmed on CoinGecko’s halving tracker. That is a fact about software, not a fact about markets. What history layers on top of that fact is a pattern: each of the four completed cycles has produced a new all time high, and each new high has been a smaller multiple of the one before it.

The first cycle is almost a different asset by today’s standards. Bitcoin traded near $12.24 at the November 28, 2012 halving, according to a Blockworks history of Bitcoin halvings, and reached roughly $1,177 by November 25, 2013, a run driven as much by early exchange infrastructure, and its failures, as by anything resembling institutional demand. The second cycle, following the July 9, 2016 halving, rode retail mania and the 2017 initial coin offering boom to a $19,783 peak that December. The third, after the May 11, 2020 halving, unfolded against a backdrop of zero interest rates and pandemic era stimulus, topping out at $68,789 in November 2021. The fourth, following the April 19, 2024 halving, was the first to run through a full year of spot ETF flows, and it peaked at $126,198 on October 6, 2025, according to a compiled record of every Bitcoin cycle peak.

Line up the multiples and the trend is hard to miss even with only three ratios to work from: roughly 16.8x from the 2013 peak to the 2017 peak, roughly 3.5x from 2017 to 2021, and roughly 1.8x from 2021 to 2025. If that decay continued in the same rough spirit, simple extrapolation puts a fifth cycle peak somewhere between 1.3x and 1.6x the 2025 high, a wide $165,000 to $200,000 range. That is not a forecast; it is what a spreadsheet does when you stretch three ratios across a fourth gap, and it previews the exact problem the rest of this piece deals with. Even the simplest, least opinionated version of halving math produces a two and a half fold uncertainty band before anyone attaches a formula, a name, or a demand side assumption to it.

Stock-to-Flow: The Model That Started the Obsession

The best known attempt to formalize the halving into a specific number is Dutch analyst PlanB’s stock-to-flow model, published in 2019, which treats Bitcoin like a commodity whose value is a function of scarcity, its existing stock divided by its new annual flow, the same logic sometimes applied to gold, where a high stock-to-flow ratio is used to explain why it holds value better than industrial metals. CoinGecko’s explainer on the model lays out the mechanics in full. Because a halving cuts the flow in half overnight, the model’s implied stock-to-flow ratio jumps at each halving, and PlanB’s regression translated that jump into specific, often eye catching, price targets.

Those targets have not aged well. The average of the model’s outputs for the 2025 to 2026 window sits near $500,000, while actual trading for most of 2026 has stayed in a $65,000 to $75,000 band, a gap on the order of 85 to 90 percent, according to an assessment of the model’s track record. This is not a new pattern: an earlier version of the model promised a $100,000 floor by the end of 2021, which never held, and price instead fell to about $15,500 during the 2022 bear market, more than 80 percent under what the model had implied.

Ethereum co-founder Vitalik Buterin was an early, prominent critic. In 2022, as the model’s misses piled up, he wrote, as reported by Decrypt, that “financial models that give people a false sense of certainty and predestination that number will go up are harmful and deserve all the mockery they get.” PlanB has generally responded by defending the debate rather than the specific numbers, saying, as noted in the same track record assessment, “I only block insults and rude behavior. I literally invite criticism,” while attributing gaps between the model and reality to external shocks rather than a flaw in the model’s own structure.

The structural critique is simple and has not gone away: stock-to-flow has exactly one input, supply issuance, and treats demand as effectively constant across cycles. That assumption gets harder to defend the more Bitcoin’s holder base changes shape, from spot ETFs to corporate treasuries to options desks, all of which move demand in ways a pure supply model has no way to see coming. Critics have also pointed to a statistical problem underneath the headline miss: both the stock-to-flow ratio and price trend upward over time almost by construction, so a high correlation between the two is weaker evidence of a causal relationship than it first appears.

The Power Law: A Rival Kind of Determinism

A newer and mathematically more ambitious challenger comes from astrophysicist Giovanni Santostasi, who argues Bitcoin’s price follows a power law relative to time since its January 2009 genesis block, the same broad mathematical family used to describe earthquake magnitude distributions or the way city populations scale with rank, according to Cointribune’s coverage of the theory. Unlike a simple exponential curve, a power law grows more slowly over very long stretches once plotted on a logarithmic scale, which is the visual basis for the popularity of Bitcoin rainbow chart style overlays among retail traders.

In its simplest form, the model says price grows roughly with the number of days since genesis raised to a fixed exponent. Santostasi, working with a coauthor, Perrenod, put that exponent at about 5.69 in 2026 work, a fit tight enough to explain roughly 96 percent of the historical variance in log scaled price, according to an independent statistical test of the claim published on arXiv.

How did it do on 2026 specifically? Reporting on the model’s outputs had it calling for a cycle peak near $210,000 around January 2026, followed by a correction toward $60,000 later in the year and a support zone flagged around August, per the same reporting. The peak call missed badly: Bitcoin’s actual cycle high, the $126,198 print from October 2025, was already below the model’s January 2026 target, and price never approached $210,000 at any point in 2026. The trough call has aged better; at $65,858 in late July, Bitcoin is already trading close to the flagged support zone a few weeks ahead of schedule.

What a New Statistical Paper Says About the Power Law

The power law’s mathematical polish invited a harder look, and it got one this year. A 2026 paper by researchers Baquero and Menezes applies the Clauset Shalizi Newman protocol, a statistical framework originally built for testing whether distributions genuinely follow a power law, adapted into three time series specific tests, against Bitcoin’s full price history from August 2010 through March 2026, more than 5,600 daily observations, published on arXiv.

The first finding undercuts the “law” framing directly: the fitted exponent is not stable. Measured from the genesis block, it comes out near 5.65, in line with Santostasi and Perrenod’s own estimate. Shift the reference point later by 5,000 days, a perfectly reasonable alternative choice with no obvious reason to prefer one over the other, and the fitted exponent jumps to 16.49, nearly three times larger. A genuine structural law should not swing by that much depending on an arbitrary choice of starting point; that instability is the paper’s central objection to calling this a law rather than a curve fit.

The second finding is about ambiguity rather than instability. A three component sigmoid curve, essentially three overlapping S shaped growth waves stacked together, fits the identical price history decisively better in sample than the power law does, yet passes the same diagnostic tests earlier researchers used to argue for the power law’s validity. Separately, formal distribution tests on things like the spread of Bitcoin holdings across wallets and the size of daily price moves reject the power law form outright in 8 of 11 tests run, with an ordinary lognormal distribution fitting the data better instead.

The third finding is the most useful one for anyone actually trying to use the model rather than just admire it. Walk-forward testing, refitting the model using only data available up to each of eleven yearly cutoffs between 2014 and 2024 and then checking its forecast against what actually happened next, found the power law beats more flexible alternatives, including ARIMA and exponential smoothing, at long horizons of twelve to twenty four months, and loses to a naive no skill baseline at short horizons of one to three months, with the crossover landing around six months. The authors’ explanation is not that the power law captures Bitcoin’s true underlying dynamics; it is that the model’s simplicity, having very few parameters to fit, protects it from overfitting to short term noise in a way that flexible models cannot avoid. It is a workable long range heuristic dressed in the language of physics, not a validated law of nature.

That distinction matters for anyone borrowing the model’s authority without borrowing its caveats. A tool that forecasts reasonably well two years out because it refuses to bend to every wiggle in the data is a useful tool. It is a different claim entirely from saying Bitcoin’s price is mathematically destined to follow a specific curve the way a falling object is destined to accelerate at a fixed rate, and the paper is explicit that the evidence supports only the former.

The Global Liquidity Model: Forget the Block Reward, Watch the Fed

A third camp argues the entire halving math conversation is looking at the wrong variable. Macro investor Raoul Pal has argued for years that Bitcoin’s price tracks global money supply more than it tracks its own issuance schedule, pointing to a correlation with global M2 growth that he has put at roughly 90 percent, alongside a similar claim that liquidity explains about 96 percent of the moves in growth heavy technology stocks, according to reporting on his 2026 outlook. The logic is straightforward even where the precise correlation figure is contested: when central banks expand the money supply, that new liquidity has to find a home somewhere, and long duration, scarce assets like Bitcoin have historically been sensitive beneficiaries of that flow.

Pal has also argued the traditional four year rhythm has stretched into something closer to a five year cycle, tied to longer average sovereign debt maturities, which pushed his expected cycle peak into 2026 rather than the 2025 window the old four year cadence implied. His stated target under what he calls a supercycle scenario is $450,000 by the end of 2026, contingent on central banks unlocking a fresh wave of liquidity, including regulatory adjustments like the United States Supplementary Leverage Ratio that would free bank balance sheets to hold more government debt.

The liquidity side of that argument has, in fact, been moving in Pal’s favor. M2 growth accelerated to roughly 5.6 percent year over year by May 2026, a multi year high, with the total money supply crossing $22.67 trillion in February and adding close to $1 trillion in just seven months, according to the Mises Institute’s tracking of the data. The Federal Reserve itself changed hands mid thesis: Kevin Warsh was confirmed by the Senate 54 to 45 on May 13, 2026, and took over as the Fed’s seventeenth chair later that month, succeeding Jerome Powell, a transition covered in detail by CNBC; markets have broadly read Warsh as more open to an earlier and faster easing path than his predecessor.

And yet, with liquidity accelerating and a friendlier Fed chair several months into the job, Bitcoin is trading around $65,800, not just far under the $450,000 supercycle target but roughly flat to slightly down versus a year earlier. If the 90 percent correlation Pal describes is accurate, either the lag between M2 growth and BTC price is considerably longer than the thesis assumes, or five months of an unfinished 2026 simply have not been enough time for the correlation to show up yet. Both are plausible; neither has been demonstrated, and a thesis that can only be judged after the fact it failed to arrive on schedule is a difficult one to trade around in real time.

Three Models, Three 2026 Calls, One Actual Price

Set side by side, the three models disagree with each other by hundreds of thousands of dollars, but they agree, unintentionally, on one thing: all three overshot.

The model that has actually come closest to describing 2026 is the one with no name and no proponent: the plain observation from the baseline section above that each cycle’s peak to peak multiple keeps shrinking. That is not a coincidence so much as a feature of ambition. A model with almost no structure has almost nothing left to be wrong about.

What the On-Chain Data Says Right Now

There is a way to check where Bitcoin actually sits in its cycle that does not depend on picking a side among the three models above: on-chain valuation metrics that compare price to cost basis and to miner economics directly, independent of any narrative about supply schedules or money printing.

The MVRV Z-score, which measures market value against realized value, an aggregate cost basis for every coin in circulation based on the price each one last moved at, sat at 0.37 as of mid July 2026, with the underlying realized price estimated near $52,493, according to on-chain tracking from Bitbo. Historically, past cycle tops have printed Z-scores well into the mid to high single digits, not below 1. The Puell Multiple, which compares daily miner revenue in dollar terms to its own 365 day moving average, sat at 0.75 as of late June 2026, against a historical blow off top range typically above 4, according to Bitcoin Magazine Pro’s tracking.

Read together, none of this looks like a market that already found its cycle top. It looks like one trading close to its aggregate cost basis, with miners in comparatively lean conditions rather than the euphoric, over leveraged conditions associated with past peaks. That is a more mundane, and arguably more useful, read than any of the three headline models offered for 2026.

The Small Sample Problem Nobody Wants to Mention

Bitcoin has lived through exactly four completed halving cycles. Every model discussed here is, underneath its formula, a fit to four data points, or to fractions of four, since typically only the peaks and troughs get used. That is a remarkably thin dataset from which to extrapolate a fifth, especially once a model starts claiming precision to the nearest ten thousand dollars.

Overfitting, in plain terms, is what happens when a model becomes so good at describing the exact data it was built on that it stops describing anything general at all. Given only four cycles, it is entirely possible to build several different formulas that each fit the past almost perfectly while pointing toward wildly different futures, and no amount of in sample accuracy can tell you which one, if any, is capturing something real.

The statistical paper on the power law makes this concrete in a way that generalizes to the other two models: if a threefold swing in a supposed law’s defining exponent is possible just by picking a different, equally reasonable, starting point across the same four cycles, an in sample R-squared of 0.96 is not pinning the model down nearly as tightly as it looks. The paper’s own multi sigmoid alternative, which fits even better in sample while implying a different future entirely, proves the point directly.

It is also not obvious the four cycles were drawn from a comparable process in the first place, which is what curve fitting implicitly assumes. The 2020 cycle ran through a zero interest rate, stimulus soaked pandemic economy. The 2024 cycle opened with newly approved spot ETFs and is closing out alongside a market structure bill moving through Congress. The 2026 midpoint has a brand new Fed chair a few months into the job. Treating those as four repeated draws from one stable underlying distribution is a much bigger assumption than a clean exponent and a high R-squared let on, and it is an assumption that stock-to-flow, the power law, and the liquidity correlation all make implicitly, without stating it as a limitation up front.

Second Order Forces None of the Models Price In

None of the three models carries a variable for the regulatory calendar, and that calendar has been unusually busy this cycle. As covered in HOGE Wire’s look at Washington’s Second Clock, the CLARITY Act’s path through Congress and the SEC’s own rulemaking calendar now move markets on a schedule with no relationship to block height, one that increasingly overlaps with, or overrides, the halving’s own timing.

The derivatives market is not waiting for a verdict on which model is correct either. HOGE Wire’s look at what options markets are pricing in found positioning across the options curve reflecting a distribution of outcomes rather than a single consensus number, itself evidence that professional flow treats stock-to-flow, the power law, and the liquidity thesis as inputs to a probability spread, not as forecasts to trade literally.

Structural change on the exchange traded product side compounds this further. The mechanics detailed in HOGE Wire’s coverage of the SEC’s new crypto ETP and market structure rules changed how new demand actually reaches the spot market, a channel that barely existed during the 2013 or 2017 cycles and one that none of stock-to-flow, the power law, or a pure M2 correlation were ever built to account for.

Where Institutional Capital Is Actually Going

Faced with three headline models that disagree by hundreds of thousands of dollars, institutional allocators have mostly done the least exciting thing available to them: diversify instead of picking a side. Capital that might once have made a single directional bet on a cycle top price target has instead moved toward yield generating strategies that do not require calling the top at all. As HOGE Wire has reported on institutional restaking adoption, a growing share of that capital is going into infrastructure that pays a return regardless of which of the three price models eventually turns out closest to right, a hedge against being wrong about the direction rather than a bet on being right about it.

The same caution shows up in how people hold the coin itself. Exchange withdrawal behavior, tested directly in HOGE Wire’s comparison of Coinbase, Binance, Kraken, and OKX, is one of the few data points that does not depend on any pricing model at all; it simply measures whether holders are moving coins into self custody rather than leaving them on a venue ready to sell. Sustained self custody activity during a period when the headline price is flat to down generally reads as patience rather than panic, closer to what the on-chain metrics above imply than to any of the three 2026 price targets discussed here.

What Each Model Implies for Halving Five and Beyond

The fifth halving is expected around block 1,050,000, roughly April 2028, though estimates range from March to May given ordinary block time variance, cutting the mining reward from 3.125 BTC to 1.5625 BTC and reducing daily new supply from about 450 BTC to about 225 BTC.

If stock-to-flow is applied mechanically, its defining ratio roughly doubles again in 2028, and the model will produce an even larger headline number carrying the same blind spot to demand it has always had. If the power law holds in the narrow sense the walk-forward testing actually supports, a medium term trend heuristic rather than a structural law, it is arguably the least unreasonable of the three for that specific twelve to twenty four month window, provided nobody mistakes a least bad forecasting heuristic for a law of nature, which is precisely the distinction the academic critique insists on. If the liquidity thesis holds, the 2028 halving is close to a non event, and the variable actually worth watching is the pace of Fed easing under its new chair and how quickly that feeds into global M2.

Perhaps the more useful exercise is simply to keep score rather than pick a winner today. All three models made specific, checkable claims about a 2026 peak or target. Two years from now, at the next halving, all three can be checked against one number instead of argued about in the abstract, and whichever one turns out closest will have earned the right to be taken more seriously next time, not because of what it claims to be, but because of what it actually got right this time.

How to Actually Use These Models

None of the three should be used as a price target to size a trade around. Each has a demonstrated blind spot: stock-to-flow has no variable for demand, the power law’s own proponents cannot agree on its defining exponent to within a factor of three depending on an arbitrary choice, and the liquidity thesis has a lag structure nobody has pinned down with any precision.

What they are more useful for is as regime descriptions rather than targets. On chain readings like the MVRV Z-score and the Puell Multiple say more about where in a cycle the market probably sits than any of the three headline formulas do, precisely because they measure something happening right now rather than extrapolating a curve fit to four data points. The disagreement between the models can itself be informative, too: three independent methodologies converging on the idea that price should be higher while price sits flat is either a buying opportunity or a sign that all three share a blind spot nobody has found yet, and the honest answer is that nobody knows for certain which.

Position sizing is where this distinction earns its keep. A trader who treats a stock-to-flow or power law output as a point estimate to lever into is making a much larger bet on curve fitting than the underlying statistics support. A trader who treats the same output as one noisy vote among several, weighted against what on-chain data is independently showing right now, is using the model for roughly what it is worth.

A few questions are worth asking before trusting any halving cycle price target that shows up in a chart with a big number attached to it:

• Does the model have an actual demand side variable, or only a supply side one?
• How many independent cycles is the fit actually based on, and does the fitted parameter survive a different, equally reasonable starting point?
• Is the number being quoted a tested, published estimate with error bars, or a single proponent’s chart with none attached?

When supply side, curve fit, and liquidity side models are all pointing in the same direction while price sits flat, that gap is worth investigating on its own terms, rather than resolved by averaging three disagreeing numbers into a fourth, invented one.

Frequently Asked Questions

Is Bitcoin’s four year halving cycle still valid in 2026?

Partially. The mechanical pattern of shrinking peak to peak multiples, roughly 16.8x, then 3.5x, then 1.8x across the last three completed cycles, has held up reasonably well, and on-chain metrics like the MVRV Z-score and Puell Multiple currently look closer to mid cycle than post peak. What has not held up are the specific price targets produced by stock-to-flow, the power law, and global liquidity models built on top of that pattern; all three named a 2026 price well above where Bitcoin has actually traded, which suggests the broad shape of the cycle is more reliable than any single formula’s precise number.

What is the Bitcoin power law model and how accurate is it?

Developed by astrophysicist Giovanni Santostasi, it models Bitcoin’s price as a function of time since the January 2009 genesis block, raised to an exponent estimated at roughly 5.69, a fit that explains about 96 percent of historical price variance in log terms. A 2026 statistical paper found that same exponent swings from 5.65 to 16.49 depending on an arbitrary choice of starting date, undermining its claim to be a genuine structural law, though the model still outperformed more flexible statistical alternatives at twelve to twenty four month forecast horizons in formal walk-forward testing.

Why did the stock-to-flow model fail to predict Bitcoin’s price in 2026?

The model’s average output for the 2025 to 2026 window sits near $500,000, versus actual trading closer to $65,000 to $75,000 for most of 2026. Critics, including Ethereum co-founder Vitalik Buterin, have pointed out the model uses only supply side scarcity as an input, with no variable for demand shocks like ETF flows, interest rates, or regulation, which is also why its earlier promised $100,000 floor for late 2021 never held and price instead fell to about $15,500 during the 2022 bear market.

When is the next Bitcoin halving and how much will block rewards drop?

The fifth halving is expected around April 2028, at block height 1,050,000, cutting the mining reward from 3.125 BTC to 1.5625 BTC per block and reducing daily new issuance from roughly 450 BTC to about 225 BTC. As of mid 2026, the network has already worked through roughly half of the roughly 210,000 blocks in the current epoch, putting Bitcoin close to the midpoint of its current halving cycle.

Does Bitcoin’s price really track the global M2 money supply?

Macro strategist Raoul Pal has argued for a correlation of roughly 90 percent between Bitcoin and global M2 growth, and has pushed his projected cycle peak into 2026 on a five year cycle theory tied to longer sovereign debt maturities. M2 growth has in fact accelerated to a multi year high in 2026, but Bitcoin’s price has not moved anywhere near Pal’s $450,000 supercycle target, suggesting either a longer transmission lag than the thesis assumes or a weaker correlation than advertised over shorter time periods.

Written by Priya Reddy for HOGE Wire.