Every ten minutes or so, somewhere in the network of computers that maintains Bitcoin, a machine solves a math puzzle and earns the right to add a new page to the shared digital record. But because these computers are scattered across the planet, news of a win takes time to spread. During that brief window, two machines can solve the puzzle almost at the same moment, creating a split in the record known as a fork. One version eventually wins, and the losing block, along with all the electricity spent producing it, is thrown away.
How often does this happen, what drives it, and how much energy does it waste? A study published in PNAS Nexus builds a mathematical model to answer those questions, and estimates that in the most recent year the discarded computing effort was worth about 16,000 megawatts, roughly half the electric power generated in the United Kingdom.
A quick primer on mining and forks
Bitcoin runs on a system called Proof-of-Work. To add a block of transactions to the ledger, computers called miners race to solve a cryptographic puzzle by brute force, testing enormous numbers of guesses per second. The speed at which a miner can generate these guesses is called its hash rate. The winner appends the new block and collects newly created Bitcoin as a reward. The puzzle’s difficulty automatically adjusts so that, on average, someone wins every ten minutes.
Over the years, this competition has grown lopsided. Specialized machines and economies of scale have pushed small hobbyist miners out, and large operators have banded together into mining pools. At the time the study was written, three pools produced more than half of all new blocks. This concentration is what the researchers mean by a heterogeneous distribution of hash rates: a small number of very powerful players and a long tail of smaller ones.
A fork happens when two miners solve the puzzle nearly simultaneously and each starts broadcasting a different block. Because information travels through the network with a delay, called propagation time, the two blocks compete until the network settles on one. In Bitcoin, a new block reaches most of the network in about two seconds. The block that loses becomes an orphaned block, and its content is discarded. Forks are a natural side effect of a genuinely distributed network, but they represent wasted resources and a security weakness.
Building a model of heterogeneous miners
Paolo Barucca, Carlo Campajola, and Jiahua Xu of University College London set out to describe fork rates in a way that accounts for the real inequality among miners. Earlier work had modeled forks by assuming all miners were equally powerful. The authors relax that assumption and derive equations that treat mining as a random process, calculating the probability that the two fastest miners finish within a propagation delay of each other.
Their approach takes three inputs: the number of active miners, the way hash rate is distributed among them, and how long it takes a new block to spread through the network. Because the equations are solved analytically rather than through heavy simulation, the model can be run quickly across many scenarios.
To connect the model to reality, the team assembled data from several public sources. They pulled block information from the Bitcoin blockchain through Google BigQuery, identified which pools mined which blocks, gathered total network hash rate figures, and used block propagation times measured hourly since 2015 by a research group at KASTEL in Germany. For fork frequency, they combined a crowd-sourced repository of stale blocks with additional published data. They treated a roughly two-week window, the interval between Bitcoin’s difficulty adjustments, as a stable period for estimating hash rates.
What the numbers revealed
One of the study’s central results is that the fork rate is well approximated by a simple ratio: the median block propagation time divided by the average mining time. In plain terms, the longer it takes news of a new block to travel relative to how often blocks are found, the more often forks occur. The researchers show mathematically why this holds, and their model reproduces the ups and downs seen in historical fork data reasonably well when they use the time it takes a block to reach half the network.
The concentration of mining power also plays a part. The authors use a measure called the Herfindahl-Hirschman Index, a standard yardstick of market concentration, to capture how unequally hash rate is spread. Their equations suggest that a more concentrated, more unequal distribution of mining power actually tends to lower the fork rate. When a few giant pools dominate, near-simultaneous wins by two different players become less likely. The number of active miners has a similar effect: more miners means a lower fork rate.
These two forces have historically moved in opposite directions, which the authors say explains why propagation time alone appears to drive the fork rate in the data. As the number of miners fell and hash power became more concentrated, the effects roughly canceled out.
Spotting anomalies and estimating waste
Because the model links fork rates, network delay, and concentration, it can be run in reverse. The researchers calculate the propagation time or the concentration level that would be needed to produce the fork rates actually observed, then compare those implied values to the measured ones. When the two diverge, something unusual may be happening.
They found the implied propagation time was close to the real median after mid-2017 but noticeably smaller before that. The authors interpret this as evidence that miners tend to be better connected than the average node, hearing about new blocks before most of the network. This points to what they describe as a core-periphery structure, with well-connected mining pools at the center and loosely connected ordinary nodes at the edge. Around 2016, 2019, and 2022, the implied concentration ran higher than what block records showed, which the researchers say could reflect either geographic clustering of powerful miners, at the time largely in China, or occasional coordination between them.
The final piece is energy. When one miner wins, everyone else keeps working on the now-outdated puzzle until word of the new block reaches them. The researchers label the power spent during that interval as wasted, since it never contributes to the official ledger. Using mining hardware efficiency figures from the Cambridge Bitcoin Electricity Consumption Index, they translate that wasted effort into electricity.
The wasted hash rate itself has stayed fairly steady and even declined slightly since 2019 as mining concentrated. But the amount of energy behind each wasted attempt has climbed, because the puzzle’s difficulty has grown faster than machines have become efficient. The result is the roughly 16,000 megawatt figure for the most recent year.
A trade-off with no easy answer
The study points to a tension the authors flag rather than resolve. Greater concentration of mining power tends to reduce forks and make the consensus process more efficient in energy terms. Yet the same concentration raises security concerns, since a dominant player could in principle rewrite records or delay transactions. “Further research is needed to fully explore this trade-off,” the authors write.
Several caveats come with the findings. The model assumes miners begin working at the same instant, that hash rates hold steady within each two-week window, and that blocks propagate at a single uniform speed regardless of who mined them. It also does not capture the internal workings of individual pools. The energy estimate depends on those simplifications and on the accuracy of crowd-sourced fork data, which the authors note tends to under-report. Even so, they present the framework as a way to quickly estimate the natural fork rate of a Proof-of-Work system and to flag when a network is behaving in ways its basic rules would not predict.
