The author of the Bitcoin Energy Consumption Index makes fundamentally flawed assumptions, causing it to demonstrably overestimate the electricity consumption of Bitcoin miners by 1.5× to 3.6×, and likely by 2.0× to 2.5×.
The main fault amongst others, in BECI’s model, is making the overly simplistic and wrong assumption that “65%” of mining revenues are spent on electricity. “65%” is essentially pulled out of thin air due to a misunderstanding from the author.
This motivated me to research and publish my own estimates using a model built from real-world data: Electricity consumption of Bitcoin: a market-based and technical analysis bounds the annual consumption with certainty to the range 2.85 to 6.78 TWh. By comparison BECI claims a consumption of “10.23 TWh” as of 1 March 2017.
About a month ago I had written a first version of this BECI critic. At the time the author made the even worse assumption that 100% of mining revenues were spent on electricity. After discussing with him, he made some changes in his “final release”. However BECI remains fundamentally flawed, so I rewrote this post from scratch by basing my arguments on data from my model.
- Critic #1: BECI fails to apply economic theory
- Critic #2: BECI’s author misread a working paper and arbitrarily decided the ratio of electrical opex to mining revenues was “65%”
- Critic #3: BECI wrongly assumes electricity consumption and Bitcoin price are correlated over a “few weeks”
- Critic #4: BECI uses misleading terminology
- How to fix BECI’s model?
Critic #1: BECI fails to apply economic theory
BECI’s entire model is based on a flawed application of economic theory. Quoting the website:
“Economic theory suggests that the marginal product of mining should theoretically equal its marginal cost in a competitive market. This would mean we can calculate the network’s energy efficiency by solving for the break-even electricity costs.”
The author erroneously assumes the marginal cost is equal to the electricity cost (opex) and makes the case that in theory (close to) 100% of mining revenues are spent on electricity. In reality the marginal cost also includes the cost of the mining hardware (capex.) Because BECI fails to take into account capex when attempting to apply this economic theory, it ignores the largest initial cost of a mining farm.1
BECI would be right to ignore capex if and only if the hash rate was stagnating or decreasing. It would mean some/all existing miners continue to mine because they recoup their electrical opex and no new miners would join in because they expect to be unable to recoup their capex. In that case, the marginal cost of continuing to mine is only comprised of electrical opex. But in reality, the global hash rate has been significantly increasing for years, precisely because miners expect to recoup their capex, so the marginal cost of adding mining capacity is comprised of opex plus capex.
Critic #2: BECI’s author misread a working paper and arbitrarily decided the ratio of electrical opex to mining revenues was “65%”
Initially, BECI’s author applied his flawed interpretation the above economic theory literally and assumed that 100% of mining revenues were spent on electricity, ie. that no profit was ever made.
I pointed out that modern 16nm ASIC miners are in fact mining many more bitcoins than the cost of electricity. He realized something was wrong in his model, so in his “final release” he attempted to find the fraction of mining revenues spent on electricity. He found and quoted an SSRN working paper by Tomaso Aste:
“Tomaso Aste (2016) […] implies that the average costs of mining are closer to 55 percent of the available miner income. Aste, however, doesn’t provide many details along with his estimate. To be on the conservative side, the average cost percentage used to calculate the Index is set at 65 percent”
However Aste never implies an exact 55%. Aste writes:
“it can be estimated that, with current hardware, the computation of a billion of hashes consumes, with state-of-the-art technology, between 0.1 to 1 Joule of energy. This implies that currently about a billion Watts are consumed globally every second (1GW/sec [sic]) to produce a valid proof of work for Bitcoin.” [Side note: GW/sec is incorrect—the unit should be GW or gigajoule/sec.]
At the time of Aste’s writings in June 2016 the network’s hash rate was 1500 PH/s, therefore “0.1 to 1 Joule” implies 150 MW to 1.5 GW, which is within order of magnitude of 1 GW. The hourly cost of 1 GW is $50k assuming $0.05/kWh, or $8333 per 10-minute Bitcoin block, which Aste compares to the per-block income of $15000 at the time, which is where the 55% comes from: 8333 / 15000.
But all these figures are merely orders of magnitude computed from “0.1 to 1 Joule.” Aste’s conclusion makes it clear:
“This is indeed the order of magnitude of the present electricity cost for the proof of work in Bitcoin.”
I even emailed Aste to erase any doubt; he replied:
“Yes Marc, we do not know which is the average consumption per GH, it depends on the hardware, we can only produce order of magnitude estimates.”
To be numerically exact, all Aste implies is that the electrical consumption is 150-1500 MW, which corresponds to a per-block electricity cost of $1250-12500, or 8.3-83.3% of the mining income.
BECI’s author misread a working paper by interpreting an order of magnitude as an exact estimate (55%) and arbitrarily picked “65%” when in fact the paper merely implies the percentage is somewhere between 8.3 and 83.3%.
Critic #3: BECI wrongly assumes electricity consumption and Bitcoin price are correlated over a “few weeks”
[Update: BECI’s author informed me he computes the average over 60 days, so this section can be ignored.]
Even if BECI estimated the correct percentage of mining revenues spent on electricity, another error would remain:
“the Bitcoin price used for determining the Index is based on a moving average over the last few weeks”
BECI is opaque: it fails to disclose how exactly this moving average is computed. Is a “few weeks” 2 weeks, 3 weeks, 4 weeks? Either way this moving average is insufficient. It takes not weeks but months to plan, finance, build and launch a significant mining farm in response to a Bitcoin price increase that opens a mining venture opportunity.2 Miners put mining hardware online in response to the Bitcoin price as of months ago, not weeks ago.
Because Bitcoin’s price has been generally increasing lately (+30% every 2 months between October 2016 and February 2017), looking at the moving average over a few weeks is causing BECI to constantly overestimate the revenues that miners plan for, hence causing its simplistic model to overestimate the global electricity consumption.
Critic #4: BECI uses misleading terminology
A more minor complaint I have about BECI is that it claims to compare Bitcoin to the energy used by countries (electricity + oil + coal + gas…) when in fact it compares it only to their electricity usage. BECI references the International Energy Agency for these numbers, and in my opinion BECI should follow this agency’s example and use proper terminology regarding energy vs electricity. Notably it should title the chart “Electricity consumption by country”, and should say “The entire Bitcoin network now consumes more electricity than a number of countries”. I reported this to the author on 30 December 2016, but he does not seem to want to fix it…
How to fix BECI’s model?
First of all it is unscientific and misleading for BECI to claim to know a precise estimate of the electricity consumption of Bitcoin. No one knows it because the market share of the various ASICs is largely unknown, and no large-scale polling or study has ever been conducted to determine it. A proper scientific method would be at least to estimate lower and upper bounds.
BECI needs to accurately estimate the percentage of mining revenues spent on electricity.
We can determine this from my analysis (Electricity consumption of Bitcoin: a market-based and technical analysis) which computed the lower and upper bounds as well as a best guess for the average energy efficiency of mining ASICs as of 26 February 2017:
- Lower bound: 0.100 J/GH
- Best guess: 0.145-0.166 J/GH
- Upper bound: 0.238 J/GH
This analysis also computed that mining hardware is profitable below 0.56 J/GH (assuming $0.05/kWh.)
Therefore the average amount of mining revenues spent on electricity is 18 to 42%3 (0.100/0.56 to 0.238/0.56), which is 1.5× to 3.6× lower than BECI’s arbitrary choice of “65%”. And my best guess is 26-30% (2.0× to 2.5× lower than BECI.)
BECI needs to calculate the average mining income by averaging the Bitcoin price over a few months, not weeks, as explained above.
BECI’s author wrote:
“In the past, electricity consumption estimates typically included an assumption on what machines were still active and how they were distributed, in order to arrive at a certain number of Watts consumed per Gigahash/sec (GH/s). This arbitrary approach has led to a wide set of electricity consumption estimates”
But it is his approach that is arbitrary, specifically his choice of “65%.”
The lower and upper bound estimates I presented are established with very high confidence. They literally assume the best and worst possible case, assuming respectively that all miners run either the most energy-efficient hardware possible or the least efficient hardware available at their time. For details see Electricity consumption of Bitcoin: a market-based and technical analysis.
As I previously offered, if your are a journalist, or researcher, or anyone who wants to write about Bitcoin’s energy consumption, send me a note. I will be happy to review your work and provide feedback before publication. It is professionally unacceptable to publish analyses that are so far off reality like BECI.
I would make the argument that the marginal cost also includes other capital expenditures (data center building, etc) and non-electrical operational expenditures (labor to maintain and operate data centers, etc.) But this is debatable, so I will not use this argument in my critic of BECI. ↩
It takes less time for a small miner to upgrade from 1 to 2 kW, than a large miner from 10 to 20 MW. And the network is mostly made of a small number of large miners, not the other way around (large number of small miners.) ↩
18-42% is calculated excluding fees. Since fees average approximately 1/10th of the block reward of March 2017, the real percentage of mining revenues spent on electricity is 16-39%. ↩