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×.
His main error, amongst others, is making the wrong assumption that a fixed “60%” of mining revenues are spent on electricity. “60%” is pulled out of thin air and miscalculated due to a misunderstanding from the author. As of 26 July 2017 he still has not fixed this incorrect assumption.
This motivated me to research and publish my own estimates using a model built from realworld data: Electricity consumption of Bitcoin: a marketbased and technical analysis bounds the annual consumption to the range 2.85 to 6.78 TWh. By comparison BECI claims a consumption of “10.23 TWh” as of 1 March 2017.
 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%” then “60%”
 Critic #3: BECI wrongly assumes electricity consumption and Bitcoin price are correlated over a “few weeks”
 Critic #3.1: BECI’s energy estimate varies by 1.57× based on the author’s frequent changes to how the “average Bitcoin price” is computed
 Critic #4: BECI uses misleading terminology
 Critic #5: BECI’s supplemental material is also flawed
 How to fix BECI’s model?
 Conclusion
 Footnotes
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 breakeven 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%” then “60%”
Initially, BECI’s author applied his flawed interpretation the above economic theory literally and assumed that 100% of mining revenues were spent on electricity.
I pointed out that 16nm ASIC miners are spending a small fraction (~15%) of mining revenues on electricity. He realized his assumption was seriously wrong, so in his “final release” he made a first attempt 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 stateoftheart 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 10minute Bitcoin block, which Aste compares to the perblock 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.”
All Aste implies is that the electrical consumption is 1501500 MW, which corresponds to a perblock electricity cost of $125012500, or 8.383.3% 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%.
In April 2017 the author realized this error, silently removed references to Aste’s paper, but strangely insisted on sticking with “65%” by making a second attempt to explain his chosen percentage. He assumed the lifetime electricity costs of a Bitmain Antminer S9 is $745.201159.20 over 450700 days, he assumed the only other nonelectrical costs are the production cost of the hardware of $500, he implied this means 6070% of Bitcoin revenues are spent on electricity, and he averaged it to 65%. This flawed logic is ridden with 4 errors:

The hardware costs $500 to Bitmain only, however the majority of S9s deployed were/are being purchased by customers between $2100 (launch price) and $1058 (price as of May 2017.)

This logic assumes miners make zero profits (electricity costs + nonelectrical costs = mining revenues.) However miners do make a profit, see the CSV in Economics of mining, or even Song’s post, itself referenced by the author.

He ignores other capex and nonelectrical opex such as: data center, labor, etc.

Somewhat less important: he wrongly assumes all miners will operate their machines until their very last profitable day (day 450 or 700.) In fact miners often upgrade before reaching the true endoflife, before electricity costs start representing a very large percentage of mining revenues. For example Economics of mining shows an S5 had already generated most (84%) of its profits by day 385, a time when electricity costs still represented only 39% of mining revenues. Many economically intelligent miners look at this and rightfully determine it is not worth to continue mining another 300400 days to gain the last 16% of the profits.
In fact, we can demonstrate how wrong the author is by calculating the actual, true, realworld revenues and costs of an S9. I did it in Economics of mining: as of 15 May 2017 an S9 has spent 16% of its revenues on electricity costs, which shows how ludicrous BECI’s “65%” estimation really is.
Shortly after, BECI’s author made a third attempt to adjust his model: he changed the 65% parameter to 60%. However this minor change remains grossly insufficient.
Critic #3: BECI wrongly assumes electricity consumption and Bitcoin price are correlated over a “few weeks”
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 electricity consumption.
Update: When prompted for more information, BECI’s author replied he computes the average over 60 days. I think 60 days is fair moving average, so this critic could be ignored. But keep reading the next section…
Critic #3.1: BECI’s energy estimate varies by 1.57× based on the author’s frequent changes to how the “average Bitcoin price” is computed
BECI assumes electricity consumption is directly proportional to the Bitcoin price: electricity costs are assumed to be fixed at 60% of the mining revenues, and revenues are determined from a moving average of the Bitcoin price. It is important for BECI to calculate this moving average in a consistent manner. Sticking to a 60day moving average would have been fine, however BECI’s author started making changes…
I noticed the first change when I was archiving copies of his site. Between 20170524 and 20170531 he changed the average to 120 days. When asked on what day the change was made, he replied vaguely “It may vary per day.”
Another change was made between 20170531 and 20170620; the average is now computed over 150 days.
Another change was made between 20170710 and 20170721; the average is now computed over 200 days. I asked him when was this change made and he replied again vaguely “Let’s say mostly during the first two weeks of June.”
Another change was made between 20170729 and 20170814; the average is now computed in an undisclosed way. Technical explanations were removed from the site.
As of 26 July 2017 the 60day moving average of the Bitcoin price is $2556, while the 200day average is $1627, a 1.57× difference. So BECI’s energy estimate varies by 1.57× depending if the price is averaged over 60 or 200 days. This is a change he had made with no explanations so far, until I asked him a 5th time to clarify. He then said the moving average was determined as such:
“Average of (Maximum of (volatility t1, decay factor × decaying volatility t1) × reference days)”
“With a decay factor so low that without a new volatility peak it’s practically static. So here’s why I’m saying it’s fine to use a static number for most parts, and I update this on the BECI page when the difference is interesting enough > there will always be some finetuning mismatches on multiple parameters. The information provided always allows for getting close enough in reproducing, as shown it did. If the finetuning is actually relevant it’s a different story, but again, that really depends on the purpose.”
Okay, now we have a bit more information. But his vague and cryptic explanation reveals more flaws:

The formula is illspecified by failing to explain: how is volatility calculated, what time period is t1, and what value is given to the decay factor. Therefore no one can validate BECI’s past numbers. This makes BECI unreproducible hence unreliable.^{3}

Why even make the moving average period dynamic instead of fixed? This appears to be a kludge the author needs as his model estimates energy based on the volatile Bitcoin price instead of the hashrate.

The author’s vague answers as to when he made the changes indicate he does not track, archive, or document them. Or at least not in an easy and proper way, as in one email he told me he would have “to go through thousands of page versions to retrieve this”. He should be publishing these changes publicly.

Frequently changing the averaging period is misleading to readers, who are not aware the energy estimate can vary by 1.57× due to a seemingly innocuous parameter change. More worrisome, this parameter is no longer explained and not even disclosed on BECI’s site!
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…
Critic #5: BECI’s supplemental material is also flawed
On 17 April 2017, the author published supplemental material that continues to make the same mistakes, and introduces new ones.
His upper bound for the total electricity consumption still ignores capex by assuming miners spends 100% of their revenues on electricity (see critic #1).
His lower bound assumes mining machines are always operated until their very last profitable day. In fact miners routinely decomission older hardware that is still slightly profitable and replace it with more efficient and more profitable hardware. Everyday miners reevaluate the economic value of their choices. At any point they may decide, if they have a given fixed electrical capacity, that it becomes more worthwhile to spend this electricity on more efficient hardware than to continue operating barely profitable hardware.
How to fix BECI’s model?
Step 1
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 largescale polling or study has ever been conducted to determine it. A proper scientific method would be at least to estimate lower and upper bounds.
Step 2
BECI needs to accurately estimate the percentage of mining revenues spent on electricity. We can determine this in 2 different ways.
The first way is to read my analysis (Electricity consumption of Bitcoin: a marketbased 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: 0.1450.166 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%^{4} (0.100/0.56 to 0.238/0.56), which is 1.5× to 3.6× lower than BECI’s arbitrary choice of “60%.” My best guess is 2630% (2.0× to 2.5× lower.)
The second way is to model exactly the costs and revenues of various machines, as I have done in Economics of mining. I showed that as of 15 May 2017 the Antminer S5, S7, and S9—various machines at different stages of profitability—have respectively spent 31%/25%/16% of revenues on electricity. This further demonstrates that BECI’s choice of “60%” is far from reality.
Step 3
BECI needs to calculate the average mining income by averaging the Bitcoin price over a few months, not weeks, as explained in critic #3.
Conclusion
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 decision to frequently change how Bitcoin’s average price is calculated, and his wrong assumption that “60% of revenues spent on electricity” when in fact evidence demonstrates the percentage is between 18% and 42%, and most likely between 26% and 30%, which is also validated by computing this percentage to be exactly 31%/25%/16% for the Antminer S5/S7/S9.
The 18% to 42% range has been calculated by modeling literally the best and worst possible case: that all miners run either the most energyefficient hardware possible, or the least efficient hardware available at their time. For details see Electricity consumption of Bitcoin: a marketbased 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.
Footnotes

I would make the argument that the marginal cost also includes other capital expenditures (data center building, etc) and nonelectrical 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.) ↩

The author also forgot when he changed the hardcoded “65%” to “60%” (he said it was done “probably around the end of March/start of April.”) ↩

1842% 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 1639%. ↩