mrb's blog

Serious faults in Digiconomist's Bitcoin Energy Consumption Index

Keywords: beci critic debunking bitcoin mining electricity energy estimation

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 11 January 2018 he still has not fixed this incorrect assumption.

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 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

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%” 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 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.

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%.

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 $745.20-1159.20 over 450-700 days, he assumed the only other non-electrical costs are the production cost of the hardware of $500, he implied this means 60-70% of Bitcoin revenues are spent on electricity, and he averaged it to 65%. This flawed logic is ridden with 4 errors:

  1. 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.)

  2. This logic assumes miners make zero profits (electricity costs + non-electrical 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.

  3. He ignores other capex and non-electrical opex such as: data center, labor, etc.

  4. 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 end-of-life, 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 300-400 days to gain the last 16% of the profits.

In fact, we can demonstrate how wrong the author is by calculating the actual, true, real-world 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 60-day 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 2017-05-24 and 2017-05-31 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 2017-05-31 and 2017-06-20; the average is now computed over 150 days.

Another change was made between 2017-07-10 and 2017-07-21; 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 2017-07-29 and 2017-08-14; the average is now computed in an undisclosed way. Technical explanations were removed from the site.

As of 26 July 2017 the 60-day moving average of the Bitcoin price is $2556, while the 200-day 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 t-1, decay factor × decaying volatility t-1) × 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 fine-tuning mismatches on multiple parameters. The information provided always allows for getting close enough in reproducing, as shown it did. If the fine-tuning 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:

  1. The formula is ill-specified by failing to explain: how is volatility calculated, what time period is t-1, 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

  2. 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.

  3. 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.

  4. 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 re-evaluate 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 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.

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 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%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 26-30% (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.


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 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.


  1. 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. 

  2. 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.) 

  3. 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.”) 

  4. 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%. 


Digiconomist wrote: First of all I'd like to state that the critism on the Bitcoin Energy Consumption Index (BECI) contains false information. It is claimed that BECI runs on the assumption that miners " never recover their investments (capex)". This has never been stated or implied by the information provided on BECI, and may relate to a misunderstanding. BECI assumes that the entire network is running at roughly break even, but this doesn't mean this is the case for every miner part of it. New machines may still earn themselves back easily under this assumption.

Second I'd like to add that the case laid out in this article is extremely optimistic on the electricity consumption of the Bitcoin network. It is stated that " the network's average efficiency falls between 0.055 and 0.27 J/GH". When this article was published, the best publicly available miner was the Antminer S7, running at ~0.25 J/GH. This one was released just a few months before. The Antminer S5+ was released just a little bit before at ~0.44 J/GH (in August). These machines wouldn't even have hit the market if the estimates in this article were true, as they would have been producing a loss as of day 1.
01 Feb 2017 21:35 UTC

mrb wrote: Digiconomist: You *do* imply the average miner never recovers their investments (capex), precisely because you imply the average miner barely stays afloat of his electrical costs only (opex). See quote from your own site in 3rd paragraph.

BECI implies the entire network recoups opex, but loses 100% of the capex. So *not* break even. To break even you'd need to recoup capex+opex.

Do you understand the difference between capex & opex?

Also you are wrong: many mining ASICs online as of Jan 2016 (when I wrote which is where our discussion started) beat 0.25 J/GH. It seems you didn't read my post. I provide links and references to each one of them in section 1 (

1. BitFury's latest 16nm chip achieves 0.055-0.07 J/GH (a 40MW data center of them launched in Dec 2015:
2. KnC's 16nm Solar 0.07 J/GH,
3. Spondoolies's 28nm PickAxe 0.15 J/GH,
4. Bitmain's 28nm BM1385 0.18-0.26 J/GH,
5. Avalon's 28nm A3218 0.27 J/GH.

It seems you don't know the market of ASICs very well.
01 Feb 2017 21:55 UTC

Digiconomist wrote: I don't think you can collect a random set of hardware and say "this is the J/GH" without even bothering to consider the economics surrounding that because it "seems fair" - while using economic arguments to tackle BECI. Some consistency would be nice.

You also published this post a bit too soon making it hard to discuss. If you had contacted me in advance I could have told you I was collecting data to cover 1 adjustment period in order to account for blocks being created faster (or slower) than 10 minutes on average. This held up the release of version 3, which includes some other adjustments as well. In particular the average costs mentioned here has been relaxed quite a bit. Looking at it from the bright side, you might like the updates. :)
03 Feb 2017 16:09 UTC

mrb wrote: But it's not a random collection of hardware. I didn't hand pick the most efficient ones to prove my point. It's all the known manufacturers of ASICs in the *world*. Literally.

Now, there are a lot of companies that never released silicon, failed, ran out of money, etc, see:

But nowadays all the known manufacturers of mining ASICs can be counted on the fingers of one hand (the list I gave, minus KnC minus Spondoolies who have failed). And when *all* of them have been shipping ASICs doing 0.06-0.15 J/GH for a while it's pretty obvious BECI's claims of 0.427 J/GH is impossible.

I'll say it again: it seems you don't know the ASIC market and that's what prevents you from understand how far off reality BECI is.
04 Feb 2017 00:29 UTC

Digiconomist wrote: But you didn't check how your estimate works out economically. You're saying the network is running at something like 0.12 J/GH. 0.15 J/GH if there has been zero improvement for a year, but that would be odd. Today the network is at 3,100 PH/s, so we're talking about 3.26-4.07 TWh per year.

We can translate this to costs directly since we can assume miners get 1 KWh per 5 cents spent on costs (per your own numbers). We get that on 3.26-4.07 TWh that translates to USD 163-204 mio in ongoing costs.

Annual income available to miners is easy to estimate as well, and it comes down to 817 mio per year (including fees). What we get is that miners are thus implied to be spending 20-25% on ongoing costs on average.

Now, of course this is in line with your example where the farm is paying 21% in costs, but you realize very well profit margins don't stay at 70-80% during the entire lifetime. On Twitter you wrote: "When I was mining with 20kW of GPUs it was pointless to mine when elec costs were ~70% of my revenues." So in my opinion you're arguing against yourself here.

If you want this to work out you're going to need something like 50% in ongoing costs on average. That's not the number I'm going with (65%), but then we're suddenly talking about BECI being just ~1.3 times the resulting estimate. That wouldn't be a massive gap at all.
04 Feb 2017 14:13 UTC

mrb wrote: I wrote a new post:

And I fully rewrote this post to take into account your "final release" of BECI which is still flawed.

My numbers prove to you that it is IMPOSSIBLE that miners spend more than 42% of mining income on electricity.

I think you fail to visualize how efficiency averages out. To calculate the average efficiency you need to average PER UNIT OF HASH RATE. And at any point in time in general most of the network hash rate is provided by newer farms (perhaps this is the crucial insight that makes it hard for you to accept my numbers?) So if 80% of the hash rate is provided by miners spending 20% on electricity, and if the remaining 20% spend 80% on electricity, the average is not 50% but 32%. Do the math. Read my new analysis ( and let me know if you have any questions.
15 Mar 2017 22:31 UTC

Digiconomist wrote: Did you really write this all just to point out that my estimate should be on the bottom end of my own error margin? From today's numbers: revenue $957M per year, costs $523M per year, so ~55.5%. As stated: "within reasonable economic boundaries one might expect to find a number that is 25 percent higher or lower". 42% costs is within that range. Anyway, anyone is welcome to pick another number if they like. I'm just trying to establish a method that produces a number that is plausible economically and not just technically (if you look at past estimates you can easily see why). BECI does that just fine.

By the way, the price is averaged over 60 days. It's not like I don't take feedback seriously ;)
16 Mar 2017 19:41 UTC

mrb wrote: Your "25%" is another figure pulled out of thin air. And this error margin is wrong too: $523M ±25% is $392-654M which is not in the bounds of $142-339M from Remember anything above $339M is provably wrong. It assumes the worst possible case of miners deploying the least efficient hardware available at their time. So your entire range of $392-654M is *really* in the wrong. You cannot keep saying "this isn't economically plausible" when I present factual, verifiable data proving your model is invalid.

You don't seem to believe in the "economics of mining" so here are numbers for a real-world miner showing that it can be quite profitable to mine (new added section):

Do something about it. Fix BECI.

PS: ok it's good that you average over 60 days. 1 (out of many) issue fixed :)
17 Mar 2017 03:01 UTC

Digiconomist wrote: I found it really hard to understand why you insist there's no overlap until I released 42% in your story isn't the same as 42% in mine, as your total revenues are based on unadjusted block rewards only. I also include fees and adjust for increasing hashrate (blocks are mined faster than once per 10 minutes on average). That leaves a serious gap of $130M between our revenue assumptions lol.

If you take 42% of the actual revenue we're going to be a lot closer, unless of course you'd like to tweak your scientific bounds in that case.
17 Mar 2017 15:05 UTC

mrb wrote: There is no overlap. My calculation is that worst case electricity costs are $339M/yr regardless of fees. The amount of fees is not a variable in my model because the model is based on what ASICs are used by miners and what are their energy efficiency.

So $339M/yr represents 42% of miner income excluding fees, or 38-39% of miner income including fees.

Arguing that your lower bound being close to my upper bound makes your model "ok" is wrong. Your bigger problem is your upper bound that should be close to $339M/yr.
17 Mar 2017 19:10 UTC

Digiconomist wrote: Okay, I really appreciate the effort you're putting into all this, so I'm checking out the new article later. But seriously, please fix this post.

I come to this page, and the first thing I see is a statement that I'm making a mistake on marginal costs. All I can say to that is that marginal costs don't include fixed costs like depreciation on buildings/machines or salaries like you're stating. So you'll then find that it really is mostly electricity costs.

Then I also find that you're just leaving out $100M+ from the revenue, and on top of the previous that really makes my brain explode.
18 Mar 2017 09:40 UTC

mrb wrote: Marginal costs do include the cost of the hardware. What is debatable is whether they include buildings and salaries (I edited this part of the post, see the new footnote about marginal costs.) But you are categorically wrong that they do not include the cost of the hardware. A miner adding one unit of mining capacity certainly needs to pay for this hardware.

In fact, the hardware cost is the largest initial marginal cost of setting up a new farm. Look at the CSV file in : an Antminer S5 cost $418 and consumes only $0.71/day in electricity. It takes more than 1.5 years for the cost of electricity to surpass the cost of the hardware.

Finally, I am not leaving out $100M of fees revenue. See the new footnote explaining how 18-42% is calculated.

Let me know when you will have fixed BECI.
21 Mar 2017 03:30 UTC

Digiconomist wrote: You should really check out the paper by Hayes (2015)

Specifically this part is relevant:

“Each unit of mining effort has a fixed sunk cost involved in the purchase, transportation and installation of the mining hardware. It also has a variable, or ongoing cost which is the direct expense of electricity consumption.”

Since sunk costs (unrecoverable expenses) aren’t relevant to marginal costs (it's not like they're not paid for), that’s how he’s left with electricity consumption.
21 Mar 2017 10:19 UTC

mrb wrote: "Since sunk costs aren't relevant to marginal costs..." → you jump to this conclusion, but no one supports this conclusion. Not even this paper by Hayes. You quoted a part that just explains "there is capex, and there is opex" which is obvious to you and I, and which is not what we are arguing about.

You try to argue that if a miner purchases an Antminer S5 for $418 and powers it for $0.71 per day, then economic theory suggests that mining revenues will amount to $0.71 per day. That is false. In reality miners expect to recover $0.71/day plus the $418.
22 Mar 2017 01:21 UTC

Digiconomist wrote: That's basic economic theory and also the reason why Hayes subsequently ignores them in the rest of his paper...

Investopedia explains this very well:

"Since decision-making only affects the future course of business, sunk costs should be irrelevant in the decision-making process. Instead, a decision maker should base her strategy on how to proceed with business or investment activities on future costs."

So basically, the price that was paid for a miner isn't relevant because it's purely retrospective. Looking forward, only electricity consumption (and some other negligible costs) matters . Putting these 100% of revenues isn't that crazy from an economic PoV (after all, the optimal output if where marginal costs = marginal revenue).

Now you're stating; I can show a new farm starting with elec costs as low as 15%, so are you kidding me with the number of miners needed at 100%+ to compensate for that.

I do agree with you that it goes against intuition, but first let's examine some reasons mentioned by Hayes why costs could exceed 100%:

"Individual decision makers may operate regardless of cost if they believe that there is enough speculative potential to the upside. Bitcoin mining may draw in those who find the features of anonymity and lack of governmental oversight attractive. Some miners may decide to hoard some or all of their lot and not regularly engage in offering mined bitcoins in the open market, a sort of bitcoin 'fetishism'"

Now I'm obviously a bit skeptical about this myself, otherwise I wouldn't have lowered the percentage.

Hayes actually mentions an important reason too why 100% could simply be too much:

"Some miners may be subject to an opportunity cost whereby it would be more profitable to expend the same electrical capacity for some other pursuit"

Objectively it should be (close to) 100% though. At least from an economic PoV. If reality differs that's not a failure of correctly applying economic theory.
22 Mar 2017 10:56 UTC

mrb wrote: I agree this economic theory makes sense in a theoretical case.

But if it was in effect in the present situation, then the global hash rate would be stagnating: existing miners would continue to mine because they can recoup their electrical opex, and no new miners would join in because they expect to be unable to recoup the sunk cost of capex. Obviously that is not what is happening. The hash rate has been increasing for years precisely because new miners expect to recoup sunk costs. Therefore this theory cannot possibly apply to the present situation.

I edited "critic #1" to better explain all this.
26 Mar 2017 02:16 UTC

lorschd wrote: What an interesting dispute ;) The typical discussion between engineering bottom-up and economic top down in energy modelling.
Questions / comments on bottom-up: mrb you wrote that the PUE of mining farms is “typically very low for mining farms, 1.05 or so.” Really? I would appreciate some empirical evidence. The PUE values appear pretty low compared to other data centers ( e.g., ). I know about liquid cooling (eg. However, there might be also some overhead for power distribution & conditioning, redundancy (n+1) or backup supply etc. Do you really think these low PUE numbers are mining industry average? From my point of view, proper lower and upper bound estimations would include the most and least efficient PUE guesstimates.
On marginal costs:
We distinguish between short-term and long-term marginal costs. Before costs are sunk, i.e. before investing, decision makers will only invest if there long-term marginal costs are covered. Broadly speaking, long-term marginal costs are the average costs and as such naturally include capex. Btw capex should not only encompass the mining hardware, but also the data center and its site infrastructure. Once investment is done or in “fixed capacity” markets marginal costs equal market price rule may apply and miners aspire positive contribution margins. For capacity expansion, however, the potential investor needs to expect that long-run marginal costs are covered.
(see e.g. ; You may also confer the discussion about the “missing money problem” in electricity markets. ).
However I think in light of inherent economics characteristics of Bitcoin - non-renewable commodity with finite availability – we may also consider that Btc may rather follow the Hotelling rule for exhaustible resources (, which would imply an exponentially increasing bitcoin price (ofc with boom/bust trading cycles, but in the long-run exponential).
11 Apr 2017 18:34 UTC

mrb wrote: lorschd: About PUE, you found yourself that Bitfury self-reports 1.02. But it's mostly from acquaintances who run farms that I know they are around 1.05. Sorry I can't provide direct evidence. It makes sense for PUE to be super-optimized. Mining is a venture with such thin operating margins that a PUE of 1.15 would cut your profits by 10% compared to a competitor at 1.05, so there is an unusually strong incentive to optimize it as much as possible.

You see the result of this optimization in the design of mining farms: they either use liquid cooling or outside air cooling (never traditional CRACs), and bring relatively high voltages directly to servers (480/277 or 415/240 VAC) to eliminate some power conversion steps.

There is also typically no need for power redundancy or backup supply, so none of that affects the PUE. Backup supply/gas generators are too expensive per kWh to mine with. And redundancy is not needed because miners don't need high availability. They could tolerate even a subpar public utility having outages ~1% of the time. That would only cut their revenues by ~1% unlike traditional businesses that would be much more severely impacted.

Finally, I agree capex includes the facility and infrastructure. Ignoring/underestimating capex is one of the main errors that Digiconomist commits.
12 Apr 2017 23:25 UTC

Digiconomist wrote: Hmm... before investing "fixed cost" could indeed be marginal costs. But try asking the question; who is the investor? From a new miner's perspective these could be quite high, but it's less extreme for a manufacturer. In fact, it's an entirely different model there (their fixed costs are the machines to produce the miners). 15 Apr 2017 15:01 UTC

Digiconomist wrote: Added details with regard to the previous statement to the BECI page. IMO that covers #1 and #2 (the BECI was never based on Aste's work to begin with; Hayes deserves the credits). You're also very fixed on that 65% number; "the goal of the Index is not to produce a perfect estimate, but to produce an economically credible day-to-day estimate that is more accurate and robust than an estimate based on the efficiency of a selection of mining machines." The index cost % is capped at 65 and you should apply an error margin of 25% (supported by the lower bound in the supplement).

As for #3 and #4. These have been addressed. It's sufficiently clear that it concerns electricity consumption.

And with regard to #5. Well, I followed your method to determine the machines that should be active at the very least. The only economic part is that it is assumed that miners run while it's profitable to do so whether that is 1% or 99% profits. That's a lot safer than guessing what miners may or may not do.
26 Apr 2017 14:28 UTC

mrb wrote: You say "could indeed be marginal costs," but they *are*. We exchanged dozens of messages and so far you have failed to explain every single time why you ignore capex (this is critic #1). On Twitter you said they should be taken into account if new hardware is deployed, and my point is that new hardware is constantly being deployed: the hash rate is shooting up every day. At least it seems you are slowly taking into account capex by assuming, at least, that a fraction of mining revenues is spent on costs other than electricity...

About critic #2, I am "fixed" on this 65% because it is the single and only variable in your model that determines all your numbers, and the percentage is very wrong. You cannot justify it by having a disclaimer tucked down at the end of your page ("the goal of the Index is not to produce a perfect estimate"). This makes BECI highly deceptive. Neither is your 25% error margin sufficient to justify your position: 65±25 implies your index cost percentage is between 40-90%. I have shown in my article the real percentage is in the range 18-42%. So you assuming it could be anything beyond 42% is, simply put, grossly flawed.

You responded to my critic #3, thanks.

You still have one more fix needed to fully resolve critic #4. Replace energy with electricity in "the entire Bitcoin network now consumes more energy than a number of countries."

Regarding critic #5, you are missing the point of what a lower bound is. A lower bound means you are absolutely certain that miners cannot possibly consume less energy than a given bound. You make a (wrong) guess/assumption that *all* miners run *all* their mining farms until their very last profitable day. But to make it a lower bound, you must prove it. You fail to do so because your guess is incorrect. Ironically you say your model is "a lot safer than guessing what miners may or may not do" but you are doing precisely that: guessing! What do you think Bitfury did once their 16nm hardware rolled out of the factory floor? You think they were waiting for the 28nm gear to stop being profitable to upgrade to 16nm? You think they spent a fortune building *additional* 16nm farms besides their 28nm farms? The answer to both questions is: no! They decommissioned their 28nm hardware right away (even if still somewhat profitable) to replace it with much more profitable 16nm hardware.

You are not a miner. You have never talked to, researched, or studied the mining industry. You have never met and interviewed professional miners. If you had done so, you would realize how flawed your assumptions and entire model is.
15 May 2017 01:51 UTC

Digiconomist wrote: "BECI’s author’s implicit acknowledgment his earlier models would be overestimating electricity consumption by 1.57"

Okay, official reaction from BECI's author to this: I explicitely stated that BECI was fine IMO at any point in time, so this is BS, please don't spread lies.

Second, changes are far from random, even informed you of the method. The lag depends on volatility, so it if it was lower before that's because volatility was lower before. Again, you're spreading lies.

Also it's completely insane to state I would like to “keep BECI down”? What possible motive do I have???? There's no complete data on Bitcoin's actual energy consumption anywhere, so there's ZERO need for adjustments. You have offered NO information that would somehow lead me to think otherwise, and I've been trying to explain that for some time - but you don't seem to get it.

If you have to lower yourself to slandering to make a point that's absolutely pathetic.
03 Aug 2017 15:34 UTC

mrb wrote: You seem to be making 3 points (and the email dump you published seems to have also been made in response to the same 3 points):

(1) I said your moving period average changes (60 days → 120 days → 150 days → 200 days) implicitly acknowledge you overestimated consumption by 1.57×. I was documenting the positive changes you made, since in my opinion they brought BECI a little bit more in line with reality (not completely though). But instead you reject this mildly positive critic and insist BECI was fine at any point? Ok, I removed that sentence and edited critic #3.1.

(By the way, BECI was certainly not fine "at any point." For example: you used to assume 100% of revenues were spent on electricity.)

(2) You said you have no motive to "keep BECI down". Well I assumed good faith on your part: I assumed your "motive" to keep BECI down by increasing the moving average period was to try to shift BECI's numbers to be closer to reality.

(3) I said you do not track, archive, or document changes to the moving average period and that the changes look random. I said it because it took 5 emails where I kept asking when you made the changes, before finally obtaining your partial best answer (an ill-specified formula). You had not yet given me the formula at the time I had last updated this post. I have now updated it to remove the "random" critic. However as you said in an email, answering the question of when did you make the changes would force you "to go through thousands of page versions to retrieve this." Therefore my main criticism remains valid: you do not track the changes in an easy/proper way, you do not want to or cannot answer, and you certainly do not *document* the changes publicly. It is therefore impossible to verify/reproduce BECI's numbers, past and present (the current moving average period is no longer documented on the site.)

You say I have offered no information that would change your mind, but that is an understatement. You have yet to refute the (updated) information I gave you in critic #1, #2, #3.1, #4, and #5. Plus I gave you my other post full of facts, data, charts, and CSV files: I gave you many counter-arguments over the last few months, many of which you have never replied to.

I am certainly NOT slandering you, but instead presenting you with facts and data disproving your model.
31 Oct 2017 21:59 UTC

Digiconomist wrote: >I gave you many counter-arguments over the last few months, many of which you have never replied to.

I did, but you didn't seem to care about what the arguments were (per your emails you certainly didn't have any troubles publishing on an unfinished discussion). One way or another, it's not very pretty what you did here.

In any case, I've abandoned this discussion. We can discuss forever, but all we'd be doing would be arguing whether Bitcoin's energy consumption is insane or even more insane.
11 Dec 2017 15:10 UTC

mrb wrote: You claim you replied to my critics. This is an outright lie.

For example you have completely avoided replying to my main point (critic #2): the 4 logic errors you made in choosing your model's main parameter, the "60%" percentage. See the list items numbered 1-4 concluding critic #2. Zero response from you.

Seeing you abandon this discussion simply betrays your fundamental inability to defend your flawed model.

PS: This blog post is a live document, updated as our debate progresses. It will always be "unfinished".
07 Jan 2018 03:17 UTC

Digiconomist wrote: Please update it with Morgan Stanley's latest work. They did a production based analysis and concluded the cost of mining 1 Bitcoin is between $3,000 and $7,000. My model puts it at just $2,100 per coin at the same time. MS also assumes a bit higher price per KWh, so it's in the same energy range (although on the low side, but the model was supposed to be conservative). ;)
12 Jan 2018 22:15 UTC