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The author of the 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: 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.
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 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: “ [] 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. • 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.) • 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.”) • 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. 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. 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*. 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. 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.' Download Free Software Audyssey Microphone Calibration File.
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. 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%. Read my new analysis (and let me know if you have any questions. 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. 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. 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. 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. 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. 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. 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.
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. 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. 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).
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. 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. 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.
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. 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.
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. 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'.