Predicting difficulty - a different take based on historical trends

[erpbridge]

Using the following resources:
https://docs.google.com/spreadsheet/ccc?key=0AmcTCtjBoRWUdHVRMHpqWUJValI1RlZiaEtCT1RrQmc#gid=0
(linked from https://en.bitcoin.it/wiki/Difficulty)

Its obvious that using static difficulty to predict out future diff is also not accurate. We've seen posts from this time last year predicting rises of 14 pct with a diff of 40 mil by now.

Its also pretty obvious the days per difficulty adjustment are becoming fewer as new equipment is rolling out. The 65nm rollouts seem to be coming off the lines faster than before, and 28nm is around the corner in Q1 or possibly Q2 2014. Where it used to be 13-14 days between diff increases at end of year 2012, its now 10-11 days now.

I took the average of the last 10 rounds of Days (delta), and it comes out to -.208 days trend.

Now for the actual difficulty value... it would be silly to try to extrapolate today's 29-30 pct average difficulty change forward, just as it was silly to extrapolate 14 percent a while back. Its rising, steadily. I ended up looking at what the average difference between percentage increases was for the last 10 changes (2.09 percent increase), and adding that plus .1 percent each week to show some growth (just as it wasn't a steady flat percentage at any time in the last year, and as new inventory is being added to the network all the time.) I threw in a minus 20 percent about once every 8 weeks and recover almost the lost amount the next week, as that's what the trend seems to show also (a point in time when people pull back for a bit and cut miners, like a bear market week when price plumments far below profitable... then a bear market rally back to status quo pricing the next week.)

(I personally think even these numbers in both cases are quite low and quite conservative... I think the days will increase even faster as time goes on, rather than a steady change... to the point where by Feb or March we'll probably have 3 rounds of 5 days each, and by end of 2014 have diff changing every day or every other day. I also don't quite subscribe to the steady change in difference, as the past few months showed us close to a double in difference percent, as did the few before that. However, calculating something like that out put us at 60 pct difference increase per round in January, and over 100 percent difference increase... aka doubling difference... by about April. I honestly still think that could quite possibly become a possibility.)

Time will show how true THESE predictions are, compared to the ones of a year ago. The criticisms most likely to come up below will be "will price hold, or will people shut off even smaller items Jalapeno miners before X point", and "this won't happen, 65nm will level out in late Q4 2013 and 28nm is a pipe dream until late Q2 2013, so diff will level out." Another criticism will point to how rapidly the transition from 1B to 10B to 100B takes place. I'll just ask you look at historical numbers, try to continue trends out, and judge for yourself. They are right there on that Google doc I linked above, and that's not made by me.

One more thing: I really hate to say this, but these numbers make even GenesisBlock look tame with its current projection of _monthly_ increases of 80-120 percent. With this... we're looking at those monthly numbers climbing to 200, 250, 300 percent. Then again, if GenesisBlock had been a big name back in Sept 2012, it would have been forecasting monthly increases of 25 percent for every month up to current.

----
My numbers, along with a snippet of current info.

Code:

Date of Diff change	Days Delta	Days Delta diff	Difficulty	Increase %	delta increase %
7/11/2013		11.42		-1.28		26162876	22.63%		12.31%
7/22/2013		11.73		0.31		31256961	19.47%		-3.16%
8/3/2013		11.7		-0.03		37392766	19.63%		0.16%
8/13/2013		10.31		-1.39		50810339	35.88%		16.25%
8/24/2013		10.83		0.52		65750060	29.40%		-6.48%
9/4/2013		10.59		-0.24		86933018	32.22%		2.82%
9/14/2013		10.81		0.22		112628549	29.56%		-2.66%
9/24/2013		10.602		-0.208		148275485	31.65000%	2.09%
10/4/2013		10.394		-0.208		165549579	11.65000%	-20.00%
10/15/2013		10.186		-0.208		217532146	31.40000%	19.75%
10/25/2013		9.978		-0.208		290601194	33.59000%	2.1900%
11/3/2013		9.77		-0.208		394868903	35.88000%	2.2900%
11/13/2013		9.562		-0.208		545985232	38.27000%	2.3900%
11/22/2013		9.354		-0.208		768528813	40.76000%	2.4900%
12/1/2013		9.146		-0.208		1101686053	43.35000%	2.5900%
12/10/2013		8.938		-0.208		1608902312	46.04000%	2.6900%
12/19/2013		8.73		-0.208		2027860474	26.04000%	-20.00%
12/28/2013		8.522		-0.208		2956417785	45.79000%	19.75%
1/5/2014		8.314		-0.208		4392645545	48.58000%	2.7900%
1/13/2014		8.106		-0.208		6653540208	51.47000%	2.8900%
1/21/2014		7.898		-0.208		10277058205	54.46000%	2.9900%
1/29/2014		7.69		-0.208		16191505202	57.55000%	3.0900%
2/5/2014		7.482		-0.208		26026225461	60.74000%	3.1900%
2/12/2014		7.274		-0.208		42690817624	64.03000%	3.2900%
2/20/2014		7.066		-0.208		61487584624	44.03000%	-20.00%
2/26/2014		6.858		-0.208		100704366097	63.78000%	19.75%
3/5/2014		6.65		-0.208		168347488804	67.17000%	3.3900%
3/11/2014		6.442		-0.208		287301824392	70.66000%	3.4900%
3/18/2014		6.234		-0.208		500623429004	74.25000%	3.5900%
3/24/2014		6.026		-0.208		890809329569	77.94000%	3.6900%
3/30/2014		5.818		-0.208		1618867794626	81.73000%	3.7900%
4/4/2014		5.61		-0.208		3004942400385	85.62000%	3.8900%
4/10/2014		5.402		-0.208		5697671285370	89.61000%	3.9900%

[1713528445]

1713528445

[Puppet]

Just extrapolating numbers without reasoning doesnt make a lot of sense. Its fun, but you need to be looking at the causes.
Where is difficulty really headed? Its headed towards the point where miners are no longer interested in buying new hardware at a price per TH thats below what vendors are able to provide. That is your clue.

To guestimate that number, you need to know what those asics cost to produce. I posted my estimates in various threads, depending on how big those 28nm asics turn out to be (only hashfast is known to be 18x18mm) and what prices those vendors can obtain from the fab (Im conservatively assuming $4000 per 300mm 28nm bulk silicon wafer) and some smaller unknowns like yield, costs for testing/packaging etc. Pure silicon processing cost for hashfast works out at $22 per chip candidate, if you add defects, testing, packaging, operating margin, you end up somewhere around $40-$50 for their 400GH chip (assuming they achieve that). Below that point, it makes not much sense for hashfast to produce extra batches, above that point, its still marginally profitable for them considering the maskset and design is all paid for.

Then do the math where difficulty needs to be for miners to be no longer interested in buying extra mining hardware at ~$100 per TH given their electrical efficiency (assuming hashfast is one of the more competitive 28nm designs, which remains to be seen).

BTW, since miners are not likely to predict combined asic production rates (therefore difficulty) accurately, and all sales are presales these days, they are likely to overbuy. And even asic vendors may not be able to accurately predict this point since they dont know what their competitors are producing, so they may also overshoot this point and over produce, and be forced to sell their inventory at a loss. So its not unlikely the above balance point will actually be exceeded by some margin.

The other important question is how long it will take to get there. The answer is fairly simple, as long as it will take all asic vendors combined to produce, ship and deploy that hashrate. If they all end up as inept as BFL at handling supply chains it may take decades, but if at least one or two of them get it right, we could be getting close to it perhaps as soon as the end of next year.

[Le Happy Merchant]

For the difficulty to change in a single day 2160 blocks would need to be mined in that time.

Let's call it 24 hours. 2160/24 is 90 blocks per hour, 1.5 per minute, or one every 40 seconds.

The ratio between 40 seconds and the target of 600 seconds is 15. To achieve this, the hashing rate of the network would need to multiply by 15 in a very short period of time, and to have several days like this it would need to constantly grow by a factor of 15 every single day.

Personally, I find the idea exciting, and I admit that I don't know much about the mining process, but any rational observer should question the feasibility of a 15x increase in hashrate in such a short period.

I could see a possible 6 day retarget, but I would be shocked to see anything less.

Also, it's worth considering the time until the next halving. If we see daily difficulty adjustments we could see the halving years in advance.

[bcp19]

For the difficulty to change in a single day 2160 blocks would need to be mined in that time.

Let's call it 24 hours. 2160/24 is 90 blocks per hour, 1.5 per minute, or one every 40 seconds.

The ratio between 40 seconds and the target of 600 seconds is 15. To achieve this, the hashing rate of the network would need to multiply by 15 in a very short period of time, and to have several days like this it would need to constantly grow by a factor of 15 every single day.

Personally, I find the idea exciting, and I admit that I don't know much about the mining process, but any rational observer should question the feasibility of a 15x increase in hashrate in such a short period.

I could see a possible 6 day retarget, but I would be shocked to see anything less.

Also, it's worth considering the time until the next halving. If we see daily difficulty adjustments we could see the halving years in advance.

2016 blocks