:

[chodpaba]

:

[hoo2jalu]

Block Number: 122976

Difficulty
Lower Quartile: 138920
Median: 159421
Upper Quartile: 178980

Assuming linear progression. We've got accelerating generation capacity. My coins are on > 190000 

[marcus_of_augustus]

Is this your model based on bitcoin price that has predicted the shown difficulty distribution plot?

[Clavulanic]

So that is about a 45% increase in difficulty (going off your median) from where we stand now. Is the difficulty linear? As in would one have to increase their Mhash/sec by ~45% to continue earning the same amount of BTC after the difficulty increase?

At the current rate of 8.33blocks/hour it looks like we'll get to the next level at about 8 days, or 193 hours.

[epii]

Is the difficulty linear? As in would one have to increase their Mhash/sec by ~45% to continue earning the same amount of BTC after the difficulty increase?

Correct.

[epii]

Block Number: 122976

Difficulty
Lower Quartile: 138920
Median: 159421
Upper Quartile: 178980

http://bitcoin.sipa.be/ has your prediction looking very plausible.  Kudos for putting math to good use!   

[marcus_of_augustus]

Is this your model based on bitcoin price that has predicted the shown difficulty distribution plot?

I have since refined the model a bit, and it is very pretty. There is a strong correlation between the 12 week moving average and difficulty as shown by Pearson (.99!). Difficulty is arrived at as the product of the 12WMA and a factor that increases linearly with time. I only just discovered this linear increase.

The probability distribution is the variance of this mostly linear factor about a straight line median. It demonstrates to be a Gaussian distribution (pink markers). By matching the median and standard deviation for a normal random variant it is easy enough to run a Monte-Carlo simulation to reconstruct the probability distribution of the product of the projected factor and the 12WMA (1000 trials, blue markers). Then it is just a matter of calculating the quartiles.


This leads to some interesting conclusions presuming an exponentially increasing Bitcoin price. More to come...

Intriguing, that's sounds almost too predictable for such a seemingly chaotic system growth ... are you going to write it up and publish?

I'd be interested to read it at least.

[marcus_of_augustus]

Looks like this puppy is pretty much dialed in now.

The median forecast Difficulty for block 122976 was 159421, the actual difficulty is 157426... A variance of only 1.3%...

Now let's see how well the model works on the next re-target.

So what's the difficulty increases for the next 6-12 months look like on your model?

[TTBit]

Would there be interest if I re-opened the difficulty wagering at BSB for a specific block #?

It would still be in beta, and would not charge any fees. As a reminder, it's pari-mutual. If you calculate a 40% chance of being over X on block Y, you should bet in the ratio of 2:3. An gambler/miner would wager on one side or the other as a hedge.

[wareen]

Date   Block   Difficulty
2011-05-23   124992   223428
2011-06-06   127008   272448
2011-06-20   129024   333313
2011-07-04   131040   414183
2011-07-18   133056   501461
2011-08-01   135072   558063
2011-08-15   137088   638970
2011-08-29   139104   784430
2011-09-12   141120   967117
2011-09-26   143136   1191055
2011-10-10   145152   1464570
2011-10-24   147168   1787604
2011-11-07   149184   2168768
2011-11-21   151200   2609618

Thank you very much for the interesting analysis - one note however: as difficulty increases, the time needed for 2016 blocks to be computed will be lower than the expected 14 days.
So if we have have for example a steady 40% increase in hashing power, difficulty adjustments will occur every 10 days.
This makes your numbers even scarier

[bitcoinBull]

Good work.

+1 on the suggestion for a writeup.

Actually, the chaotic bit is on the currency exchange end. It seems to drive the rest of the growth process, which is quite a bit more orderly. System growth only looks chaotic because of this driver, but once you realize that there is extremely tight coupling between price and Difficulty the rest starts to fall into place.

I'm not sure I'd qualify the coupling between price and difficulty as "extremely tight".  That's the question I'm trying to answer with my price over difficulty charts, but since there's only about six months of reasonable data available, its hard to know from which scale to view them.  Zoom out enough and the ratio looks smooth, but zooming in there's plenty of variation.  They are certainly coupled to some extent, which is good to know.

That is a good point, and it is probably a necessary refinement to the model, but that is actually a little more complicated to project since there is not a very reliable record of network hashing capacity, which is itself only arrived at in a derivative manner. It is statistically possible using high resolution data to estimate fairly accurately, but that fruit hangs a little higher than the easy to get, once per re-targeting period data I have been using... I suppose a reasonable analog could be arrived at just using the change in average time to solve a block between re-targets. I will think about it when I have more time.

blockexplorer.com has a netHashPerSecond calculation to a maximum resolution of every five blocks:  http://blockexplorer.com/q/nethash/5

Very choppy at that high of a resolution though.  Replace the 5 with any higher number for lower resolutions..