Relationship between luck and network hashrate?

[crazyates]

I got a question! I was looking at charts like this one:

I starting thinking about the relationship between network variance and overall network hashrate.

Now I don't know much about statistics, so bear with me. Basically, if the network grows to enormous rates, say 1000x what it is today: 25PH/s. Difficulty is somewhere around 3Billion. Would the charts like the one I just posted look smoother, or more jagged?

It seems to me that as the network grew, variance would more easily be absorbed by the enormous network hashrate. Yet the chart seems to be in flux, as we've got some pretty hefty variations (as a % of overall network) within the past month or two. Seems to really have gotten worse around August, but just seems to constantly be fluctuating. I would have expected the opposite result?

Idk tho. Anyone more knowledgeable about statistics care to comment?

[yogi]

Variance, if expressed as a percentile, should remain within the same limits regardless of overall computational power.

[crazyates]

Variance, if expressed as a percentile, should remain within the same limits regardless of overall computational power.

So when we hit 2PH/s, the variance could be seen as swinging hundreds of TH/s in a 3 day window?

[yogi]

Variance, if expressed as a percentile, should remain within the same limits regardless of overall computational power.

So when we hit 2PH/s, the variance could be seen as swinging hundreds of TH/s in a 3 day window?

The recent swing is probable influenced by the reward drop and should not be considered natural variance.

[Meni Rosenfeld]

Variance, if expressed as a percentile, should remain within the same limits regardless of overall computational power.

So when we hit 2PH/s, the variance could be seen as swinging hundreds of TH/s in a 3 day window?

You should always expect to find up to 15% deviations from the mean in a 3-day window. But whatever you are seeing now may or may not be pure variance.

The estimated network hashrate is
(number of blocks found in time window) * (average number of hashes required to find a block) / (length of time window)
Block finding is always a Poisson process with rate of about 1 per 10 minutes, so the number of blocks will always follow the same distribution (Poisson distribution with mean (time window / 10 min)). If you increase the number of hashes per block, both the mean and the standard deviation scale by the same factor, so you have the same relative variance.

On the other hand, if instead you estimated using the difficulty-1 shares found, you would indeed have less variance, as there are more of the individual items you're tracking. But if you track blocks, and the difficulty of finding blocks scales to maintain a given rate, it doesn't matter.