My stats are a little rusty, but as far as I see, it doesn't, it goes up.
Hashing is
Bernoulli trial, either you beat the target or you don't. That gives mining a
geometric distribution, and so the variance (in number of hashes required) is (1-p)/p
2. The re-targeting algorithm tries to keep the hashrate directly proportional to 1/p, so the variance in time quadratically increases with the hashrate. Right?
I guess the phenomenon above was a much higher variance in hashrate because of people turning their computers off at night, whereas now the variance is greatly reduced due to increased numbers and because miners tend to keep the gear running 24/7.
Only 'technically', on a very small scale, is the variance different. In reality it is unobservable at different difficulties.
Hashing is typically modeled as an exponential distribution, a continuous series, however it is actually a geometric distribution. The probability is so low though, that the R statistics package fails to compute due to overflow errors with statistics on much more than difficulty 1.
The variance is given for a geometric distribution as:
![](https://ip.bitcointalk.org/?u=http%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FGeometricDistribution%2FInline63.gif&t=665&c=KgY2ryWBgCU8ag)
![](https://ip.bitcointalk.org/?u=http%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FGeometricDistribution%2FInline64.gif&t=665&c=TBod_bDIgggHxQ)
![](https://ip.bitcointalk.org/?u=http%3A%2F%2Fmathworld.wolfram.com%2Fimages%2Fequations%2FGeometricDistribution%2FInline65.gif&t=665&c=OR7SeegRhEXPFQ)
You can see that for extremely small p (probability of one hash finding a block), the top numerator approaches 1, becoming insignificant compared to the p
2.
The high block times around 20000-30000 has something to do with the satoshi miner and others not making much hashes during that time, there was much less than difficulty 1 worth of mining being done. I could eliminate the first year of Bitcoin to get a better list of long blocks, long due to variance rather than low hashrate.