Post
Topic
Board Mining
Topic OP
Audit your pool with better stats
by
grau
on 25/08/2015, 16:21:37 UTC
We know that the expected production of a mining pool is linearly proportional to its market share (x%), it is 24*6*x% blocks per day.
 
The actual production however follows the Possion distribution for reasons you find in the first paragraph of https://en.wikipedia.org/wiki/Poisson_distribution
 
"... the Poisson distribution ... expresses the probability of a given number of  events occurring in a fixed interval of time and/or space if these events occur with a known average rate and independently of the time since the last event."

The probability of not finding a block within a time span in which one would expect n blocks is simply e^-n
Remark: This is the CDF with i = 0 and lambda = n

This means one can assign probability to an observed production outcome and quantify how likely is it.
A probability measure is more informative than "luck" used on many sites and you only need a pocket calculator for the check.

Historic Example:

Slush did not mine a single block for two consecutive days between 19 and 21. Jun 2015 while reporting 9.516 PH/s miner at pool.
see https://mining.bitcoin.cz/stats/blocks

The difficulty implied a network total in the same period was 355.711 PH/s, see https://bitcoinwisdom.com/bitcoin/difficulty
This translates to a historical market share of 2.68%

With that market share one would have expected 2*24*6*0.0268 (means nearly 8 ) blocks in two days.

How probable was not having any blocks in the same time just bad luck? 

Exp[-2*24*6*0.0268] = 0.04%

for me that falls into the practically impossible bucket.