Calculating the mining centralisation index

0. Introduction
I introduced the mining centralisation index a couple of days ago in this post. Judging by email, I haven't done a very good job explaining how to calculate it - so I've done it again, but with a visualisation to help.

Step 1. Arrange the block making miners in order of size

• Pick a time period, calculate the number of blocks created by known block creators. 
• Unknown block creators are grouped into "Unknown". 
• Sort the block creators from largest to smallest.
• Calculate the cumulative sum of blocks created by each entity.
• Split into groups consisting of the larger and smaller pools (in the plot below, red and blue respectively).
• Paraphrased, the red group is the largest block creators that make most 50% of network blocks for the time period, and the blue group is the smallest block creators that make at 50% of network blocks or just over.

 Step 2: Calculate mean for each group.

•  Calculate the mean blocks per block maker for each group.

Step3: Subtract from ratio of means from 1.

• Divide the mean of the smaller group by the mean of the larger group - in the example above that would be 27.9 / 164.3 = 0.1698.
• Near zero, the average block solve rate of the smaller makers is much less than the larger makers, and at 1 block solve rate of the smaller makers approaches that of the larger makers. 
• This is opposite to the other indices, so subtract the ratio from 1
• 1 -  0.1698 = 0.8302.

Centralisation index: 

1 - mean(block rate smaller makers) / mean(block rate larger makers)

Email me if I still haven't explained this well enough for you.




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