var num = ['0.1495', '0.1174', '0.1139', '0.1103', '0.1032', '0.1032', '0.1975', '0.0854', '0.0783', '0.0356', '0.032', '0.0214', '0.0178', '0.0071', '0.0071', '0.0071', '0.0100'].map(num => Number(num));
var difficulty = 14363025673660;
function centralization(x, y){
var sum = 0;
for(var i=0; isum += difficulty**(y[i])
}
return sum;
}
Where x the difficulty (which is fixed) and y the array of the distribution. The num variable can be passed through the function as y. I just wrote the above javascript code, it may not be mathematically proper. I'd really want someone to correct me.
Given an array num of the Bitcoin distribution and a difficulty of 14363025673660, we get centralization = 668.18.
If instead of 4 pools owning the 14.95%, 11.74%, 11.39%, 11.03%, 10.32%, we had one owning the 14.95% + 11.74% + 11.39% + 11.03% + 10.32% = 59.43% of the total computational power offered, we'd get centralization = 65971206.1.
Generally, centralization increases explosively if a pool approaches 0.5.
However, it seems not enough to simply use the difficulty (the whole network computing power) and the computing power distribution to form a function.
We can introduce some formulas that have been verified repeatedly,I found a very interesting paper when I was looking up the information, and I will share it with you
Measuring Decentralization in Bitcoin and Ethereum using Multiple Metrics and Granularities
[b]Gini coefficient[/b]: The Gini coefficient is often used as a gauge of economic inequality,
measuring wealth distribution among a population. In the scenario of measuring decentralization in blockchains,
the Gini coefficient could be used to indicate the inequality of the distribution of mining power among miners .
[b]Shannon Entropy[/b]: In 1948, Shannon pointed out that information has redundancy,
and the amount of redundancy depends on the distribution of probabilities, or uncertainty, within the information, which could be quantified by the notion of Shannon entropy.
[b]Nakamoto coefficient[/b]: The aforementioned two metrics are a bit abstract and the degree of decentralization quantified via them is not directly associated with the security in blockchains.
Therefore, we adopt the Nakamoto coefficient as the third measurement metric in this paper.
Nakamoto coefficient is defined as the minimum number of entities required to collude for gathering over 51% of the overall mining power to compromise a blockchain system.
The end result is that, the degree of decentralization in Bitcoin is higher, while the degree of decentralization in Ethereum is more stable.
The specific conclusion can be viewed in the link, this is a pdf link and will not increase the number of clicks for this article
By the way, I just briefly looked at the methods and conclusions mentioned in the paper, and it does not represent the author’s point of view.