The Nakamoto coefficient: Measuring network decentralization

By Hennadii Cholovenko 724 28 Jan 2023

A lot of cryptos boast full decentralization without providing any proof. The Nakamoto coefficient helps to identify whether a network is truly decentralized.

What does the Nakamoto coefficient measure?

The Nakamoto score measures the decentralization of any given network (blockchain). It also shows the minimum number of nodes required to disrupt the network. The higher the Nakamoto coefficient, the more decentralized the blockchain is considered to be.

The Nakamoto coefficient was first described in 2017 by former Coinbase CTO Balaji Srinivasan. He named it after Satoshi Nakamoto, the anonymous founder of Bitcoin.

Amid the emergence of a significant number of new blockchains, Srinivasan wanted to find a clear method of determining how decentralized any given system was. He settled on a model based on a combination of a Gini coefficient and a Lorenz curve. Usually, these instruments are used to measure income inequality within an economic population, but Srinivasan believed that they were ideal for measuring the degree of blockchain decentralization.

The Nakamoto coefficient considers all components and areas that affect the blockchain, and how many elements would you have to compromise before gaining control of each component of the blockchain. In other words, this model calculates the minimum amount of effort it would take to destroy the blockchain. A high coefficient means high decentralization. A low coefficient means that the system is too centralized and has a high risk of disruption.

Calculating a Nakamoto coefficient

Calculating a Nakamoto coefficient is a little bit more tricky than just plugging certain numbers into a simple formula.

The threshold to obtain control over the blockchain is considered to be 51% (hence the name of one of the types of attacks). However, the reality is that not all blockchains could be controlled even with 51%. In some cases, it may require around 60% or even 75%, but by default, the formula uses the minimum threshold value of 51%.

Each blockchain is affected by six components: mining, users, developers, exchanges, nodes, and holders. Each one of these components has its unique statistical data set that you need to take into account.

Mining – the amount of reward users earn for mining within a set amount of time;
Users – the total number of accounts per user;
Developers – the number of commits on a project’s GitHub.
Exchanges – the trading volumes on all exchanges within a set amount of time;
Nodes – the location of nodes by countries;
Holders – the asset distribution across user addresses.

When you visualize this information as a Lorenz curve on a graph, you can identify the number of elements it would take to reach the minimum threshold of 51% that will enable you to disrupt the network. This number is a Nakamoto coefficient for calculating blockchain decentralization.

This method can sound too complicated, so let's take a look at a specific example – developers.

When calculating a Nakamoto score for Ethereum decentralization, you can start by establishing the current number of developers. Geth documentation shows the total number of commits per dev. By visualizing this data on a Lorenz curve, you can see that only two of them initiated over 51% of all changes. This means that the current Nakamoto score for Ethereum developers is two which means that the blockchain is heavily centralized.

Nakamoto coefficient advantages and disadvantages

Advantages

Quick identification of decentralized blockchain. The biggest benefit of this method is that it helps to compare different blockchains. Once you calculate the Nakamoto score, you can easily tell which cryptocurrencies are more decentralized compared to others.
Identification of potential risks. This coefficient helps to identify how much effort it would take to compromise a network. It should be used to determine the weakest link in a security system. A low Nakamoto score will indicate a specific area that can potentially carry risks and problems, for example, if most nodes are located in one country or if a significant amount of assets belongs to several users.
Integrating methods for optimizing decentralization. One of the main reasons Srinivasan created this coefficient was to optimize blockchain decentralization metrics. The Nakamoto score allows you to quickly calculate how proposed changes will affect the blockchain. After you test different scenarios, it becomes clear which changes will be for the best.

Disadvantages

The coefficient is easily manipulated. When calculating the Nakamoto score, your data set is incredibly important. For example, if during your analysis of holders, you include wallets with small balances in your statistics, the blockchain may seem very decentralized. However, if you only look at holders that have over $10,000, the crypto may seem too centralized.
Complex statistical calculations. The Nakamoto coefficient isn't calculated by just adding or subtracting a few numbers. There is no simple unified Nakamoto coefficient formula at the moment. You have to spend a lot of time to obtain several input data sets, visualize them on a Lorenz graph, and only then analyze the obtained results.

Comparison of networks by the Nakamoto coefficient

Bitcoin has the highest Nakamoto coefficient of 7,349 having more than 14,400 nodes. All other networks are far behind the first cryptocurrency. Significant progress is shown by Polkadot with 82 points, but compared to Bitcoin, this level of decentralization still looks weak. Interestingly, the well-known blockchain platform Binance Smart Chain has a ridiculous Nakamoto coefficient of 7 (that's the level of decentralization!) and Ethereum is not reported at all. If someone would decide to calculate the Nakamoto score for Ethereum, they would probably get poor results in many directions – whales, developers, nodes (especially after PoS migration), and considering the significant share of pre-mined coins during network launch.