Nakamoto Coefficient: A Reliable Measure of Decentralization?

Measuring decentralization is tricky. While blockchains are mainly considered decentralized as they store data onchain instead of corporate-owned servers, they have different levels of decentralization. 

Say, the founders or investors of a project are in charge of making decisions and control most of the computational power, or the majority of nodes. Then, a network can’t truly be called decentralized. 

The Nakamoto Coefficient aims to answer the question of how decentralized a network is. 

How? Read on to find out. This article covers: 

• What is the Nakamoto Coefficient? 
• Who created the Nakamoto Coefficient?
• Why is the Nakamoto Coefficient needed? 
• How is the Nakamoto Coefficient measured? 
• Which blockchains have the highest Nakamoto Coefficient? 
• Is the Nakamoto Coefficient a good metric to measure decentralization?

What Is the Nakamoto Coefficient? 

The Nakamoto Coefficient measures the minimum number of entities needed to change or manipulate the network. It’s a widely used approach in the blockchain industry to measure decentralization.

The higher the Nakamoto Coefficient, the more decentralized the blockchain is considered. For example, if the Coefficient is 5, that means the network can be controlled or influenced by just 5 nodes.

In blockchain, decentralization matters because it reduces censorship risks, where a single party can control network operations and decide, for example, to selectively prevent transactions.

Heard of 51% blockchain attacks?

They happen when a group of attackers gains control of more than 50% of the network's power. With this majority, they can reverse transactions, double-spend coins, or halt the network.51% attacks present risks for both Proof-of-Work and Proof-of-Stake blockchains. At the same time, risks are higher for smaller blockchains with fewer nodes.

These factors are important for understanding and addressing a blockchain's risks. 

Who Are the Creators of the Nakamoto Coefficient

The Nakamoto Coefficient is a new decentralization metric created by former Coinbase CTO Balaji Srinivasan and blockchain researcher Leland Lee. They proposed the concept in the article “Quantifying Decentralization” published in 2017. 

Balaji Srinivasan and Leland Lee proposed the Nakamoto Coefficient in the “Quantifying Decentralization” article: Source: Medium

There’s little information about Lee, except that he co-wrote the proposal. More information is available about Balaji Srinivasan, who has a strong online presence with over 1 million followers on X. 

Balaji is a Stanford University graduate who earned a Bachelor's degree, a Master's degree, and a PhD in Electrical Engineering, along with a Master's degree in Chemical Engineering.In 2014, Balaji co-founded Coin Center, a non-profit crypto research and advocacy organization. He invests in crypto projects and runs his own podcast, “The Network State.”

If you follow crypto events, you've probably caught Balaji Srinivasan chatting about different topics in the space, like tech democracy and the challenges the industry is dealing with.

Why There Was a Need for the Nakamoto Coefficient

The creators of the Nakamoto Coefficient write in their paper: 

We must be able to measure blockchain decentralization before we can improve it.

They compare too much centralization to too much inequality and were motivated by two popular economic concepts for measuring inequality when creating the NC:

1. Lorenz Curve
2. Gini Coefficient

The Lorenz Curve is essentially a graph that shows income or wealth distribution within a population. When everyone has the same income, the curve is a perfectly straight diagonal line. But when some people earn significantly more than others, the curve dips below that line, highlighting income inequality. The more the curve dips away from the diagonal, the greater the inequality.

The Lorenz Curve can be adapted to measure different resources. In blockchain, for example, it can measure the distribution of computational power and how protocol tokens are distributed.

The Gini Coefficient is directly linked to the Lorenz Curve and measures its concentration, indicating how far the Lorenz Curve is from the diagonal line of equality. The Gini Coefficient can take values between 0 and 1; the lower the value, the closer the graph is to the line, indicating a smaller inequality gap, while a value closer to 1 indicates greater inequality.

The Gini index gets higher to show increased inequality depending on the Lorenz Curve (the red line). Source: Quantifying Decentralization paper

In blockchain analysis, the Gini Coefficient has been used to look into multiple addresses and how cryptocurrencies are distributed among network participants.

Building on this concept, the Nakamoto Coefficient expands it further by indicating how many individuals or entities are required to compromise the system.

Since the Gini Coefficient is restricted to a scale of 0 to 1 and focuses on evaluating wealth distribution, it does not allow us to measure this number. Therefore, there was a need for a new and more comprehensive metric, the Nakamoto Coefficient, to assess how independent entities control key areas of a blockchain.

How Is the Nakamoto Coefficient Measured? 

To assess the overall decentralization of a system, the Nakamoto Coefficient evaluates its subsystems. This metric is not stable and responds to changes within the network. For example, a few large transactions by several significant wallets may lower the decentralization index.

The creators of the Nakamoto Coefficient define six subsystems of a blockchain, using the Bitcoin Network as an example:

• Mining decentralization: Mining is the process of validating and adding new transactions to Bitcoin and other Proof-of-Work blockchains. To become a part of the network, miners provide computational resources and receive rewards. NC takes the amount of mining rewards to understand decentralization. 

A network is decentralized when mining power is spread across many independent participants, reducing reliance on any single entity. This metric is important as it indicates that everyone has an equal chance to mine blocks and that operations are ensured by many network participants instead of a small group. 

The same goes for Proof-of-Stake blockchains, like Ethereum. In those systems, block producers are called validators, and they need to stake cryptocurrencies to become eligible for the role. 

• Client decentralization: To connect to a blockchain, miners and validators use software applications, in computational language called clients. There are different client software programs used for various purposes, including storing network history, ensuring consensus, and executing smart contracts. Imagine if a blockchain relies on one client software that crashes because of a bug or an attack; that would compromise the whole chain. Decentralization reduces these risks. A measure of client decentralization can be the number of unique codebases.

• Developer decentralization: ​​The next aspect measured by the Nakamoto Coefficient is developer decentralization. Developers contribute to a blockchain’s codebase and implement changes. When the development process is decentralized, decisions and updates are made collaboratively. Conversely, when power is concentrated in the hands of a few developers, they may change protocol rules and control funds. This can be assessed by examining developer commits to the main client.

• Exchange decentralization: When most of a cryptocurrency’s supply is concentrated on a few exchanges, issues related to delistings, operational hurdles, regulations, and insider trading can lead to price drops, market manipulation, and other risks. The exchanges holding most of the tokens can potentially influence how the token is managed and traded. Insights can be gained from examining the 24-hour trading volume.

6 subsystems of public blockchains the Nakamoto Coefficient considers. Source: “Quantifying Decentralization” paper

• Node decentralization: Computers or any devices connected to the blockchain network and performing specific tasks are called nodes. Nodes exchange information about transactions, blocks, and the state of the blockchain. It's important for nodes to be distributed across different countries and server entities to mitigate technical and security risks. If one node goes down or gets hacked, the others can still keep the network running. Node decentralization can be measured by their distribution among countries.

• Ownership decentralization: The 6th subsystem considered in the Nakamoto Coefficient is ownership. To measure this, the index sets a threshold based on balances that hold a specific number of tokens. For example, the initial paper used the distribution among addresses with a balance of over $500,000 as a metric. The ownership index examines how many holders possess significant amounts and how those tokens are spread out. If just a few holders control a large portion of the token's supply, it suggests concentrated ownership. Conversely, if tokens are distributed among many holders, it indicates a more decentralized ownership structure.

Now, the main question: How is the Nakamoto Coefficient measured? 

The index takes the lowest score across the different aspects to define the overall decentralization of the blockchain.

Even if most aspects demonstrate high decentralization, if one aspect is controlled by just a few entities, the overall Nakamoto Coefficient will be low.

One can compromise a decentralized system if one can compromise any of its essential decentralized subsystems,

– the authors noted.

Which Blockchains Have the Highest Nakamoto Coefficient?  

Blockchain subsystems and the Nakamoto Coefficient can change over time. This metric can rise or fall based on the redistribution of mining or staking power, protocol updates, changes in token control, and other factors.

A common method to measure the Nakamoto Coefficient of a Proof-of-Stake network is to define the number of nodes that together control more than one-third (33.33%) of all stakes on the network.

You can find this information on data platforms and blockchain explorers, such as Dune Analytics or Blockchain.com, as well as dashboards specifically designed to calculate the Nakamoto Coefficient.

One such dashboard is Nakaflow, which calculates the Nakamoto Coefficient for a limited number of blockchains based on real-time data. Here’s how it looks at the time of writing.

Nakamoto Coefficient based on the number of nodes controlling the network. Source: nakaflow.io

The higher the number, the more decentralized the network is considered to be. Among the blockchains tracked on Nakaflow, the most decentralized ones are:

• Mina Protocol: 364
• Polkadot: 116
• Thorchain: 32
• Avalanche: 26
• Aptos: 23
• Solana: 19

Interestingly, the Bitcoin Network and Ethereum are missing from this list. However, we can estimate they are considered more centralized according to the Nakamoto Coefficient.

If we look at the hashrate distribution of the Bitcoin Network, around 80% is controlled by three major miners. Developer decentralization is also low for Bitcoin, as the main team contributing to the blockchain is Bitcoin Core (this is also mentioned in the original Nakamoto Coefficient proposal). Meanwhile, Ethereum staking data reveals that the market share is dominated by Lido, Coinbase, and Binance.

Not a Perfect Metric for Decentralization: How Accurate Is the Nakamoto Coefficient?

The Nakamoto Coefficient can be a useful tool for evaluating a network’s subsystems and understanding the risks presented by various attacks. However, it’s not an absolute metric for decentralization due to several challenges and limitations.

For instance, identifying the number of token holders can be problematic, as individuals often use multiple addresses, and custodial wallets may represent different users.

Another limitation is that the Nakamoto Coefficient does not consider the number of tokens or resources required to become a node operator. High requirements for node operation can hinder equal participation, leading to greater centralization within the network.

It’s also important to know how many nodes are connected to a network. In the Bitcoin Network, this metric currently exceeds 18,600 across different countries. Bitcoin has the largest number of network participants, which itself suggests decentralization, as operations depend on so many individuals.

Taking all these factors into account, the Nakamoto Coefficient is a simple metric that doesn’t capture all the nuances of what makes a network decentralized. However, it does provide insights into various aspects of a blockchain, drawing attention from developers and users to areas that can be improved.

FAQ

1. Why Is Decentralization Important? 

Decentralization improves security, censorship resistance, and trustlessness by distributing control across multiple entities, preventing any single point of failure or authority.

2. How Does the Nakamoto Coefficient Measure Decentralization?

The Nakamoto Coefficient measures decentralization by identifying the minimum number of entities that control over 50% of a blockchain’s resources, such as mining, staking, or validation power.

3. Is the Nakamoto Coefficient a Reliable Metric to Measure Decentralization?

The Nakamoto Coefficient is useful but limited. It doesn’t account for factors like governance, geographic diversity, or node requirements, making it an incomplete measure of decentralization.

4. What Else Is Important for Blockchain Besides Decentralization?

Other aspects to look at in blockchains are how fast, and secure they are and how they ensure privacy. When researching a blockchain, it’s better to pay attention to different factors to understand how the greater picture looks. 

5. Is the Nakamoto Coefficient Created by Satoshi Nakamoto? 

No, the Nakamoto Coefficient was created by Balaji Srinivasan and Leland Lee, who proposed the concept in their 2017 article, “Quantifying Decentralization.”