Topics Blockchain
Bybit Learn
Bybit Learn
Intermediate
Jul 18, 2022

Nakamoto Coefficient: An Accurate Indicator for Blockchain Decentralization?

If you're interested in blockchain decentralization, you've probably come across a few discussions on the Nakamoto coefficient. This concept might sound very complex, but once you understand it, it's quite simple. Our guide will tell you everything you need to know about the Nakamoto coefficient so you can use it in your financial decisions.

What Is the Nakamoto Coefficient?

The Nakamoto coefficient measures decentralization and represents the minimum number of nodes required to disrupt the blockchain's network. A high Nakamoto coefficient means that a blockchain is more decentralized.

The Nakamoto coefficient was first formally described in 2017 by former Coinbase CTO Balaji Srinivasan. This measurement is named after Satoshi Nakamoto, the presumed founder of Bitcoin. However, the Nakamoto coefficient isn’t a Bitcoin-only measurement. Instead, a Nakamoto coefficient can be used for analyzing a variety of blockchains.

Srinivasan's initial plan was to find a quantitative way of determining exactly how decentralized any system was. To calculate this, he proposed a method that combined the Gini coefficient and Lorenz curve. These measurements are generally used to look at inequality and non-uniformity within an economic population, but Srinivasan had the revolutionary idea of applying them to blockchain decentralization concepts. The Nakamoto coefficient is created by combining these inequality measurements with blockchain subsystem analysis.

The Nakamoto score considers how many subsystems a blockchain has, and how many entities you would have to compromise before gaining control of each subsystem. Simply put, a Nakamoto score describes the minimum amount of effort it would take to disrupt any given blockchain. A high coefficient means that a blockchain is harder to disrupt, because it’s more decentralized. Meanwhile, a low coefficient means that a system is heavily centralized, and has a high risk of disruption.

Calculating a Blockchain’s Nakamoto Coefficient

Calculating a Nakamoto coefficient is a little more complicated than just plugging basic numbers into a simple formula. The formal definition of a Nakamoto measurement is the minimum number of entities in a given subsystem that can add up their amounts of proportionate control to take control of the subsystem. There are several different techniques you may need to use when calculating this coefficient. You'll need to select your Nakamoto coefficient formulas based on the sort of situation you want to analyze.

First of all, you need to determine the minimum threshold for takeover. How much of any subsystem is needed in order to sway it? The standard number is 51%. However, the reality is that not all blockchains operate on a system where a simple majority gains control. Some systems might require something like 60% or 75% of the network to be in agreement about altering the system. Unless a score says otherwise, you can assume the Nakamoto coefficient formula uses 51% as its minimum threshold.

Next, you have to consider the ways in which each type of blockchain subsystem can be compromised. Srinivasin proposes that any blockchain can be divided into six individual subsystems: Mining, clients, developers, exchanges, nodes and owners. Each one of these subsystems has its own statistical data set you need to consider.

  • Mining: The amount of rewards users get for mining within a set amount of time

  • Clients: The number of users for each client

  • Developers: The number of commits developers make

  • Exchanges: The volume of exchanges made within a set amount of time

  • Nodes: The node distribution across countries

  • Owners: The distribution across individual addresses

Once you have this individualized information plotted as a Lorenz curve on a graph, you can identify the number of entities it would take to reach a minimum threshold percentage for system disruption. You'll need to find the minimum number of entities whose proportionate control adds up to 51%, or whatever other disruption percentage you set. This number is the Nakamoto coefficient for blockchain decentralization.

We know the Nakamoto coefficient formula can sound a little complicated, so let's take a look at a real-world example to make things simpler. For example, when considering the Nakamoto score for Ethereum dev decentralization, you would start by looking up the number of engineers who have made commits. (Geth documentation shows the total number of commits and the number of commits per engineer.) By plotting the number of commits per engineer on a Lorenz curve, if you can see that two engineers alone have made over 51% of all commits, the Nakamoto score for Ethereum devs would be two. This would mean that Ethereum development is heavily centralized.

Nakamoto Coefficient Pros and Cons

As you can see, Nakamoto coefficients are a fairly unique concept in blockchain analysis. Compared to other measurements, these coefficients have some very specific pros and cons.

Nakamoto Coefficient Pros

Using the Nakamoto score comes with many helpful perks.

  • Quickly identify decentralized blockchains: The biggest perk of this measurement is that it makes it easy to compare and contrast blockchains. Once you calculate the Nakamoto score, you can tell at a glance which cryptos are decentralized — and exactly how decentralized various cryptos are.

  • Analyze a variety of blockchain features: The Nakamoto coefficient is very flexible. You can apply it to a variety of situations, so you can analyze the features that matter to you. For example, if you prioritize decentralized development, you can use the coefficient to find blockchains that don't only rely on a few devs.

  • Highlight potential risks: This measurement is all about identifying how much effort it would take to compromise a system. You can use it to determine the biggest security issue for any crypto. A low Nakamoto score can help you identify potential problems, such as all nodes being situated in a single location.

  • Design methods for optimizing decentralization: One of the main reasons Srinivasan created this coefficient was for blockchain decentralization optimization. The Nakamoto coefficient allows you to quickly consider how proposed changes will affect a blockchain. Blockchain users can run several test scenarios, and see which alterations would do the most to improve blockchain decentralization.

Nakamoto Coefficient Cons

Despite its many benefits, this coefficient does have some downsides.

  • Easily manipulated with data set selection: When calculating Nakamoto scores, your data set makes a huge difference. For example, if you’re looking at ownership decentralization, taking the time to account for each wallet with an infinitesimally small amount of currency would make the blockchain seem very decentralized. However, if you only look at owners who have more than $500, the crypto could be extremely centralized.

  • Complicated statistical calculations: Nakamoto scores aren't created by just adding and subtracting a few basic numbers. There's no simple Nakamoto coefficient formula to use. You have to take the time to obtain large sets of data, graph them on a Lorenz curve and analyze the results.

Nakamoto Coefficient Among Popular Blockchains

So how do popular blockchains measure up? Here are some revealing things to know about the measurements for some well-known blockchains.

Bitcoin

By just about any measurement, Bitcoin tends to have the highest Nakamoto score. Its measurements — e.g., for developer, owner and validator — are significantly higher than for most other blockchains. This makes Bitcoin one of the most decentralized blockchains overall. For example, Bitcoin has 14,409 validators and scores a Nakamoto measurement of 7,349, while most blockchains score lower than 15.

Solana

Solana was actually one of the first cryptos to popularize the idea of the Nakamoto coefficient. The measurement was brought up frequently by users, who claimed the blockchain was reasonably centralized. If you look at the total number of validators, Solana does have a decent Nakamoto coefficient of 19. It scores particularly well at things like mining pools. However, when you consider measurements for nodes and owners, Solana has fairly poor scores for blockchain decentralization.

Avalanche

Avalanche tends to rank consistently high across multiple Nakamoto coefficient measures. It has a score of 26 for the total number of validators, and its various subsystems get high scores as well. This comes as no surprise to supporters of Avalanche. From the start, this blockchain's priority has been decentralization. As Nakamoto score analysis shows, Avalanche is the most decentralized proof of stake (PoS) blockchain.

Ethereum

Finding the overall Nakamoto score for Ethereum is tricky enough to require its own separate article. Ethereum has such a large network size that its total number of validators cannot be determined. However, some blockchain experts have managed to look at Nakamoto scores for smaller subsystems of Ethereum. When it comes to things like developer decentralization and owner decentralization, Ethereum tends to have low-to-moderate scores. However, it does excel at providing a decentralized node network. Ethereum actually scores higher than Bitcoin when you consider node distribution.

Is the Nakamoto Coefficient Useful?

The Nakamoto coefficient is certainly one of the most useful methods for measuring blockchain decentralization. Most other measurements just determine whether a blockchain is either centralized or decentralized. Meanwhile, the Nakamoto coefficient shows that blockchain decentralization is on a continuum. It can determine precisely how decentralized any given chain is. Furthermore, it can help to identify a blockchain's strengths and weaknesses so that you can more easily find decentralized blockchains.

The Nakamoto coefficient can be handy, but it does have some faults. To get the most out of this measurement, you need to take the time to really analyze it. You can't simply read that "Blockchain A has a higher Nakamoto coefficient than Blockchain B" and automatically assume that Blockchain A is therefore more decentralized. A lot of different factors go into any given Nakamoto score. To work with the Nakamoto measurement, you need to take a close look at which blockchain subsystem it’s evaluating. Keep in mind that there are multiple ways in which any blockchain can be decentralized. Even if a blockchain scores well for a specific type of decentralization, another one of its more important systems might be centralized. You also need to take the time to discover what data set was being used. Some Nakamoto scores are calculated over short periods of time, or with a very broad set of users, rendering these blockchain decentralization scores less reliable.

The Bottom Line

The Nakamoto coefficient is very helpful as long as you take the time to analyze the data behind any given Nakamoto score. By using a Nakamoto score to analyze subsystems, you can easily rank various blockchains based on their level of centralization. This makes the Nakamoto coefficient one of the most useful tools for determining blockchain decentralization.