July 23, 2023 - 14 min read
Almost all public blockchains claim to be fully decentralized, but many are far more centralized than they claim to be. Fortunately, there’s a mathematical way to measure the decentralization of a blockchain; the Nakamoto Coefficient. The Nakamoto Coefficient helps measure the minimum number of validators or nodes that would need to agree to prevent a blockchain from operating correctly. The larger the Nakamoto Coefficient is compared to the number of nodes or validators, the more decentralized the blockchain network is. Hence, the safer the network is from node collusion and other types of 51% attacks.
The Nakamoto Coefficient, which was named after Bitcoin founder Satoshi Nakamoto, is a relatively new metric, as it was originally promised by former Coinbase CTO and General Partner at a16z, Balaji S. Srinivasan, and Leeland Lee, Vice President at Galaxy Digital, in their 2017 article, Quantifying Decentralization.
In Quantifying Decentralization, Srinivasan and Lee propose the development of a metric that can: ”measure the extent of a given system’s decentralization, determine how much a given system modification improves or reduces decentralization, [and] design optimization algorithms and architectures to maximize decentralization” by using two well-known principles; the Gini Coefficient and the Lorentz Curve.
Srinivasan and Lee use two major metrics to calculate a blockchain’s Nakamoto Coefficient; the Lorenz Curve and the Gini Coefficient. The Lorenz Curve, developed by American economist Max Lorenz in 1905, measures the differences between populations and was designed to measure the distribution of resources among a population (i.e., to measure economic inequality), as well as the distribution of other traits. The Gini Coefficient is another measure of income distribution populations. Together, they can be used to measure the decentralization of many things, including blockchains.
As represented by the illustration and caption below, a Gini coefficient of zero represents perfect equality. In contrast, a Gini coefficient of one represents perfect inequality, in which one individual or a small group of individuals receive 100% of the economic resources of a population. In essence, too much inequality generally leads to too much centralization, both in decentralized protocols like blockchains and other systems.
The Lorenz curve is shown in red above. As the cumulative distribution diverges from a straight line, the Gini coefficient (G) increases from 0 to 1. Figure from Matthew John.
Srinivasan and Lee think of blockchain decentralization in terms of subsystems, as every decentralized system is made up of a variety of subsystems. According to the authors:
“By determining how many entities in each subsystem one needs to control, one can make reasonable assumptions on the degree of effective Decentralization in a network. The higher the value of subsystems one needs to control, the higher the Decentralization.”
The Nakamoto Coefficient and Byzantine Fault Tolerance (BFT) are closely connected. In a Byzantine Fault Tolerant system, 51% of the validators need to come to a consensus to alter the blockchain. As of mid-2023, data from crypto data firm Bitnodes estimated that there were nearly 17,000 reachable Bitcoin nodes. This means it would take a traditional Nakamoto Coefficient of around 8,700 nodes to disrupt the entire network, which is relatively decentralized, at least compared to most other blockchains. Disrupting a blockchain network can be ruinous to security and can allow users to “double spend,” in which one entity can spend their cryptocurrency twice.
When discussing Nakamoto Coefficient, as we just mentioned, there may be limiting factors other than the pure number of validators that actually lower a chain’s Nakamoto Coefficient. This can be measured by looking at any one of the various previously mentioned “subsystems” that can lead to network centralization.
This is because, with a high level of subsystem centralization, it could take far fewer nodes to disrupt a blockchain network than the number of nodes would indicate. The creators of the Nakamoto Coefficient specifically looked at six different subsystems, which could lead to more centralization, including node, exchange, mining, dev, ownership, and client centralization/decentralization.
Each of these is an essential subsystem that can exert significant influence on the potential centralization of a decentralized system. In most cases, a decentralized protocol is only as decentralized as its most centralized component.
Therefore, in theory, a true Nakamoto coefficient, or “minimum Nakamoto Coefficient,” might be a number modified to reflect both node count and these other factors, which we delve into below:
Where are most of the nodes of a given blockchain located? Is there a substantial proportion of nodes in one (or a few) countries? Are many nodes located in countries with unstable political systems or particularly unfriendly crypto legislation? (as this could significantly disrupt node operation).
The volume of a cryptocurrency traded among the top exchanges is also an important measure of decentralization. When only a few exchanges have the majority of the trading volume of a specific cryptocurrency, the price can be more easily manipulated, leading to centralized influence over a blockchain network.
What is the distribution of block rewards (for Bitcoin) or staking rewards (for Ethereum)? For example, research in 2019 indicated that Ethereum mining may be more centralized than Bitcoin mining; however, as of mid-2023, it appears that Bitcoin mining is substantially more centralized than Ethereum staking.
How many developers have worked on the core infrastructure of the blockchain? When it comes to the decentralization of this subsystem, more is almost always better. For instance, the infrastructure of chains with fewer devs may be influenced more by the personal opinions of a few devs rather than a true consensus among a large founding team. In addition, the more developers, the more likely any faults or bugs will be discovered and fixed quickly.
The ownership distribution of an asset’s core currency is also a good measure of decentralization. A higher concentration of wealth in fewer wallets indicates that a small number of individuals have greater control over the price of the blockchain’s native cryptocurrency, which can significantly impact that chain’s popularity and overall operations.
In general, the greater the distribution of mining or staking software clients, the more a blockchain network is decentralized. More clients make it less likely that an error or security flaw in one client will not impact a large number of miners at once, potentially disrupting the network and making what was once a decentralized network into a highly centralized system. In a worst-case scenario, client developers could intentionally introduce a flaw or backdoor into the network, which could be disastrous.
When the founders of the Nakamoto Coefficient wrote their initial article, they calculated a 0.92 Gini coefficient for both chains, considering that most Bitcoin miners used Bitcoin Core and most Ethereum miners (now stakers) ran Geth.
Major ETH staking pools. Souce: Dune Analytics.
We already mentioned that Bitcoin, as of mid-2023, had a Nakamoto Coefficient of around 8,700. In contrast, Ethereum, which, according to Etherscan. as of mid-2023 had close to 11,000 nodes, meaning that it would have a Nakamoto Coefficient of around 5,500. However, these numbers may actually be way off. This is because it’s very important to note that the vast majority of nodes are part of mining pools, with just 2 mining pools on both Etheruem and Bitcoin operating close to–or more than– half of the nodes.
Top Bitcoin mining pools. Source: BTC.com.
For instance, right now, Lido and Coinbase combined stake more than 42% of all ETH staked globally. Bitcoin mining is considerably more centralized, with just two mining pools, Foundry USA and Antpool controlling more than 54% of all Bitcoin mining worldwide.
While it’s true that pools are full of independent actors that might leave the mining pools if the mining pool operators wanted to, for example, disrupt the Bitcoin network, we can’t predict human behavior, so it’s better to assume that all miners would stay within the pool. In this case, by using the worst-case scenario as a base, we can provide the most accurate measure of blockchain decentralization.
This could mean that, in reality, the true minimum Nakamoto Coefficient of Bitcoin or Ethereum may be closer to three. Despite this, they are still arguably the most decentralized blockchains in the industry due to their incredibly high number of well-distributed node operators/miners, even with their high level of mining pool centralization.
Examining the Nakamoto Coefficient of Ethereum Layer-2 blockchains can be more complex than looking at Layer-1 chains since Layer-2s depend on Ethereum for their security and decentralization. Therefore, it’s safe to say that a Layer-2 chain can only be as decentralized (or have a Nakamoto Coefficient as high as) as Ethereum, but it could be significantly less decentralized. Therefore, Layer-2s, in theory, will always have lower Nakamoto Coefficients than Ethereum itself. However, as long as the Ethereum mainnet maintains its level of decentralization, a Layer-2 chain can still potentially be quite decentralized.
We should note that, in addition to getting its core security from Ethereum, each Layer-2 has its own method of consensus and, in most cases, a proof-of-stake token that can be used as a governance token to vote on DAO proposals. The distribution of the ownership of this token, therefore, fully mirrors the distribution of voting power, and, as with most assets, a small number of whales generally own more than 51% of the token.
Some chains, like Optimism, are experimenting with decentralized voting systems that go beyond “one token, one vote.” These systems include the use of Souldbound tokens (tokens that cannot be transferred to a different wallet) as digital voting IDs. These types of systems could significantly increase decentralization and limit the influence of whales.
In general, to determine the decentralization of a Layer-2, one should start with the Ethereum mainnet’s Nakamoto Coefficient as a base and then should factor in individual consensus methods and token distribution (as well as node distribution) in order to fully determine a Layer-2 chain’s coefficient.
Below, we will provide the basic Nakamoto Coefficients of major non-Ethereum and non-Bitcoin blockchains, including Ethereum Layer-2s. Due to the myriad of factors that could influence this metric, we first will calculate a basic coefficient, looking only at the number of nodes (estimated at 51%) that would be needed to collude to make changes to the network.
Then, we will calculate a roughly estimated “minimum coefficient” based on other well-known factors about the blockchain in question. For brevity, we will refer to Nakamoto Coefficient as “NC.”
As previously mentioned, networks with a higher Nakamoto coefficient are more decentralized, while a lower Nakamoto Coefficient represents more centralization.
Addresses’ share of $ADA supply.. Source: AdaScan.
Nodes: Unknown; some estimate the network had around 1200 nodes as of Dec. 2022, and some estimate 2,924 validators in Oct. 2021
The initial token distribution of blockchains including Cardano, Solana, Fantom, and Polkadot. Source: Messari.
In general, newer blockchains have significantly fewer validators and hence far lower Nakamoto Coefficients. Unfortunately, there is really only one way to fix this, and it’s by recruiting more node operators, ideally in diverse locations and from diverse backgrounds. Of course, as previously discussed, even if there are many validators, the true Nakamoto Coefficeint may be far less due to another limiting factor, such as a high centralization of mining or staking pools.
However, as we’ve seen from looking at the Nakamoto Coefficient of chains like Binance Smart Chain/BNB Smart Chain, we can see that some chains simply don’t want to become more decentralized, especially if they have a corporation (or a corporate-like DAO) behind them that still wants to retain control, as some might describe TRON and TRON DAO.
The Nakamoto Coefficient, while not a perfect metric, does shine quite a lot of light on the true decentralization level of many blockchains. Unfortunately, it seems to indicate that the vast majority of blockchains, including Bitcoin and Ethereum, are far more centralized than most people think. In fact, many chains feature almost no level of true decentralization and can often be disrupted by just one or two entities. However, without understanding the true nature of the problem, there’s little hope of fixing it, so measuring decentralization is the first step in increasing it.
Overall, the blockchain and crypto sector could significantly benefit from further use of the Nakamoto Coefficient as an industry-standard metric. Giving chains and projects something to measure themselves against may encourage more centralized blockchains, like BNB Chain (formerly Binance Smart Chain), to further their decentralization efforts, as well as encourage members of decentralized chains to continue to aggressively decentralize and improve network security. In addition, by calculating and sharing live Nakamoto Coefficient data, blockchain networks can gamify the decentralization process and add further motivation for networks to decentralize.
Finally, when dealing with government regulators, the use of the Nakamoto Coefficient could provide blockchains with the evidence they need to prove that they are truly decentralized. This could help prove that many cryptocurrencies are not actually securities and should not be regulated as such. In turn, this could help convince regulators that many cryptos should remain lightly regulated or classified as commodities, which are far less regulated than securities.
In the end, the use of the Nakamoto Coefficient as a standard measure of decentralization could help alleviate the impacts of the “crypto crackdown” in the U.S. and other countries. If the use of the metric encourages further decentralization, it could indirectly boost crypto prices, improve accessibility, and foster overall growth in the crypto and blockchain industries, all while furthering the core mission of blockchain developers worldwide.
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