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Metrics Definitions

Metric Name: Alpha Score Definition:
We first compute how many days an entity (network, dex, pool, etc) is the leader in terms of a metric chosen, among its group. Then, we get the top leader among all days, and divide the number of days in the leadership by the number of days. This is a metric of how long the longest leader was in leadership. For example, consider the metric to be evaluated is volume, and a network stayed 67 days in the leadership in the terms of volume (not necessarily consecutives), in a total of 100 days of evaluation. For this calculus, consider that this network has been dominant in terms of volume, among all networks. Then, the alpha score is 67/100 = 0.67.

Metric Name: Total TVL (in USD) Definition: How much value measured in USD is locked in the total number of liquidity pools that enable access to the synthetic token.

Metric Name: Nakamoto Coefficient Definition: The Nakamoto coefficient represents the minimum number of entities that collectively control more than 50% of the resources. For example, the majority of dexes / pools volume at a given point in time. In terms of liquidity, it can be used to assess the minimum number addresses that control more than 50% of the liquidity.

Metric Name: Max Power Ratio Definition: The max power ratio represents the share of the volume that is owned by the most “powerful” entity, i.e. the most traded dex / pool. In the liquidity case, it represents the liquidity share of the most powerful address.

Metric Name: Network Volume Share Definition: The percent volume broken by network.

Metric Name: Total Entities Definition: The sum of entities that are part of said group (i.e. total dexes, total networks, addresses providing liquidity).

Metric Name: Stability Definition: Is the ratio of the lowest price to the highest price. Mathematically, Stability = low / high. In other words, 1 - Stability = (high - low) / high. In absolute terms, 1 - Stability is equivalent to the maximum price change from low to high, which can represent a volatility metric.

Metric Name: Redemption liquidity Definition: Accessible capital or reserves within a DeFi protocol that enable users to swap or redeem a wrapped asset or stablecoin for its underlying collateral.

Metric Name: Daily Amihud Definition: The ratio between the daily return (in usd) divided by the daily volume (in usd). According to Fong et al: “The daily version of Amihud is the best daily cost-per-dollar-volume proxy.”

Overview Liquidity Distribution Metrics

  1. Nakamoto Coefficient

The Nakamoto coefficient represents the minimum number of liquidity providers (LPs) that collectively control more than 50% of the total liquidity in a token. This helps understand how concentrated the token's liquidity is among major holders.

  1. Gini Coefficient

The Gini coefficient measures the inequality in liquidity distribution among LPs. Values near 0 indicate liquidity is evenly distributed among providers, while values near 1 show liquidity is concentrated among few providers.

  1. Shannon Entropy

Shannon entropy measures the diversity of liquidity distribution. Higher entropy values indicate liquidity is well-distributed across many providers, suggesting better market resilience. Lower values indicate concentration risk.

  1. Herfindahl-Hirschman Index (HHI)

HHI measures liquidity concentration by summing the squared percentages of each LP's share. Values near 0 indicate liquidity is distributed among many providers, while values near 10,000 show high concentration with few dominant LPs.

  1. Theil Index

The Theil index measures the deviation from perfect liquidity distribution. Values near 0 indicate liquidity is evenly distributed among providers, while higher values show increasing concentration among fewer LPs.

  1. Power Ratio

Overview Volume Distribution Metrics

  1. Nakamoto Coefficient

The Nakamoto coefficient represents the minimum number of pools/DEXes/networks needed to account for 50% of the total trading volume. This indicates how distributed trading activity is across different venues.

  1. Gini Coefficient

The Gini coefficient measures inequality in trading volume distribution. Values near 0 indicate trading volume is evenly distributed across pools/DEXes/networks, while values near 1 show volume is concentrated in specific venues.

  1. Shannon Entropy

Shannon entropy measures how predictably trading volume is distributed. Higher entropy suggests trading activity is well-distributed across different venues, while lower values indicate volume concentration in specific pools/DEXes/networks.

  1. Herfindahl-Hirschman Index (HHI)

HHI measures market concentration by summing squared percentages of trading volume shares. Values near 0 indicate trading is distributed across many venues, while values near 10,000 show high concentration in specific pools/DEXes/networks.

  1. Theil Index

The Theil index measures the deviation from perfectly distributed trading volume. Values near 0 indicate trading activity is evenly spread across venues, while higher values show volume is concentrated in specific pools/DEXes/networks.

  1. Power Ratio

The power ratio represents the percentage of total trading volume handled by the most active venue (pool/DEX/network). This shows the dominance of the most popular trading venue.