§ Specification

This document outlines how rug pull index's algorithm is ranking data sets.

§ Data Acquisition

When ranking all data sets sold on Ethereum, the first step is acquiring meta data of all markets on Ocean Protocol and Big Data Protocol. Both projects host a version of the oceanprotocol/market. They take their data from an off-chain meta data cache called Aquarius and a protocol-specific subgraph implementation.

The following sources are used to collect all relevant data to generate a ranking:

• From RPI's Ethereum Ergion node, we download the pool's metadata e.g. prices and liquidity.
• From the Ocean and BDP subgraph, we get all data token addresses including their names and symbols.
• From ethplorer.io and covalent, we download the top token holders for each liquidity pool.
• From oceanprotocol/list-purgatory, we download both the list-accounts.json and list-assets.json.
• From coingecko, we download the latest price of OCEAN/EUR and BDPToken/EUR.

We call the software that downloads all this meta data the "crawler". In the past, there have been nights where the crawler failed. This was when the main page wasn't showing any reasonable results. When the crawl fails an administrator can manually login to fix the problem by e.g. re-running the crawl.

Once the crawl has finished, we perform a number of calculations that flow into the final ranking.

§ Calculating the Equality of Liquidity Providers in the Pool ("Gini coefficient")

The Ocean Protocol uses Automated Market Makers (or short: "pools") of Balancer's version 1. When staking e.g. QUICRA-0/OCEAN, the balancer pool returns a separate ERC20 token that represents a staker's liquidity in the pool.

As we want to rate a data set's factor of decentralization and hence the potential (or risk) it has of a single user "pulling the rug" - for each data set -, we calculate a Gini coefficent from the pool's population of liquidity providers.

In the following paragraphs, we define the Gini coefficent on an intuitive basis rather than by deriving it from the Lorenz curve [1]. As matrix $M$, we represent the differences of all stake pairs in the pool, with $d_{ij} = | x_i- x_j|$:

$$M = \begin{bmatrix} d_{11} & d_{12} & ... & d_{1n} \\ d_{21} & d_{22} & ... & d_{2n} \\ ... & ... & ... & ... \\ d_{n1} & ... & ... & d_{nn} \\ \end{bmatrix}$$

As a formula, we can represent $M$ as $PD$, where $n$ represents the population's size:

$$PD = \frac{\displaystyle\sum_{i = 1}^n \sum_{j = 1}^n | x_i - x_j |}{n^2}$$

However, for us to make a statement about the relative inequality of a data set's pool, it requires us to put the absolute difference $PD$ in relationship to the a population's worst case inequality. Namely a scenario where one member earns all total income while others earn nothing. We define this case $M_T$ with $T$ being the population's total income as:

$$M_{T} = \begin{bmatrix} 0 & 0 & ... & 0 & T \\ 0 & 0 & ... & 0 & T \\ ... & ... & ... & ...& ... \\ T & T & ... & T & 0\\ \end{bmatrix}$$

As a formula, we can represent it as $PD_{T}$:

$$PD_{T} = \frac{2 (n - 1) T}{n^2}$$

Where we define the Gini coefficient $G$ to be a relation between $PD$ and $PD_{T}$:

$$G = \frac{PD}{PD_{T}}$$

Additionally, since we've discovered an unfair advantage for pools with many small liquidity providers, for data sets with greater than 100 liquidity providers we only consider pool shares of more than 0.1% in the above calculation. For pools with less than 100 LPs, a stake counts towards the Gini coefficient $G$ only when its share is more than 1% of the pool.

§ Determining the EURO Value of a Data Set

As outlined in the section "Data Acquisition", a data sets price in OCEAN or BDPToken is downloaded from Acquarius. The latest tickers for OCEAN/EUR and BDPToken/EUR are downloaded from coingecko. The EUR value $v$ of an OCEAN data asset which price is $p_{d}$ is then calculated by multiplying it by the price of an OCEAN $p_{o}$:

$$v = p_{d} \cdot p_{o}$$

§ Calculating the Daily Ranking of Data Sets

rug pull index fetches and calculates - as previously mentioned - a set of meta data daily. Given an exemplary market of only two data sets $A$ and $B$, over a timespan of two days, a fictional state of rug pull index's data base could look like this:

To now calculate a daily ranking, considering the data of both days (June 22 and June 23), rug pull index does the following: In the "liquidity (EUR)" column, the overall highest value ("max value") is selected by searching the data base (it is "10" on June 22). Additionally the smallest Gini coefficient ("min value") is determined ("0.24" on June 23 for). These "min" (Gini coefficient) and "max" (liquidity (EUR)) values are then used as benchmark to evaluate the current day's data sets. Assuming the date to be June 23, 2021 we'd calculate the overall ranking of $A$ to be:

$$A = \frac{5}{10} \cdot \frac{0.24}{0.24} \cdot 100 = 50\%$$

and $B$:

$$B = \frac{7}{10} \cdot \frac{1}{0.24} \cdot 100 = 2,91\%$$

Hence, the main page's ranking would yield the following table for June 23, 2021:

Generally speaking, on a day $d$ the rating $r_d$ of a data set, can be calculated using the overall minimal Gini coefficient $g_{min}$, the overall maximal liquidity in EUR $l_{max}$, the data set's current liquidity in EUR $l_d$ and the data set's current coefficient $g_d$:

$$r_d = \frac{l_d}{l_{max}} \cdot \frac{g_d}{g_{min}} \cdot 100$$

§ Changelog

We pledge to update this specification with every update made to rug pull index's algorithm.

• 2021-09-05: We stopped using Aquarius entirely.
• 2021-08-09: We stopped retrieving price information from Aquarius and instead now use RPI's Ethereum node.
• 2021-08-02: We found a more intuitive and, for small populations fitting, derivation of the Gini coefficient from Walter Escudero [1] and replaced it with the original formula from Wikipedia.
• 2021-06-22: Specification document first published.

§ Feedback and Questions

If you have questions or feedback with regards to this document, please contact us.

§ References

1. ESCUDERO, WALTER, 2018, A NOTE ON A SIMPLE INTERPRETATION OF THE GINI COEFFICIENT. Portal.amelica.org [online]. 2018. [Accessed 2 August 2021]. Available from: http://portal.amelica.org/ameli/jatsRepo/196/196830001/html/index.html