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Nansen helped develop Arbitrum airdrop distribution backed by on-chain data analyses using Nansen Query.

‍TL;DR

• The Arbitrum Foundation, in partnership with Offchain Labs, has just announced the airdrop of the first governance token for Arbitrum, one of the leading layer 2 blockchains
• Offchain Labs, The Arbitrum Foundation, and Nansen have worked together on designing a token distribution model that bases eligibility for Arbitrum community members on their organic participation in the Arbitrum ecosystem
• This distribution model relies on Nansen on-chain data and labels, allocating eligibility points to wallets according to their past on-chain activity, with wallet addresses gathering at least three points to gain eligibility to the airdrop
• The list of eligible wallets represents 625,143 addresses or ~28% of those having bridged to Arbitrum One since inception and as of the late snapshot date of February 6, 2023
• Protocols that have a community-governed treasury that have been pushing the Arbitrum ecosystem forward were also invited to participate in the distribution of a portion of the tokens for their own communities

Introduction
The Arbitrum Foundation, in partnership with Offchain Labs, has just announced the airdrop of a governance token for Arbitrum, one of the leading layer 2 blockchains, and the distribution of the token to the Arbitrum community of users and stakeholders.
The Arbitrum Foundation and Nansen have worked together on designing an airdrop distribution strategy and a model to quantify the extent to which each wallet or on-chain entity address has met defined airdrop eligibility criteria. These criteria aim to include and acknowledge those who have helped and continue to help the Arbitrum ecosystem.
Figure 1: The rise of L2 chains, Arbitrum daily transaction number crossed above Ethereum for the first time last February 

Given the number of addresses that have interacted with the network, and the desire to distribute governance to users aligned with the success of the protocol, The Arbitrum Foundation has mandated Nansen to ensure that: 

• Distribution decisions would be backed by on-chain data analyses: Arbitrum datasets were queried via Nansen Query
• Analyses would undergo robustness checks under various parameters and criteria
• Analyses from Nansen would be marked against hypotheses prepared by The Arbitrum Foundation’s service provider, Offchain Labs

It is important to keep in mind that on-chain analysis has heuristic inputs, and, even by utilizing a strict analytical framework, our airdrop token distribution model includes estimates.

In this note we go through the process and on-chain model underlying Arbitrum token’s airdrop distribution.

Part 1 and 2 review airdrop design variables and the specific objectives of the Arbitrum airdrop. Part 3 illustrates the iterative process between distribution criteria and on-chain analysis. Part 4 and 5 detail eligibility criteria and associated “points”. Part 6 introduces the sybil identification process. Part 7 summarizes statistics on the final list of eligible wallets. Part 8 focuses on eligible Dapps and protocols.

1. Distribution as one of the key success factors for airdrops
Token airdrops are complex operations, generally crafted to optimize for protocol users’ participation and governance decisions. However, a protocol can define specific airdrop objectives, which aim at supporting its long-term fundamental goals (see part “2. Airdrop’s principles and objectives” below).

Once defined, these objectives should trickle down to every airdrop variable. In this project, Nansen has focused exclusively on the distribution variable, helping The Arbitrum Foundation craft distribution criteria and come up with a recipient list for the new token. But other factors bear equal relevance for a successful airdrop design:

• Demand-side factors: The demand for the newly-issued token is related to its use for participating in governance of the protocol
• Supply-side factors: The supply side is governed by issuance quantity (how many tokens to issue via the airdrop vs other channels), time (potential vesting schedule to influence future behaviors), and distribution (the scope of this article). 

Figure 2: Airdrop distribution variables

2. Airdrop’s principles and objectives
Via the airdrop, The Arbitrum Foundation aims at the optimal distribution of governance of the Arbitrum protocol.  One way of doing this is trying to understand patterns that indicate organic activity. “Organic” activities include finding utility in transacting on Arbitrum, helping develop Dapps and protocols available on-chain, or contributing to the economic and technological governance of the protocol. These desirable behaviors can be measured on-chain and over time and classified in a distribution ranging from moderately to highly active wallets on Arbitrum chains.

A wallet that initiates multiple transactions may not necessarily do so for a genuine economic reason and is therefore not guaranteed to remain active post-airdrop. Therefore, another objective of on-chain data analysis has been to help identify ambiguous wallets that behaved like “sybils” e.g. wallets that very likely used Arbitrum chains with no other purpose than to become eligible to a future potential token airdrop. This second objective was tackled by the introduction of “negative criteria” most likely to be associated with sybil behaviors, and by clustering models run by Offchain Labs sybil researchers, based on Nansen Query Arbitrum and Ethereum on-chain data. Removing sybils is a necessary step in ensuring that the distribution of the governance is broad. Sybils, by definition, represent a concentration of tokens which is antithetical to the goals of the distribution. 

3. Distribution criteria and on-chain analyses: a back-and-forth process
The Arbitrum Foundation and Nansen defined ex-ante desired “organic” behaviors, translated these behaviors into quantitative criteria and thresholds, and then scrapped, amended or validated these criteria and thresholds via iterative on-chain analyses (see figure 3). 

Figure 3: Project process, from first-principle criteria to data validation

The research project followed the steps below: 

• Step 1: First-principle definition of activities worth distributing tokens to, according to the airdrop’s objectives

This step defined ex-ante criteria for which on-chain activities qualified as “organic”. At this point we attempted to answer the following questions before looking at on-chain data: How many transactions should a wallet have initiated to qualify for the airdrop? What should an organic behavior look like over time? What would be the corresponding USD value bridged and spent? etc.

•  Step 2: On-chain data collection and quantifying eligible activities

At this stage, we modeled the qualitative assumptions defined earlier to transform those into quantitative criteria using Arbitrum One data streamed and processed by Nansen, including traditional fields such as transactions, transfers, logs, traces, as well as Nansen labels (see figure 4).

Figure 4: Nansen Query interface. Arbitrum One token transfers by wallet address

• Step 3: Sensitivity analysis

With the eligibility criteria combined in a point allocation model, provisional outputs of address lists were created. The model attributed a certain number of positive or negative points to each criteria.

We reviewed the provisional address lists to assess whether our criteria and point allocation were too strict because they only captured the top percentiles of addresses on Arbitrum, or, vice versa, whether they were too loose. We illustrated this process by visualizing wallet histograms for select distribution criteria (figures 5 to 8).

This step covered multiple iterations, and ultimately led to threshold and criteria optimization. For example, the model had to capture addresses scoring above the median thresholds illustrated in figures 5 to 8: e.g. the criteria “number of distinct months when transactions were conducted” was given a threshold of two months and more, above the one-month median.

Aside from sensitivity analysis, we also conducted intersection analysis to ensure that various categories of eligibility criteria were complementary and capturing the main behaviors of an engaged Arbitrum user.

Figure 5: Address histogram by number of initiated transactions, snapshot on February 6, 2023 (Arbitrum One)

Figure 6: Address histogram by duration between first and last transaction, snapshot on February 6, 2023 (Arbitrum One)

Figure 7: Address histogram by number of distinct months with transactions, snapshot on February 6, 2023 (Arbitrum One)

Figure 8: Address histogram by total USD value sent, snapshot on February 6, 2023 (Arbitrum One)

• Step 4: Criteria finalization and Sybil analysis
• Criteria determining eligible vs disqualifiable activities were revised and the point system altered based on on-chain analysis results. At this stage some criteria disappeared and others were added (notably on Arbitrum Nova as complementary criteria to Arbitrum One). We re-ran the model until a satisfactory result was obtained. 
• The Sybil analysis was driven by Offchain Labs researchers who modeled clusters of historical transactions and transfers on Arbitrum and Ethereum. Likely sybil wallets were carved out from the eligibility list.
• Step 5: Pre-final list of wallets eligible for token airdrop

The final model yielded a new list of eligible wallets. The “functional” wallets belonging to exchanges, liquidity pools, “burn” addresses, and bridges were flagged for exclusion, using Nansen cross-chain labels. The wallet list was ready for a last, qualitative, review.

4. Eligibility criteria and other distribution parameters
The process described above led to a final list of criteria defined around the following broad categories (see figure 9): 

• Quantitative thresholds on the number, value, and time span of transactions and / or transfers initiated by wallets
• Aggregate liquidity brought to Arbitrum by these wallets
• Experimentation and use of new Arbitrum chains like Nova
• Separately, the following stakeholders were highlighted: Dapps with community-controlled treasuries were given a portion of the airdrop to distribute to their communities in a way that aligns with the goals of the airdrop. Localizing decision making with the distribution of governance has been a key component of Arbitrum as an ecosystem and community. This is further covered in section “8. Distributed Governance".

Figure 9: Airdrop criteria categories

Historical data gathered by Nansen started from the first block of Arbitrum One and were frozen:

1. at block number 22,207,817 on August 31, 2022, just before Arbitrum’s upgrade to Nitro
2. at block number 58,642,080 on February 6, 2023, to account for the increase of activity on Arbitrum post-Nitro

Complementary eligibility criteria were added to cover another chain, Arbitrum Nova, in order to acknowledge the wallets who took the initiative to test this new chain early. These criteria were secondary to Arbitrum One’s criteria, though, and obtained lesser points in our allocation model. The snapshots on  Arbitrum Nova were:

1. block number 499,342 on October 2, 2022
2. block number 2,108,676 on February 6, 2023

Each “organic” activity earned positive (behaviors to encourage) or negative points (behaviors to discourage). The amount of tokens that a wallet received in the airdrop was a function of how many points it collected. In order to participate, a wallet had to hit a minimum threshold of three points. The more points earned, the higher the allocation claim. Points at the “early” and “late” snapshot dates were combined to determine the final number of points allocated to each address.

5. Point system and examples of eligible wallet profiles

Figure 10: Criteria and associated points on Arbitrum One and Nova

By summing up the points above, we obtained various behavioral profiles of eligible wallets, for example: 

• A wallet that bridged to Arbitrum One and conducted more than ten transactions over two distinct months, and had a non-null balance at the time of the airdrop’s snapshot
• A wallet that bridged to both Arbitrum One and Arbitrum Nova and conducted at least 25 transactions over One during two distinct months. On Nova, the wallet conducted more than ten transactions
• A wallet that bridged more than USD 250k to Arbitrum One, conducted more than 100 different transactions during nine distinct months for a value exceeding USD 250k. On Nova, this same wallet initiated more than ten transactions

6. Identifying Sybils 
Within the list that initially qualified to receive the Arbitrum token, some addresses likely did not pursue a utility purpose but rather anticipated a potential future airdrop (see figures 11 and 12). These addresses were deemed less probable to have been using Arbitrum because of their belief in the technology and community and would not be likely to actively participate in governance. 

Even with the help of clustering models, sybil addresses have usually been difficult to segregate from genuine addresses, as demonstrated in past airdrop operations. Both types of addresses could exhibit the exact same patterns on-chain but with divergent objectives, one using a chain or protocol genuinely, the other only hunting for potential airdrops. 

Tracking sybil addresses therefore requires a qualitative evaluation step with a human assessment of whether the model used to detect sybils “punishes” the behaviors that go against the airdrop’s objectives and the protocol’s values (see here).

Offchain Labs researchers worked on identifying likely sybil wallets by running clustering algorithms on from_address / to_address transaction pairs sourced from Nansen Query, and also incorporating traces and token transfers on Arbitrum and Ethereum. A human “check” for false positives complemented the algorithm. See Arbitrum Foundation Github for more details on the sybil detection work.

Figure 11: Example of sybil-like behaviors: Two addresses part of a group of ~400 with very similar activity (that sent funds to the same centralized exchange deposit address)

Figure 12: Example of sybil-like behaviors, chain of addresses funded by token transfers from the same address and with similar behavior

7. Overview of eligible wallet list and statistics
Out of ~2.3 million wallets having bridged on Arbitrum One before February 6, 2023, 625,143 or ~28% obtained more than 3 cumulative points and were eligible to receive the newly issued Arbitrum Token. This eligibility number is ex-sybil ex-functional-entity. ~37k addresses were associated with functional wallets - e.g. a bridge smart contract, a centralized exchange wallet, or a burn address - and were not included in the eligibility list. ~135k were identified as sybils and were also excluded .

To visualize the token allocation per address, we drew the following pyramid chart. Only ~8.6% of total eligible addresses obtained 4,000 tokens and more:

Figure 13: Eligible wallets by number of tokens collected

8. Distributed Governance
The criteria above did not cover all the positive contributions to the Arbitrum ecosystem. In addition to a technology stack, Arbitrum is a community of developers, builders and users, and a prominent objective was to distribute governance to this community. Accordingly, a component of the airdrop was allocated to community-owned treasuries that are on Arbitrum for distribution in accordance with the values of each of these sub-communities. These entities covered various Dapps and protocols operating on Arbitrum. Points were attributed to the protocols:

• Based on when they deployed to Arbitrum
• Whether they are Arbitrum native, Arbitrum + Ethereum or multichain protocols
• According to how many total and daily transactions have occurred…
• … and the financial value of the activities that occurred,…
• … in proportion to the activity statistics of the respective Dapps they represented (illustrated in figure 14 is the share of total contract logs and transactions intra-entity, by entity, since Arbitrum One inception)

By including dApps as part of the airdrop distribution, the goal was to build a broader set of stakeholders who would be qualified to contribute to the future developments of Arbitrum. This was in agreement with one of the core objectives of the Arbitrum token distribution: transitioning to a more decentralized decision making model for Arbitrum.

Figure 14: Share of total transactions and contract logs intra-entity until 6 February 2023, distributed by Arbitrum One entity labeled by Nansen

Conclusion: “All for one and one for all!”
By leveraging on-chain analysis to propose a list of wallets eligible to receive the newly-issued Arbitrum token, The Arbitrum Foundation and Nansen have attempted to answer the question: “How to fairly acknowledge all those who have helped and are likely to continue helping the Arbitrum ecosystem to strive? “.

Under the final distribution model, one third of Arbitrum One addresses are eligible as of the snapshot date, as well as a selection of key protocols and Dapps on Arbitrum.