Please note: This is a technical note, intended for researchers and analysts. A post for a more general audience is in the queue. This research uses the Hyperline platform and the Octan onchain reputation score.

My recent Medium article, Onchain PageRank as Predictor of Post-Airdrop Lifetime Value, reports a technical result connecting the Pagerank of users to their future revenue. Specifically, the article shows that the top Arbitrum addresses, as ranked by Pagerank, spent more in transaction fees after the airdrop than the addresses which actually claimed the airdrop.

The Arbitrum result is both preliminary and very promising, in that it points toward a simple, algorithmic, credibly-neutral criterion for identifying a cohort with close-to-optimal future revenue. In the case of airdrops it provides a practical way to target network users with high lifetime value.

The summary of the result on Arbitrum is:

• 21.4% of users from before the snapshot claimed the airdrop.

• The 21.4% of users who claimed the airdrop went on to contribute 62.5% of transaction revenue during the year after the airdrop.

• By comparison, the top 21.4% of users as ranked by Pagerank contributed 73.8% of transaction revenue the year after the airdrop.

One way to frame this result is this: Instead of making a larger set of users eligible, with 21.4% of users actually claiming the airdrop, the Arbitrum foundation could have directly distributed tokens to the top 21.4% of addresses by Pagerank. With this targeting, the transaction volume from the recipients would have been substantially larger.

The original airdrop targeting, documented at the Arbitrum github repo, involved clustering algorithms on large graphs, along with other advanced analytics. Pagerank, by contrast, is commoditized, having been in wide use for over 20 years. It is available through most open source graph libraries, such as networkx.

Claimants vs Eligible Addresses

The set of addresses who claimed the Arbitrum airdrop was separate from the set of addresses who were eligible. Arbitrum announced the eligible addresses in March 2023, and addresses had until September 2023 to claim the airdrop. Addresses who had not claimed their tokens by September forfeited them. Of all addresses who had used Arbitrum before the snapshot date Feb 6, 2023, 22.8% were eligible according to the Arbitrum methodology.

We know that 21.4% of all addresses claimed the airdrop, and that their total revenue was smaller than the top 21.4% of addresses as ranked by Pagerank. What if we consider the 22.8% of addresses who were eligible, rather than the 21.4% of addresses who claimed the airdrop?

The 22.8% of addresses eligible for the airdrop generated 85.1% of the transaction revenue in the year following the airdrop, and ranking the top 22.8% of addresses by Pagerank only captures 74.8% of the transaction revenue.

This result is somewhat counter-intuitive, and it is less promising than the corresponding result for claimants. While claimants underperformed Pagerank targeting, the eligible cohort outperformed.

(Note: Pagerank has several hyperparameters, which allow the model to be further tuned. The stated result uses the standard hyperparameters in the Octan reputation model.)

Even with this result, there are many reasons to prefer Pagerank for eligibility. The Pagerank algorithm is transparent, reproducible, and credibly neutral. It therefore has the potential to largely circumvent the frequent controversies surrounding airdrop eligibility, increasing the perception of fairness.

Claimants of the airdrop might be considered among the “best” of the eligible users, and reasonably expected to contribute the most revenue. However, the result shows that, among the eligible addresses who did not claim the airdrop, there were high revenue users.

• Who were the high-value eligible users who did not claim the airdrop? What did their spending look like before and after the airdrop?

Optimism Airdrop 1

Prior to the Arbitrum airdrop, Optimism did an airdrop which was in some ways similar. However, for the Optimism airdrop, there was no difference between eligible addresses and claimants, as all eligible addresses with unclaimed rewards received their tokens automatically on September 15, 2023.

For a revenue metric, we can compare the aggregate transaction volume in the year following May 31, 2022, the day of the first Optimism airdrop claim.

The Optimism recipients comprised 53% of addresses active before the snapshot day. Those recipients accounted for 94% of the aggregate post-airdrop revenue. By comparison, the top 53% of recipients by Pagerank accounted for 92.4%. The revenue numbers are very close, with the aforementioned advantages of a credibly-neutral Pagerank targeting.

Taking other percentiles of top-ranked addresses by Pagerank allows us to associate an aggregate transaction revenue with any size cohort, as shown in the chart. In addition to the benefits of credible neutrality and transparency, targeting by Pagerank gives the airdrop designer maximum flexibility. The designer can choose a target percentage of future revenue or a target percentage of the network addresses, obtaining a prediction for the other.

Note the almost vertical increase between 30 and 40 on the x axis. This implies that a cohesive set of high-value addresses were ranked lower than they could have been. A simple modification of the features or Pagerank hyperparameters may cause the model to perform even better.

Next steps and additional questions

• In these examples, the Pagerank and the transaction revenue are tied to an airdrop, but they can be computed for any point in time. The Arbitrum and Optimism results show that Pagerank is predictive of future revenue. Is this always the case, even without an airdrop? Or is there something special about airdrops that make this true?

• Why do the eligible addresses for the Arbitrum airdrop outperform a Pagerank approach, but the claiming addresses underperform? What kinds of addresses are in the set difference between eligible and claiming addresses, and why is their revenue so high?

• Pagerank has a number of hyperparameters, such as damping, edge weighting, and personalization. What is the optimal tuning of the hyperparameters for specific cases and in general? In particular, why is there a “step” between 30 and 40 on the x axis in the chart of the Optimism percentages? Can we rank those addresses higher, obtaining an even better prediction of transaction volume?

The application of Pagerank to future revenue, as well as related problems like Sybil prevention, is very promising, as shown by the results above. Designing airdrops around a Pagerank score not only optimizes for future revenue, but it is credibly neutral, transparent, flexible, and difficult to attack.