In his latest article Preston Byrne dug up a interesting looking chart that shows the inflow of bitcoins to the ethereum presale in the first two weeks.

The chart looks very smooth, almost too perfect for an uncoordinated effort of several thousand contributions over two weeks, especially compared to charts from other fundraisers like Kickstarter, Swarm or Tezos ICO.

Why should we care about that? Ethereum is currently at risk of being classed as a security. While most people don’t doubt that the ethereum presale was likely a securities issuance, they argue it is now decentralized enough to no longer fit that bill. If it turned out today that the Ethereum Foundation controls a larger supply of ether than they admit and use it to move the market in meaningful ways or even to influence consensus once ethereum has moved to proof-of-stake, that would clearly hurt their decentralization argument. So whether or not there were irregularities in the ethereum presale might be a question of public interest right now. So I set out to understand the formation of this chart a little better.

Confirming the chart

First I confirmed that is indeed from the wallet, which wasn’t hard. For example the Ethereum blog has a post where they review the first 2 weeks of the sale and post the same data.

And my own chart in comparison, over the full presale:

If you want to download the same dataset, go to https://blockchain.info/address/36PrZ1KHYMpqSyAQXSG8VwbUiq2EogxLo2?filter=2# and then click “Filter” -> “Export History”.

The rules of the presale

In order to understand what lead to a graph like this, we need to go back in time and understand the dynamics of the Ethereum presale.

The sale would go from July 22 until September 2, a total of 42 days.

The price of ether per bitcoin would be 2000 in the first two weeks, then linearly decline to a final rate of 1337 and stay flat for the last 6 days.

There was no fixed amount of eth to be sold that investors compete for, instead the eth would be created after the presale is over.

Then another 19.8% of additional ether would be created and given 50/50 to early contributors to the project and the Ethereum Foundation.

Yearly inflation through block subsidy would start at 26% for the first year and then decline from there.

Sources (1 2 3)

This is how they expected the distribution of eth to develop over time:

https://de.slideshare.net/mids106/ethereum-presale, slide 13

The players

Given that we know the rules of the presale, what players are there and how do we expect them to behave?

Speculators: they want to control a large relative amount of ether and hope for demand from the other players only after the sale is over, so they hope to see low interest and then buy as late as possible. At the same time they are price sensitive, so they probably want to buy right before the discount ends and then maybe again before the sale ends. Actual users (who buy ethereum as gas, either for using or developing on the platform): they don’t really care when to buy. On the one hand eth gets more valuable to them as more people have already contributed (network effects), on the other hand some of them get incentivized by the early discount. Early contributors: here it gets interesting. They know that around 8.3% (~10% of 120%) of all eth created will go to them, so you can think of it as an 8.3% bonus on every purchase. At the same time they benefit from getting others to contribute as much as possible (like an affiliate deal, they receive 8.3% from each purchase). So we would expect them to participate generously and probably early, to spin up demand and signal to the other players.

Insiders

Because they are the key to this analysis, this fourth player deserves her own paragraph. An insider would be someone who colludes in some way or form with the Ethereum Foundation to gain an unfair advantage over others.

Goals to such collusion could be:

to signal (“fake”) demand to other players to raise more money

to make additional short- or midterm profits by selling on the open market (even cornering it)

to secretly control a larger share of the monetary base, either to manipulate prices or influence consensus in a PoS system

What allows all three options to work in the first place is that an insider and the Foundation could be sharing the same bankroll. So whatever money the insider spends, is not really gone but can be returned to him by the Foundation, greatly reducing the cost to him. I illustrated that dynamic here:

In step 1, we see an honest user buying 2000 eth for 1 btc. He is +2000 eth but -1 btc and the foundation is +1 btc and +200 eth (because of the free 10% they are printing). The foundation+insider coalition controls 200 eth (10% of the supply) and 2 btc.

In step 2, we see that an insider that spends the same 1 btc, gets the same 2000 eth but the 1 btc never leaves his shared bankroll with the foundation. The foundation+insider coalition now controls 2400 eth (55% of the supply) and 2 btc. They just printed money for free.

There are three caveats to this situation:

The coalition needs some Bitcoin to begin with. There might be a cost associated to sharing a bankroll, for example a tax on whatever money flows back from the foundation to the insider. There could be an additional cost if their collusion ever came out.

These aspects make the collusion a little more costly, but by no means unprofitable. So just based on these incentives, we expect that collusion is likely to happen. Maybe not in this case, but given a large number of dice rolls (ICOs) the dice will come up 6 (an unethical founding team) a reasonable amount of the time.

The reality check

In summary we expect a big spike in the beginning as well as towards the end of the discount. Apart from that, there should be a noisy baseline of demand from actual users.

If we compare these expectations to the actual demand, we can that they fit the chart (taken from here):

There was a big spike in the beginning and another one right before the end of the discount (red line). The rest of the time daily demand was surprisingly stable, with another small bump towards the very end.

There is still the question why the graph looks so damn smooth. So I rearranged the transactions in two more ways.

By size in BTC, over time