Modeling Bitcoin’s Growth With The UTXO Set – Bitcoin USD (Cryptocurrency:BTC-USD)



There have been no shortage of people who have come forward with their own tweaks to Metcalfe’s Law when trying to apply it to Bitcoin (BTC-USD)(COIN)(OTCQX:GBTC). Some use the value transmitted via on-chain transactions, others use the number of “users” (which must be estimated since nobody knows this figure for sure), some have used the number of unique addresses, the number of wallets (which we only know for sure on certain sites like or (COINB)), and recently people have started to talk about the UTXO set as being another valid approach.

Before we get started, let’s define the UTXO set as all unspent outputs that exist in the Bitcoin network. The smallest output would be a single Satoshi, or 0.000000001 of a Bitcoin. If I were to send you some Bitcoin, the UTXOs in my transaction would change ownership from me to you. The total of the outputs will include the amount I’m sending, and then a change address for your wallet to send back the remainder.

Outputs are broken up into smaller pieces as they are used. If you have too many outputs, your wallet is said to have collected “dust.” This dust can be consolidated by most wallets, if you care to do so and the network fees at the time are not cost prohibitive.

Unique Addresses and The UTXO Set

You can think of the UTXO set like the big brother to the number of unique addresses, with the relationship being that one unique address can contain multiple UTXOs.

Taking into account what we’ve just learned, let’s look at the UTXO set and the number of Unique addresses on the same chart.


Isn’t that cute? They’re growing up together, aww….

Now, you may recall from my previous work that the number of unique addresses is one way to model the number of users. It’s clearly not a 1:1 relationship, but it’s something. Additionally, as the number of users grow (as evidenced by the number of unique addresses), the price of Bitcoin tends to grow too since you know, limited supply and increasing demand.

When we take the average of the number of unique addresses per month, and the average market cap of Bitcoin each month, and then look at the two in log scale; we see very high levels of correlation. Does this mean users are causing the market cap to go up, or that a higher market cap brought in more users? Ponder that question while you look at this regression analysis.

unique addresses and bitcoin market capSource: Seeking Alpha

Now, the question in my mind was if a similar relationship might exist with the UTXO set; and even better if the relationship were to be stronger. However, we do have a limitation with the UTXO set data, and that is the fact that we can only go back to the end of September, 2011. With the unique addresses, we were able to get data back from August of 2010 or even earlier.

But, before we run the regression analysis, let’s try a trick my old stats professor taught me. Let’s just look at the data first in a scatter plot.

Source: and author’s Excel

Hmm, looks like we might be onto something here. In general, charts that point up and to the right represent a positive relationship. Pointing to the right but not up is no relationship, as is having no discernible pattern. Pointing down and to the right is a negative relationship (one goes up, the other goes down).

Alright, enough already let’s run this regression!

utxo set regressionSource: Author’s Excel and

Ohh-la-la! With a correlation of 0.93 this is a very strong relationship indeed. P-values are nice and low, T-stat is nice and high. It’s worth noting that approach did come in with a slightly lower correlation than the unique addresses; but we also have a smaller set size because of the missing year (85 observations versus 94).

However, I think this approach has great value in giving us another viewpoint on the current market cap of Bitcoin and the state of the market at this time. Let’s look at the predicted values generated by the model.

Source: Author’s charts and

The UTXO set seems to run a bit smoother than the unique addresses. Additionally, the gap between the value today and what was predicted also differs between the two models. Let’s look at the Z-scores over time.

Source: Author’s Excel and

There are a couple interesting things about this plot. First, on the low side we do see that values have approached -1. Using unique addresses, the lowest Z-score found was -0.54, where using the UTXO set we got down to -0.90.

The second thing that I noticed here when comparing to the unique addresses Z-scores was that we’re sitting at 0.6 right now with this model, and over 2.0 using the old approach.

See the table below:

UTXO Set Unique Addresses
Lowest Z-score -0.90 -0.54
Highest Z-score 3.86 3.88
Current Z-score 0.6 2.0
Current Prediction (Mkt Cap) $45.5B $24.6B

It seems that the UTXO set is coming in more moderate right now, but it does tend to error on the low side.

Let’s look at the IQRs next.

Source: and Author’s charts

The shorter history is a bit of a bummer, but if this approach has validity then we may be much closer to a “fair” market cap than previously assumed.

Metcalfe’s Law Revisited

I am a big fan of Metcalfe’s law, even if simply squaring the number of users may be too simplistic. We have to understand that speculation plays a huge part in the price too. My personal opinion is that in the long term the network value is determined by the users and their activity, while in the short term the price and volume can attract or repel users causing wild swings in either direction.

It might be worth while to qualify the “network” as those people who take part for more than just short term speculation; but then we start getting into heaps of assumptions about people’s behavior that can be impossible to quantify. Sure, fear and greed are massively powerful; but I think there’s more going on than that.

Bitcoin is kind of like the cheese and the speculators are like mold. You can’t have the mold without the cheese, but the more cheese you have the more mold is possible. However, with enough mold it gets difficult to see the cheese underneath. I am going to suggest that the cheese is growing, and with it, so is the mold!

moldy cheeseSource: Google Images

Back to the value

Therefore, I propose that the best way to take on the network value is to start by asking these questions:

  1. How many unique addresses are in use?
  2. How large is the UTXO set today?
  3. How many transactions are being sent over the main network?
  4. If possible, how can we map the number of addresses, UTXOs and transactions to the number of users?
  5. If possible, how much activity is occurring on second layers and side chains (like Lightning and Liquid)?

Ideally, we would like to combine these variables or multiply them in some way. This is because a billion users transmitting no value doesn’t help, and the same is true about one guy sending himself a billion dollars over and over (looking at youwash traders).

For an in-depth analysis of this issue, check out this interview of Travis Kling from the “Off the Chain” podcast.

Source: YouTube – BlockWorks Group

In addition to this, as Nic Carter points out; we need to think about the average value transmitted. If there are five transactions, but each one is moving $10M, that’s very different from five transactions each moving $5.

Transaction count is an inferior measure

It is popular to measure Bitcoin by looking at its daily transaction count or ‘tps’ — transactions per second. New blockchains often advertise tps rates in the millions or billions and sneer at Bitcoin’s measly 3 – 4 tps rate (it fluctuates between 200,000 and 350,000 transactions per day).

But this is an incomplete picture. There are at least three important variables to consider when holistically appraising a value transfer system, and the transaction rate is just one of them:

  • Transaction capacity, TPS
  • Typical transaction characteristics (transaction size)
  • Settlement assurances

Together, transaction rate and average transaction size give you the economic throughput of the system; a measure of its financial bandwidth per unit of time. The settlement assurances tell you what sort of a system it is. How certain are you that you won’t face a chargeback or be defrauded? Does your transaction settle immediately, like physical cash? Or is there a 90-day chargeback period prior to settlement, as with most credit cards? – Nic Carter via Medium

The following chart makes this clear by putting value transmission methods on the same scale.

value transfer by typeSource: Nic Carter via Medium


I’m interested in feedback from the community on this issue. Do you guys think the UTXO set might be a better way to establish a fair price for Bitcoin’s market cap? Do you think it is or could be better than using the number of unique addresses? Let me know in the comment section below.

In the future, I’d like to experiment with using some combinatorial methods where inputs and the number of transfers are added up or multiplied in some way. I don’t know if this would make our predictions better or worse, but I do plan to research this further.

Until we can answer the important questions from above, we may not know the true value of the Bitcoin network. But, welcome to Planet Earth, where imperfect data is the norm.

Thanks for reading,


This article was published first in Crypto Blue Chips.

Disclosure: I am/we are long BTC-USD.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

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