Summary

Metcalfe's Law has been used to approximate the network value of tech companies such as Facebook and Twitter which are based on social interaction.

The equation for calculating the value of the network is n^2, where n is the number of participants.

Metcalfe's Law has also been applied to Bitcoin, but I suggest that some changes are required due to Bitcoin's unique nature.

The Lindy Effect suggests that the longer Bitcoin survives, the longer its lifespan will be.

I demonstrate that the Bitcoin Z-Signal does just this, and I also provide some interesting visuals.

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### Introduction

Some of you may have read my review of Cryptolab capital's NVM ratio. If you have, then you will know that there are three ways in which Metcalfe's law has been applied to cryptocurrency, specifically Bitcoin (BTC-USD)(OTCQX:GBTC)(COIN).

One important thing to note is that Metcalfe's Law is already being adapted from its original form by Cryptolab Capital and others.

Image Source: Cryptolab Capital

Today I'm going to discuss my own spin on this concept, and why I think we need a new approach when it comes to Bitcoin.

### The Problem

There are two main problems that I've seen creep their way into Metcalfe's Law calculations for determining Bitcoin's network value. They are the following:

- We don't know how many Bitcoin users there are. Using the number of "wallets" is incorrect, because the number of wallets must be added up by platform. The wallet count you see on blockchain.com for example, is just the number of wallets created on blockchain.com's website, it's not all wallets that exist.
- Some users are inactive, and some users are very active. It would be incorrect to treat them all as the same in regards to their importance to the network.

So, what can be done?

### My Solution

From the standpoint of Bitcoin, there is only one source of activity. That source is a Bitcoin address that contains an unspent output (a part of the UTXO set). That is to say, a Bitcoin address with some Bitcoin in it.

The event that matters most, the primary function of Bitcoin is to be able to send a transaction. Only addresses with some Bitcoin can send a transaction (except for a coinbase transaction, which is when a miner received the block reward; this is when new Bitcoin enters the system).

So, I think we can say that the total value of the network should be related to **both** the number of participants, and the activity level of those participants.

The next question you're probably thinking is: "can we determine these things?" Fortunately, the answer is yes.

The number of unique addresses in use, and the number of daily transactions confirmed on chain get us very close.

### Testing The Theory

In order to test this theory, I want to try a different approach. I remember back to a statistics class that I took years ago. The professor told the class, that before we do anything fancy, we should just create a scatter plot and look at the data. Doing this gives you a clue as to what might be going on. Only afterwards, would we actually "do something" with the data, in order to try and confirm our suspicions.

Let's start off by doing that. Without any transformations at all, I present the number of daily transactions and the Bitcoin price.

Source: blockchain.com and author's charts

Hmm, what do you think? I'm not super convinced here. But, I seem to remember that with Bitcoin, we need to think in log scale. So, let's take the log base 10 of the transactions, and do the same for the price, and look at this data again.

Source: blockchain.com and author's charts

Well, look at this. That looks like a positive linear relationship in log scale if I've ever seen one.

**Unique Addresses**

Let's check out the number of unique addresses in the same way.

Source: blockchain.com and author's charts

I think I sort of see a relationship here, pointing up and to the right. But, is there a way to view this data that could improve on our intuition?

Source: YouTube

Oh yeah, log!

Source: blockchain.com and author's charts

Jumpin' Jehoshaphat! Something is going on here.

Now, some of you are thinking "Yeah, I know Hans. I've been reading all your articles. What have you got for me that's new?"

### Metcalfe's Law V2.0 in 3D

I've been working with a new graphing library called plotly.js. It's been a real big help. I started thinking, what if we could visualize all this data at once?

I took the Bitcoin price, the number of unique addresses, and the number of daily transactions all into the same chart (in log scale of course). Then, I rendered it in 3D. This was the result.

Source: blockchain.com and author's new charts

Unfortunately, Seeking Alpha does not like to render GIFs in an article, so you'll have to **click here** to see this in live action. Please take a moment to watch the 10 second GIF before you continue with the article.

**What the heck am I looking at?**

What you are looking at here is very informationally dense. Let's unpack this a bit.

- The "point of origin" is the point where the Log Price, Log Activity, and Log Participants is at the lowest. If you're looking at the image above, that's the area nearest the blue points in the center of the graph, near the bottom.
- A point near the origin would be a point where the number of unique addresses was low, the daily transactions were low, and the price was low.
- If you imagine this like you're inside a big cube, with the point of origin in one corner, the opposite point is the place where prices are high, unique addresses are high, and daily transactions are high.
- As you can see, the points make a sort of spiral from the point of origin to the opposite corner of the cube. This indicates that as X increases, Y and Z increase as well.
- In other words, X, Y, and Z move together.

If the result of this plot had been a perfectly straight line, going from one corner to the opposite corner, then we would have a model with no variance. Unfortunately, this rarely happens in the wild.

If we had a model with zero variance, then we could predict the exact Bitcoin price if we had the number of daily transactions and the number of unique addresses. But, we don't have that. So, where does that leave us?

### Where do we go from here?

The fact that we don't have a perfect model is both a blessing and a curse. One the one hand, we can't be too certain about what to expect. But, on the other hand, this model puts us ahead of the curve given that Bitcoin is so new. Very few people have any point of reference at all that's based on data. Many people are just going off the opinions of others.

You have to think about the price of Bitcoin at any given point in time as existing in a field of probability, or a probability cloud. The center of this cloud is the predicted value. The actual price of Bitcoin is some point in the cloud. It's technically possible for the Bitcoin price to be anywhere, but we are more likely to find it closer to the center of the cloud.

Of course, we know from experience that it tends to bounce around. These are the Bitcoin bubbles! Bitcoin's price sort of orbits the center point (which itself is moving), sometimes it's too low and sometimes it's too high.

It is possible to build a model in which we simply take the number of daily transactions, and the number of unique addresses, and then use them to create a price prediction. The results are not bad, even though the data is not normally distributed.

**Is there an even better way?**

Let's talk about the Lindy Effect for a moment. This idea was first suggested by Goldman in 1964, but it was referenced again by Mandelbrot and eventually by Nicholas Nassim Taleb in 2007, and again in 2012.

If a book has been in print for forty years, I can expect it to be in print for another forty years. But, and that is the main difference, if it survives another decade, then it will be expected to be in print another fifty years. This, simply, as a rule, tells you why things that have been around for a long time are not "aging" like persons, but "aging" in reverse. Every year that passes without extinction doubles the additional life expectancy. This is an indicator of some robustness. The robustness of an item is proportional to its life!

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What if we were to include an element that reflected the passage of time? I tried this, and was pleasantly surprised by the results. By adding a third input, the total of all confirmed transactions, the predictive value jumps up and the standard error drops. I attribute this improvement primarily to these two factors:

- The number of unique addresses and the total transactions are not perfectly independent of each other. Because they tend to move together, some of the potency of the model is limited by using both inputs.
- The Lindy Effect is having an impact. The longer Bitcoin survives, the more comfortable people get with it. Each time a bubble pops, but Bitcoin recovers afterwards (which has happened many times already), more people take note.

**Back To The Bitcoin Z-Signal**

It just so happens that the Bitcoin Z-Signal is the model I described above. The Z-Signal (and its cousin, the Z-Complex) are approaches to deriving the value of Bitcoin from the network, weighted by time under the assumption that the longer Bitcoin survives, the more likely it is to persist.

**The Bitcoin Z-Complex**

Let's look at the latest Bitcoin Z-Complex chart. But, before we do, I want you to think about the Z-scores at the bottom as an expression of the current distance of the Bitcoin price from where it was predicted to be (because that's what it actually is, in terms of the number of standard deviations).

Source: blockchain.com and author's new charts

Does this chart make a bit more sense now?

Also, remember what Hal Finney said:

Every day that goes by and Bitcoin hasn't collapsed due to legal or technical problems, that brings new information to the market. It increases the chance of Bitcoin's eventual success and justifies a higher price.

- Hal Finney, June 4th, 2011 -Bitcoin Talk Forum

### Conclusion

I contend that in order to properly apply Metcalfe's Law to Bitcoin, we need to look at the number of participants and the amount of activity that is occurring. After all, a million people sitting around doing nothing is not exactly a healthy network, and the same could be said about one person sending himself a million transactions per day. Only when many people send many transactions, do we have a healthy network.

In addition, by adding in the total number of transactions ever confirmed to the mix, we can produce an even more powerful metric, which I call the Bitcoin Z-Signal (the Z-Complex is the Z-Signal with the predicted price included).

This point is best illustrated by the following table:

Unique Addresses | Daily Transactions | Z-Signal | |

R^2 | 0.909572602 | 0.925638558 | 0.942293654 |

Standard Error | 0.378436335 | 0.476216125 | 0.317717411 |

Source: blockchain.com and author's models

The Z-Signal is more predictive, and has a lower standard error than either of the Metcalfe's inputs by themselves. So, I submit that this approach is a way to extend and enhance previous models that came before it.

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.

**Additional disclosure: **Articles now require a "bullish," "bearish" or "neutral" rating. However, they do not ask for a time frame. My official position is that in the long term, I am very bullish, but in the short term I think the price could move further down. Therefore, short term bearish, long term bullish.

Metcalfe’s Law has been used to approximate the network value of tech companies such as Facebook and Twitter which are based on social interaction.

The equation for calculating the value […]