Internet Adoption as an Indicator of Bitcoin’s Future Price (June 2023)

Internet Adoption as an Indicator of Bitcoin’s Future Price 2 June 2023

RESEARCH NOTE 3 June 2023

Internet Adoption as an Indicator of Bitcoin’s Future Price Executive Summary 

Bitcoin’s adoption curve is very similar to that of the internet.

This is confirmed quantitatively.



Bitcoin’s price may never reach the $1 million mark. It will probably remain below $500,000 for over a decade.

Background In 2020, we published “Estimating Bitcoin’s Adoption Curve and Maximum Price.” That note explored Bitcoin's potential maximum price and adoption curve, drawing parallels to the diffusion of innovations theory and the internet adoption model. The analysis suggested that Bitcoin's maximum price could range from $1 million to $10 million USD, likely to be reached within the next 15 to 30 years.

This research note differs from that in that it uses updated data and quantifies the relationship between internet adoption and bitcoin adoption, specifically the data in Figure 3 of “Estimating.”

Methodology Month-end price and address data sourced from coinmetrics was used with the data series commencing 31 December 2011 through 31 December 2022. Internet user data was obtained from https://ourworldindata.org/internet, https://data.worldbank.org/ and https://www.internetworldstats.com/emarketing. htm.

Relationship Between Bitcoin Users and Internet Users When quantifying the network size of Bitcoin and the internet, the term "user" refers to individuals or entities that actively engage with the respective networks.

For Bitcoin, a "user" typically refers to individuals or organizations that hold and transact with Bitcoin. This includes individuals who own Bitcoin wallets, participate in mining or validating transactions, and actively use Bitcoin for various purposes such as making payments, investments, or trading. The number of Bitcoin users can be estimated based on metrics like active addresses and non-zero balance addresses.

On the other hand, an "internet user" refers to entities that have access to and utilize the internet.

Internet users are people or organizations who can connect to the internet using various devices such as computers, smartphones, or tablets. They can browse websites, use online services, communicate through email or messaging platforms, and engage in various online activities.

The number of internet users is typically measured based on the number of entities that have internet access and regularly use it.

Both Bitcoin users and internet users are essential for the growth and functionality of their respective networks. The number of users plays a crucial role in evaluating the network's adoption, potential value, and overall impact on society and the economy.

When quantifying network economics and network effects, the exact number of "users" is not always necessary because the value and

3 June 2023 impact of a network are not solely determined by the absolute number of users, but rather by the interactions and connections between users within the network.

Metcalfe's Law, a concept often applied to network effects, states that the value of a network is proportional to the square of the number of users. Mathematically, this can be represented as V ∝ n2, where V represents the value of the network and n represents the number of users.

However, the key insight from Metcalfe's Law is that the value of a network increases disproportionately with the growth of users. For example, if a network has 10 users, the potential 2 value can be estimated as ½ × 10 = 50. If the number of users doubles to 20, the potential value becomes ½ × 202 = 200, a four-fold increase.

This exponential relationship demonstrates that the value of a network is not solely dependent on the exact number of users, but rather the interconnections and interactions that occur within the network. Each additional user brings the potential for more connections, communication, and network effects, leading to an exponential increase in value.

Therefore, when analyzing network economics, it is often more important to consider the growth rate, connectivity, and engagement levels within the network rather than focusing solely on the precise number of users. This approach acknowledges that the value of a network is derived from the relationships and synergies between users, rather than just the user count itself.

The first derivative of Metcalfe's Law is useful for quantifying network growth rates and, consequently, assessing the value of a network. By examining the rate of change of the network's value with respect to the number of users, we can

Internet Adoption as an Indicator of Bitcoin’s Future Price

gain insights into the network's expansion and potential future trajectory.

Mathematically, the first derivative of Metcalfe's Law can be expressed as dV/dn, where V represents the value of the network and n represents the number of users. This derivative measures the rate of change of the network's value as the user base grows.

Analyzing the first derivative provides several key insights: 1. Growth Rate: The sign of the first derivative indicates the network's growth rate. If dV/dn is positive, it suggests that the network's value is increasing as the user base expands. A positive growth rate signifies a healthy network with potential for further development.

2. Acceleration: The magnitude of the first derivative indicates the rate at which the network's value is accelerating or decelerating. A larger positive value suggests a network experiencing rapid growth, while a smaller positive value indicates slower growth. Conversely, a negative value suggests a declining growth rate.

3. Inflection Points: The first derivative can help identify inflection points, where the growth rate of the network changes direction. An inflection point occurs when the first derivative changes from positive to negative or vice versa, indicating a shift in the network's growth trajectory.

By examining the first derivative over time, we can analyze the network's growth dynamics and make predictions about its future value. If the growth rate remains positive and the first derivative is increasing, it suggests a network with strong potential. However, if the growth rate decreases or becomes negative, it may indicate a saturation

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40

25 20 15 10 5

50.0

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0

FIGURE 3 Future Bitcoin Users Growth Based on Historical Internet User Growth Millions

250 200 150 100 50

y = 0.011x1.0602

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5.0

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0 2011

Bitcoin Addresses Millions

FIGURE 1 Bitcoin Users and Internet Users

Actual

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Extrapolation of Bitcoin Users using Internet Users Using the relationship in Figure 1, we can extend out the growth in bitcoin users, proxied by nonzero addresses, to 2038 (the equivalent to Bitcoin Year 2022) (Figure 3).

Internet-Scaled

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2013

From 1995 to 2006, the average annual growth rate in internet users was 47%. From 2011 to 2022, the average annual growth rate in bitcoin users was 48%. The speed of adoption can be attributed to the pre-existing hardware and physical architecture allowing diffusion to occur quickly. Further, younger generations that have grown up in the digital age have been more likely to accept digital money.

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2012

Figure 1 illustrates that the proportionality factor between bitcoin user growth and internet user growth is nearly 1.0. This is also apparent in Figure 2, where the number of internet users has been scaled to bitcoin user value.

50

2011

In this analysis, the 2011 data point for bitcoin is calibrated to the 1995 data point for the internet.

FIGURE 2 Actual Bitcoin Users and Internet Users Scaled to Bitcoin User Dimensions Millions

point or the need for strategic interventions to stimulate further growth.

Bitcoin Users and Bitcoin Price A plot of users and price gives the following relationship: 0.5 5

50

500

5,000

Internet Users

Millions

Internet Adoption as an Indicator of Bitcoin’s Future Price

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3 June 2023 FIGURE 4 User Growth and Price

more cautious perspective on Bitcoin's historical price performance.

Log of Lowest Price Forward

12.00 10.00

Metcalfe’s Law Metcalfe’s law is commonly expressed as

y = 1.8128x - 22.131

𝑉𝑉 = 𝐴𝐴 ×

8.00

where A is indicative of a scaling factor and diminishing marginal returns. However, it is more appropriate to express it as

6.00 4.00

𝑉𝑉 = 𝑘𝑘 ×

2.00 0.00 13.00

𝑛𝑛(𝑛𝑛 − 1) 2

15.00

17.00

19.00

Log of Users

The use of lowest price forward (LPF) (see “Lowest Price Forward: Why Bitcoin’s Price Is Never Looking Back”) can be seen as a valid implementation of the principle of conservatism in analyzing Bitcoin's price history. Conservatism, in financial analysis, suggests that one should err on the side of caution and choose the option that is least likely to overstate outcomes.

In the case of the LPF price, the methodology takes the lowest price observed for each day moving forward in time. This approach ensures that the recorded price level is conservative because it considers the worst-case scenario in terms of price fluctuations. By selecting the lowest price from each day onwards, the NLB price becomes a conservative estimate of the price range.

This method avoids potential overstatement of Bitcoin's value by not considering higher price levels or fluctuations that occurred after a particular price was reached. It focuses solely on the lowest price moving forward, ensuring that any future retracements or declines in price are not considered. This conservative approach provides a

Internet Adoption as an Indicator of Bitcoin’s Future Price

[𝑛𝑛(𝑛𝑛 − 1)] 𝐴𝐴 2

where k is the scaling factor and A is a decay in value per user connectivity as network size increases. For large n, this formulation allows expression of the first derivative: 𝑑𝑑𝑑𝑑 = 2𝐴𝐴𝐴𝐴 + 𝑘𝑘′ 𝑑𝑑𝑑𝑑

which is consistent with Figure 4. Since the coefficient in Figure 4 is 1.81, we can estimate that A ≈ 0.9, meaning there is little decay in the value as the network grows (at least at this stage of adoption).

Future Value from Forecast Users Using data from Figure 3 and the relationship in Figure 4, we can estimate bitcoin’s future price assuming it follows the same adoption curve that the internet did. The results are graphed in Figure 5; a value of $500,000 is not achieved until 2038.

However, it must be noted that these values are conservative because the lowest historical prices were used to establish the growth parameters. It is typically the case that the actual bitcoin price is about 25% above this lowest value. This is due in part to bitcoin’s inelasticity of supply which forces short-term bubbles (see “Estimating the Impact of Mempool Backlogs on Bitcoin Price”) although some of the instigating cause of these bubbles

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3 June 2023 may be manipulation (See “To the Moon: A History of Bitcoin Price Manipulation”).

before this saturation point is reached. Central Bank Digital Currencies pose one such threat.

FIGURE 5 Bitcoin Price Extrapolated from Internet Growth

Conclusion The exponential relationship between network value and the number of users, as described by Metcalfe's Law, emphasizes the value derived from the interactions and connections between users. By analyzing the first derivative of Metcalfe's Law, insights can be gained regarding network growth rates, inflection points, and potential future trajectories.

1,000,000 100,000 10,000 1,000 100 10

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2011

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Also, it does not appear that bitcoin hits the fabled $1 million mark any time soon, and perhaps never.

There are several reasons why.

First, only 60% of the world's population has internet access, roughly the same proportion that has reliable electricity.

(Continued on page 6)

Second, only 20% of the world’s population can be considered “developed” while 60% can be considered “developing” and the remaining 20% considered “frontier.”

Third, of the “developing” demographic, about 40% of those live in authoritarian regimes that restrict access to money, and certainly restrict access to permissionless systems like bitcoin. This means that the saturation point for bitcoin is the 20% residing in developed nations and the 30% residing in developing, non-authoritarian societies = 50%.

It is entirely plausible that a new digital asset system will compete with, or replace, bitcoin

Internet Adoption as an Indicator of Bitcoin’s Future Price

This research note also extrapolates Bitcoin user growth based on historical internet user growth and examines the relationship between Bitcoin users and price. The use of the lowest price forward methodology is seen as a conservative approach to analyzing Bitcoin's price history.

Additionally, consideration must be given to the limitations to Bitcoin's future growth, including the global population's internet access, development levels, and restrictions on access to money in certain regimes. It suggests the possibility of a new digital asset system competing with or replacing Bitcoin before it reaches its saturation point.

References Cane Island Digital Research. (2019). “Why Bitcoin’s Price is Never Looking Back.” https://www.caneisland.digital/s/research-note-412.pdf —. (2020). “Estimating Bitcoin’s Adoption Curve and Maximum Price.” https://www.cane-island.digital/s/researchnote-629212.pdf —. (2021). “Estimating the Impact of Mempool Backlogs on Bitcoin Price.” https://www.cane-island.digital/s/ResearchNote-816211.pdf Peterson, Timothy. "Metcalfe's Law as a Model for Bitcoin's Value." Alternative Investment Analyst Review, vol. 7, no. 2, Q2 2018, pp. 9-18.

—, —. "To the Moon: A History of Bitcoin Price Manipulation." Journal of Forensic and Investigative Accounting, vol. 13, no. 2, July-December 2021, pp. 1-23.

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Internet Adoption as an Indicator of Bitcoin’s Future Price

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Internet Adoption as an Indicator of Bitcoin’s Future Price

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