Context: This TruStory builds on two previous analyses. Chris Burniske had recently written about how Network Fundamentals for both Bitcoin and Ethereum were down less than price. The previous analyses support both his claim.
Nevertheless, implicit in his argument is the idea that network fundamental values can be assessed by their usage (transactions or active addresses). That is the subject of the current TruStory.
Claim : Metcalfe’s law (and similar laws) nearly perfectly correlate with BTC’s USD price (as of Feb 9/10, 2018); which suggests that cryptoassets can be valued by their usage (daily transactions or active addresses).
Category : Network Valuation / Token Economics
Evidence/ Argument : The following are two main claims the author makes
- Claim #1 : Pearson correlation coefficients of Metcalfe formulas (transactions) with BTC USD price is nearly perfect
- Claim #2 : Pearson correlation coefficients of Metcalfe formulas (active addresses) with BTC USD price is nearly perfect
See correlation with Metcalfe formulas (Transactions & Active Addresses) Source: https://medium.com/@clearblocks/valuing-bitcoin-and-ethereum-with-metcalfes-law-aaa743f469f6
My goal was to reproduce these numbers following the author’s logic. Here are the steps:
- Download 10-year’s worth of Bitcoin’s Confirmed Transactions Per Day, Bitcoin’s Unique Addresses, Bitcoin’s Market Price (USD), and Total Bitcoins in Circulation (Supply) from https://www.blockchain.com/charts [select “All Time” to get 10-year’s worth of data]
- Re-Create Metcalfe’s Law (M), variations (M1 – M3) and similar, but competing, laws (Sardoff’s and Zipf’s law) for both daily transactions and unique addresses (note: I used the exact formulas the author used). Then create the natural log of each number (see below).
Note: Orange columns represent the natural log of each number (i.e., Metcalfe’s, Sardolff’s and Zipf’s law and variants (M1-M3).
- Calculate the Pearson’s Correlation ® between Bitcoin’s Price (USD) and various measures of ‘usage’ (i.e., daily transactions, active addresses).
Orange rows represent the correlation after all numbers had been converted to their natural log scale.
- Special notes for calculations:
- The authors mention only having data for “every other day as opposed to daily which may affect precision”. This is necessary when downloading 10-year’s worth of data (2009 – end 2018); for datasets dating back a year or two, daily numbers are available. Source: https://www.blockchain.com/charts/
The authors omit days when the price of Bitcoin was at $ 0 (USD). I did the same, thus all analyses begin on August 16th, 2010 through December 22nd, 2018 (when Bitcoin’s price was higher than 0). This prevents price data from being unduly skewed towards zero.
c. The authors take the natural log of all their formulas because a Pearson’s correlation measures the linear relationship between two variables (i.e., fitting a scatter of data onto a straight line). However, telecom networks, and by implication, blockchain networks do not exhibit “linear” growth patterns. A casual glance at the ‘All Time’ graphs for Bitcoin’s Price, Daily Transactions and Unique Addresses reveal exponential growth. Therefore to find the Pearson’s correlation between price and usage, it is necessary to convert the formulas to their natural log scale.
i. Another way to think about this: When Bitcoin went from 90 cents (February 8th, 2011) to $1.95 (April 27th, 2011), that’s nearly a 100% increase in Bitcoin price. Nowadays, it takes a lot more to even get a 5% increase in price – a natural log scale accounts for the differences in scale.
Outcome of Calculations The authors report above average correlations between Bitcoin’s USD price and various Metcalfe formulas – on the linear scale – ranging from 0.56 – 0.64; I got a similar, but narrower range 0.59 – 0.60. When using the natural log, the authors report near perfect correlation between Bitcoin’s USD price and various Metcalfe formulas ranging from 0.92 – 0.96; I got similarly high correlations ranging from 0.92 – 0.95.
This analysis corroborates the author’s claim that Metcalfe’s Law (and similar laws) is a useful framework for valuating blockchain networks and lend credence to the idea that blockchain networks behave like telecommunication networks. So long as this continues, Metcalfe’s law can help analysts understand where the demand (usage) of blockchain networks and their price intersect and where one has “significantly outpaced the other” (https://medium.com/@clearblocks/valuing-bitcoin-and-ethereum-with-metcalfes-law-aaa743f469f6) as Chris Burniske had done in his follow-up analyses.
Addendum : Because Metcalfe’s law suggests that as a blockchain network expands in scale, it behaves more like a telecommunication network. I’d argue this is one way of valuing ‘network effects’. A cool analysis would be to compare the correlations between price and usage between 2010 – 2014 and 2015 – 2018 and see if there’s a significant difference between the two. I would expect to see stronger correlations for the latter years (as network size had increased).