(1) Metcalfe ≈ exp(-2.662352 + 1.08e-07*N + 5.21e-07*C)Using a little algebra, first we set the Metcalfe value to $1000000, and then solve for the number of bitcoins in circulation (which happily reduces to a function of the number of wallets).
The function is calculated as:
(2) No. bitcoins ≈ 0.207294*(1.52573*10^8 - no. wallets)
Substituting (2) back into (1) and solving for no. wallets, will give us a function that describes the number of users required on the network to support a value of $1000000.
 | (3) 1000000 ≈ exp(-2.662352 + 1.08e-07*N + 5.21e-07*0.207294* (1.52573*10^8 - N)) N ≈ 2.75803*10^8 |
What this indicates is that there will need to be around two hundred and seventy-five million wallets to support a Metcalfe value of $1000000. This does not seem impossible, nor even remotely unreasonable.
For example, displayed in the figure below is the current number of wallet users from blockchain.info:
 |
| Figure 1: Current wallet numbers. around a 10x increase will put the bitcoin Metcalfe value at $1000,000 |
A 10x (11.36 to be precise) increase in wallet users will result in a Metcalfe value of $1000000, and as has been established previously, the Metcalfe value is a strong support line for the bitcoin value.
Now that we have a target established, we can work on trying to magic 8 ball the number of users. The chart in figure 1 looks vaguely linear, so I will perform a linear regression on the number of users against date. All data is sourced from blockchain.info.
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Table 1: Wallet data has been normalised against the number of months available for a given year.
The maximum number of wallets was taken for each year. Upon inspection, a 4th root transformation
target has been identified for the regression.
|
. regress throotnormalisednumberofwallets year
Source | SS df MS Number of obs = 8
-------------+---------------------------------- F(1, 6) = 250.14
Model | 5267.39179 1 5267.39179 Prob > F = 0.0000
Residual | 126.344853 6 21.0574755 R-squared = 0.9766
-------------+---------------------------------- Adj R-squared = 0.9727
Total | 5393.73665 7 770.533807 Root MSE = 4.5888
------------------------------------------------------------------------------
throotnorm~s | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
year | 11.19884 .7080738 15.82 0.000 9.466249 12.93144
_cons | -22514.83 1426.416 -15.78 0.000 -26005.15 -19024.52
------------------------------------------------------------------------------
Source | SS df MS Number of obs = 8
-------------+---------------------------------- F(1, 6) = 250.14
Model | 5267.39179 1 5267.39179 Prob > F = 0.0000
Residual | 126.344853 6 21.0574755 R-squared = 0.9766
-------------+---------------------------------- Adj R-squared = 0.9727
Total | 5393.73665 7 770.533807 Root MSE = 4.5888
------------------------------------------------------------------------------
throotnorm~s | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
year | 11.19884 .7080738 15.82 0.000 9.466249 12.93144
_cons | -22514.83 1426.416 -15.78 0.000 -26005.15 -19024.52
------------------------------------------------------------------------------
This gives us the regression equation for the number of wallets based on year.
The equation is therefore:
(4) Number of Wallets = (11.19884 * year - 22514.83)^4
So how many wallets will there be in 2020? Well if the equation in 3 is to be believed, there will be around 130 million. 130 million wallets substituting back into (3) we have a bitcoin Metcalfe value of around $1000000. Looks like McAfee may have to go hungry.
Next time: Remember this?
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| Figure 2: Metcalfe value vs bitcoin price. |
Well I am going to apply some tests about these peaks to see if they are statistically significantly different to the Metcalfe value, and then explore what that means if they are.
Thanks for reading crypto addicts.
Týr
Týr
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