Empirical/mathematical method to choose which cryptocurrency community to join

[Peter R]

Empirical/mathematical method to choose which cryptocurrency community to support

I've been fascinated by the rise and fall of various cryptocurrencies, and this fascination has lead me to study what it is that gives a coin legitimacy and lasting value.  I've concluded that the value of a cryptocurrency is stored in its blockchain ledger by the shared agreement within the community that the ledger is legitimate--"money is memory" in other words.  I've concluded that the value of this ledger grows with the coin's user base and economy.  

While working on methods to quantify this, I've found some startling relationships.  Since bitcoin has the longest history, we can learn a lot from the data we already have.  The value V of bitcoin's ledger appears to follow Metcalfe's Law such that V is proportional to the square of N, where N is what I refer to as the generalized user base.  Below is a log chart of bitcoin's Metcalfe Value versus its market cap over its complete price history:




The market price dances about the value trying to predict what will happen next.  

Each community member adds a different ΔN-value to the coin.  Someone like Patrick M. Byrne (CEO of Overstock) brings a large ΔN-value to bitcoin because his involvement has a pronounced effect on the coin's economy.  Someone with 0.1 BTC that enjoys gambling at just-dice.com brings a smaller (but still positive) ΔN-value to the community.  

Let's face it, people make decisions based on their enlightened self-interest.  All other things being equal, why settle for less when you could have more?  The question then is "what community should you join if you want your contributions to be maximized?"

Since

   V = c N²,

by differentiating we get

   ΔV = 2 c N  ΔN = √(4 c V) ΔN.

This means that the value you bring to the community (ΔV) is proportional to how productive you are (ΔN) but scaled up by the square root of the value that already resides in the community.  In other words, if you know yourself to have positive productivity and if you want to maximize the value of your contributions, you should join the community that already has the most value.  

[Jamesco]

First of all I am no economist by any stretch but it seems like you have done some nice analysis. I would be very interested to see how this translates into other alt coins.

I feel like I only disagree with a minor point. That is the assumption that people make decisions based on their enlightened self-interest. I feel that most market analysis assumes perfectly rational agents which are able to make decisions based on enlightened self interest. While I would have to agree most traders intend to make rational decisions, they fall short of the mark. I could be wrong but I think most people are in a semi irrational state when it comes to trading and tend to make irrational decisions. This could explain the fluctuations in your graph and also why market sentiment(to me) seems to play a big role. If I could accurately predict market sentiment I feel I could be way more profitable than if I could predict what rational agents following the self interest would do in the same market.

Just a couple of ideas but I would love to see a litecoin/altcoin analyses, especially with the huge spike it had  last year and if it follows the same pattern BTC had in your graph.

[Peter R]

Thanks for your comments Jamesco.

I think you and I are both correct regarding the decisions people make based on their enlightened self-interest.  I am right because people tend to make the decision they think is best given their current emotional state and knowledge of the system dynamics at play.  You are right that the decision they actually make may often be suboptimal due to these emotions and the asymmetry of their knowledge (e.g., and fall prey to what (at least in my opinion) are obvious pump and dumps (e.g., Auroracoin)).

Regarding your other suggestion, I would love to do similar plots for Litecoin and the alts.  Hopefully when time permits.

[cryptowho]

i always wonder how Karmacoin would look in such a graphical analysis. Hope its good.

[hellscabane]

This is a nice analysis. I’m still trying to figure out how you solidly arrived at c=1.5 and c=0.3. I think this could have added benefit if you used Beckstorm’s Law (or something that incorporates an iterated summation) for this particular analysis and saw how well the fit was.

[Peter R]

This is a nice analysis. I’m still trying to figure out how you solidly arrived at c=1.5 and c=0.3.

Thanks for the compliment.  c=1.5 and c=0.3 are just best-fit parameters to Metcalfe's Law.  Depending on how you weight the residuals in your regression, and depending on whether you attempt to remove outliers, you can get a range (similar) c values.  For example, c = 1.43421 and c = 1.604983 look good on the plot too.  I simply picked numbers that (a) produced a good fit, and then rounded them so (b) they would be easy to remember (i.e., a buck-fifty per TX^2).  

I think this could have added benefit if you used Beckstorm’s Law (or something that incorporates an iterated summation) for this particular analysis and saw how well the fit was.

Yes, it would be interesting to attempt to model the market cap with Beckstorm's Law indeed (although I do appreciate the pure simplicity of Metcalfe's Law).  

[Zzzack]

This is a nice analysis. I’m still trying to figure out how you solidly arrived at c=1.5 and c=0.3.

Thanks for the compliment.  c=1.5 and c=0.3 are just best-fit parameters to Metcalfe's Law.  Depending on how you weight the residuals in your regression, and depending on whether you attempt to remove outliers, you can get a range (similar) c values.  For example, c = 1.43421 and c = 1.604983 look good on the plot too.  I simply picked numbers that (a) produced a good fit, and then rounded them so (b) they would be easy to remember (i.e., a buck-fifty per TX^2).  

I think this could have added benefit if you used Beckstorm’s Law (or something that incorporates an iterated summation) for this particular analysis and saw how well the fit was.

Yes, it would be interesting to attempt to model the market cap with Beckstorm's Law indeed (although I do appreciate the pure simplicity of Metcalfe's Law).  

Can you do this with Beckstorms and note the differences? I'm interested

[hellscabane]

This is a nice analysis. I’m still trying to figure out how you solidly arrived at c=1.5 and c=0.3.

Thanks for the compliment.  c=1.5 and c=0.3 are just best-fit parameters to Metcalfe's Law.  Depending on how you weight the residuals in your regression, and depending on whether you attempt to remove outliers, you can get a range (similar) c values.  For example, c = 1.43421 and c = 1.604983 look good on the plot too.  I simply picked numbers that (a) produced a good fit, and then rounded them so (b) they would be easy to remember (i.e., a buck-fifty per TX^2).  

I think this could have added benefit if you used Beckstorm’s Law (or something that incorporates an iterated summation) for this particular analysis and saw how well the fit was.

Yes, it would be interesting to attempt to model the market cap with Beckstorm's Law indeed (although I do appreciate the pure simplicity of Metcalfe's Law).  

I agree, simplicity is very nice. I just brought it up because I'm intrigued by what the correlative values between both models would be (based on similar fitting exponential curves). Although, the iterative summations could be needlessly more complicated than the information that would be gleaned out.

Thank you clearing up where you got the values of c from. I wasn't sure if you were using best fits or if those numbers came from another analysis. (I thought there were clearly obvious reasons for the numbers and that I was going crazy. Ha!)

Once again, very nice job with this! I look forward for more analysis from you, when time permits (as someone mentioned seeing the curves of other crypto-currencies would be quite intriguing).

[Peter R]

Can you do this with Beckstorms and note the differences? I'm interested

I have several projects on the go, so I'm not sure when I'd get around to doing this.  I will share the following Mathematica code if you wanted to contribute:

Code:

fetchBlockchainInfo[url_String] := {AbsoluteTime[{#[[1]], {"Day", "Month", "Year", "Hour", "Minute", "Second"}}], #[[2]]} & /@ Import[url]

Now, if you want to import the latest data from blockchain.info direct for analysis into Mathematica, just feed this function the appropriate URL. For example, this is the URL for the market cap feed:

Code:

fetchBlockchainInfo["https://blockchain.info/charts/market-cap?showDataPoints=false&timespan=all&show_header=true&daysAverageString=1&scale=1&format=csv&address="]

The function AbsoluteTime[] converts the dates into an integer number of seconds since January 1, 1900.  This way you don't have to mess around with date strings.