Using Average BTC holdings (in USD) vs # of Users to Understand USD/BTC

[bb113]

The x-axis shows the number of Bitcoin users and y axis the average (arithmetic mean) value of their bitcoin holdings in dollars. Taken together these allow us to know what the current price is. Of course the distribution of bitcoins held will not be normal, it probably follows some kind of power law. I still think that using the mean can be informative. The heatmap and contours show the USD/BTC ratio for the given possible combinations of users and average holdings. For example, given a price of $600 either there are 2 million users holding a little under $4k worth of bitcoin each, or 1 million users holding on average ~$7.5k worth.

To predict the future price we would need to guess the distribution of how much each would be willing to hold as well as growth/loss of users.

[koryu]

very interesting.

how would you estimate the current number of users?

there is a lot of information on blockchaininfo, like Number Of Unique Bitcoin Addresses Used per Day
stil its hard to guess the real number of users.

are there any other reliable sources f.e. number of verified users on exchanges? and whats your guess?

/edit: your graph shows the current situation, means with 12.5mio btc in circulation?

[oda.krell]

The x-axis shows the number of Bitcoin users and y axis the average (arithmetic mean) value of their bitcoin holdings in dollars. Taken together these allow us to know what the current price is. Of course the distribution of bitcoins held will not be normal, it probably follows some kind of power law. I still think that using the mean can be informative. The heatmap and contours show the USD/BTC ratio for the given possible combinations of users and average holdings. For example, given a price of $600 either there are 2 million users holding a little under $4k worth of bitcoin each, or 1 million users holding on average ~$7.5k worth.

To predict the future price we would need to guess the distribution of how much each would be willing to hold as well as growth/loss of users.

Interesting idea, trying to get what exactly you're doing though... You make no further assumptions rather than that coin holdings are following a normal distribution (probably not the case, but like you said: let's roll with it for now), but is there any empirical input? Is the 'number of users' value based on actual statistics, or does it follow from the assumption above? If the former, where does the data come from, if the latter, how?

[koryu]

The x-axis shows the number of Bitcoin users and y axis the average (arithmetic mean) value of their bitcoin holdings in dollars. Taken together these allow us to know what the current price is. Of course the distribution of bitcoins held will not be normal, it probably follows some kind of power law. I still think that using the mean can be informative. The heatmap and contours show the USD/BTC ratio for the given possible combinations of users and average holdings. For example, given a price of $600 either there are 2 million users holding a little under $4k worth of bitcoin each, or 1 million users holding on average ~$7.5k worth.

To predict the future price we would need to guess the distribution of how much each would be willing to hold as well as growth/loss of users.

Interesting idea, trying to get what exactly you're doing though... You make no further assumptions rather than that coin holdings are following a normal distribution (probably not the case, but like you said: let's roll with it for now), but is there any empirical input? Is the 'number of users' value based on actual statistics, or does it follow from the assumption above? If the former, where does the data come from, if the latter, how?

imo the only data is the amount of btc in circulation, users and average are variables you have to guess.

formula should be: users * average / 12.5mio = price

[oda.krell]

The x-axis shows the number of Bitcoin users and y axis the average (arithmetic mean) value of their bitcoin holdings in dollars. Taken together these allow us to know what the current price is. Of course the distribution of bitcoins held will not be normal, it probably follows some kind of power law. I still think that using the mean can be informative. The heatmap and contours show the USD/BTC ratio for the given possible combinations of users and average holdings. For example, given a price of $600 either there are 2 million users holding a little under $4k worth of bitcoin each, or 1 million users holding on average ~$7.5k worth.

To predict the future price we would need to guess the distribution of how much each would be willing to hold as well as growth/loss of users.

Interesting idea, trying to get what exactly you're doing though... You make no further assumptions rather than that coin holdings are following a normal distribution (probably not the case, but like you said: let's roll with it for now), but is there any empirical input? Is the 'number of users' value based on actual statistics, or does it follow from the assumption above? If the former, where does the data come from, if the latter, how?

imo the only data is the amount of btc in circulation, users and average are variables you have to guess.

formula should be: users * average / 12.5mio = price

makes sense. but then, in addition to normal distribution, max users (set to 12M here) is also a huge assumption, no?... guess I'm just trying to squeeze out what is the truly speculative part of the map, and what are the (simplifying) assumptions I can, more or less, subscribe to.

[koryu]

makes sense. but then, in addition to normal distribution, max users (set to 12M here) is also a huge assumption, no?... guess I'm just trying to squeeze out what is the truly speculative part of the map, and what are the (simplifying) assumptions I can, more or less, subscribe to.

i think its not his intention to speculate about a maximum amount of users. with a very high amount of users the average will converge towards zero while the price goes to infinity.

this is more a analysis of market capitalization than price speculation.  however you can guess the number of users and average for the future and the map shows you what the price would be in that case (without consideration of new btcs mined).

thats my interpretation.

[cbutters]

The number of unique wallets being generated is increasing exponentially! 

[bb113]

Koryu's interpretation is correct. The price is calculated simply as (#users X AvgHoldings)/#Coins. I actually used 12 million coins because rounding and lost coins.

Oda, the 12 million number is the estimated number of coins (not number of users). This chart contains no data other than the number of coins in circulation, which is actually an upper limit. I do not assume a normal distribution in making the chart. I mentioned that just because interpreting a mean is somewhat non intuitive for the extremely skewed distribution that probably describes bitcoin holdings per user. However it is still valid to calculate the mean and use it as a summary statistic.

I found the chart interesting because it is an intuitive way of showing the dependance of price on the number of users, wealth of those users, and their sentiment towards bitcoin. Even though the chart shows the mean, and the mean can be unintuitive when describing a skewed distribution, we also know that the mean cannot be less than the minimum.

So the way I looked at that chart is to ask "Is it plausible that there are 2,000,000 people out there willing to store at least $4k of value in bitcoin?" If that many people are willing to store at least that amount of value, some will be willing to store more and thus the users will be able to support an even higher price. I think that this is plausible and so the current price of $600 is not insane or anything like that.

I have no data for this however and was hoping others had estimates of users and average btc wealth.

[bb113]

So, did anyone calculate the average fiat value of btc holdings from the mt gox leak? The data may not be representative (or even real) but if it is that would tell us the number of users supporting the current price.

[elebit]

Interesting. It is worth noticing that MtGox had a million users and losses were somewhere between half a billion and one billion dollars.

That means we should already be at a few million users since not all users had MtGox accounts. Those who did stored on average $500 there, mostly in Bitcoins. But how large part of their holdings did the average user put in? (And how average were MtGox's users, really?)

These numbers should at least put is in the right ballpark. I am a bit surprised that we are this far ahead really. That the valuation of Bitcoin is in its future promises, and not in today's economy, should not come as a surprise to anybody, but I think your heatmap shows that we are not really that overvalued. Especially not considering what dot-com companies are worth, and Bitcoin is not just a company but a whole potential economy, should it work out.

I do however think that your axis are skewed. Should Bitcoins become widely used, I think the average worth per user should be expected to drop (since its value as an investment lessens) but the number of users should be expected to be at least an order of magnitude larger than twelve million. Facebook alone has over a billion users. Two and a half billion use email. How many users wants the ability to pay someone effortlessly over the Internet?

[bb113]

Interesting. It is worth noticing that MtGox had a million users and losses were somewhere between half a billion and one billion dollars.

That means we should already be at a few million users since not all users had MtGox accounts. Those who did stored on average $500 there, mostly in Bitcoins. But how large part of their holdings did the average user put in? (And how average were MtGox's users, really?)

These numbers should at least put is in the right ballpark. I am a bit surprised that we are this far ahead really. That the valuation of Bitcoin is in its future promises, and not in today's economy, should not come as a surprise to anybody, but I think your heatmap shows that we are not really that overvalued. Especially not considering what dot-com companies are worth, and Bitcoin is not just a company but a whole potential economy, should it work out.

I do however think that your axis are skewed. Should Bitcoins become widely used, I think the average worth per user should be expected to drop (since its value as an investment lessens) but the number of users should be expected to be at least an order of magnitude larger than twelve million. Facebook alone has over a billion users. Two and a half billion use email. How many users wants the ability to pay someone effortlessly over the Internet?

[aminorex]

Should Bitcoins become widely used, I think the average worth per user should be expected to drop (since its value as an investment lessens)

Say what?  It's difficult for me to react temperately to a statement like this which so offends my reason.  Am I misinterpreting it?  Please expand.

[aminorex]

This whole thread appears to boil down to a multiplication table.  Also there is no normality assumption, because the sum is over all the coins.  The multiplication table still holds even if one person has all the coins.

[bb113]

This whole thread appears to boil down to a multiplication table.  Also there is no normality assumption, because the sum is over all the coins.  The multiplication table still holds even if one person has all the coins.

Yes, if one person holds all the coins they determine the "price". It would be whatever they sell them for. I agree it is a simple multiplication table. It is easier to get intuitive estimations of number of users and average holdings than price, price is more mysterious at first glance. We could make the same chart for USD vs anything, cryptos are special because we do know the upper bound of how much is in existence.

[koryu]

MtGox leak analyzed

Code:

	69266	951441		
mBTC+	#	#BTC	avg	
10 000k	5	130 809		26161,8000
1 000k	96	212 762		2216,2708
100 000	1266	318 490		251,5719
10 000	7291	219 331		30,0824
1 000	17851	62 630		3,5085
100	16389	6 834		0,4170
10	13675	528		0,0386
1	12693	57		0,0045

It seems that among the claimed 1 million Mt.Gox users, there was 69266 accounts with a balance of at least 1mBTC. In total, they were supposed to hold BTC951,441.

- This is 13,744mBTC per holder, which is more than double the average general holding of 5,900mBTC.
- The median of about 500mBTC was significantly higher than the general median of only 70mBTC.
- Distribution parameter j was found to be between 0.34-0.42 whereas it was assumed to be 0.25 when making the last general distribution. Adopting this makes the distribution more "middle-classed" as the bulge in the middle sized holdings is higher.
- In general the results confirmed the distribution model.

=> Due to findings above ("j", median, and the fact that Gox had only 70,000 customers despite the claims), I will be prompted to revise the Bitcoin # number of users downward from the 2.0 million in the previous month.

quoting rpietila's post here from another thread. so there is some data to play with. there are only arround 70.000 users@gox holding > 0.001btc. ofc a lot of people will have cashed out before.

i will add that there are 1.3m mywallet addresses: https://blockchain.info/de/charts/my-wallet-n-users

so i think 2m users are quite possible. that would mean an average of around 4000$ would be needed to backup the current 630$ price.

[elebit]

Should Bitcoins become widely used, I think the average worth per user should be expected to drop (since its value as an investment lessens)

Say what?  It's difficult for me to react temperately to a statement like this which so offends my reason.  Am I misinterpreting it?  Please expand.

It is only a supposition. Do you think it is incorrect? Please expand on your thoughts.

The reason I expect it to hold true is because as Bitcoin gets more widely used and more valuable, people would come to expect less gain in its future value. We have already seen more than a thousandfold increase in value (or even more), but even an optimist would consider such an increase again to be unrealistic. A stable Bitcoin could probably not sustain a value of millions of dollars each.

I also think that as the user base increases above and beyond the globally well off, less new adopters would have access to thousands of dollars to invest.

[elebit]

so i think 2m users are quite possible. that would mean an average of around 4000$ would be needed to backup the current 630$ price.

Today's price is based on what Bitcoin could become, not what it's worth today. Think of it as stocks in a startup, if you will.

The Bitcoin economy has the potential to develop completely payment mechanisms for the web, including the fabled micro payments. We have already seen new tipping mechanisms. That's just the start of what's possible.

Considering only Paypal has 150M accounts, I don't think it is unreasonable for Bitcoin to grow at least two orders of magnitude. I'm even starting to think it is probable.

(Do I think a user base in the hundreds of millions would stash 4k$ each in there? No. See above.) So if Bitcoins become widely deployed on the Internet, and I think we're starting to see some early signs of that, today's value is vastly undervalued.

[aminorex]

Should Bitcoins become widely used, I think the average worth per user should be expected to drop (since its value as an investment lessens)

Say what?  It's difficult for me to react temperately to a statement like this which so offends my reason.  Am I misinterpreting it?  Please expand.

It is only a supposition. Do you think it is incorrect? Please expand on your thoughts.

The reason I expect it to hold true is because as Bitcoin gets more widely used and more valuable, people would come to expect less gain in its future value. We have already seen more than a thousandfold increase in value (or even more), but even an optimist would consider such an increase again to be unrealistic. A stable Bitcoin could probably not sustain a value of millions of dollars each.

I also think that as the user base increases above and beyond the globally well off, less new adopters would have access to thousands of dollars to invest.

I see.  You think that current prices are discounting future gains, and as price approaches long-term value, it will necessarily discount less gain.  Makes sense.  However, we mustn't neglect the risk factor.  Risk adjustment means that early prices discount at a larger rate, and probably exponentially, on behavioral grounds.  I would expect coins to be cheap now, relative to a purely rational risk adjustment.

The reason I found it offensive was that I was not thinking about instantaneous market price, but about the underlying economic value to which price stochastically converges.  The value increases with increasing transaction volume and decreasing velocity, after PQ=MV.  PQ should increase and M decrease while V increases as the log, with increasing number of users. 

[elebit]

I see.  You think that current prices are discounting future gains, and as price approaches long-term value, it will necessarily discount less gain.

Yes. ("Future gains discount", took a minute to parse that.)

Risk adjustment means that early prices discount at a larger rate, and probably exponentially, on behavioral grounds.

Agreed. The behavioural grounds being that it is impossible to calculate risks (since "risk" here means "we don't know").

(Risk is funny like that. The last few months has been the worst realistically possible ones for Bitcoin, with China and MtGox, and price hovers around twice the spring bubble of 2013. I would have expected the reaction to be worse.)

The reason I found it offensive was that I was not thinking about instantaneous market price, but about the underlying economic value to which price stochastically converges.  The value increases with increasing transaction volume and decreasing velocity, after PQ=MV.  PQ should increase and M decrease while V increases as the log, with increasing number of users. 

I failed to parse this. Do you mean converges statistically at any single moment, or the longer term convergence?

Also, I'm not sure velocity will decrease. It could very well increase on increasing volume, if the price stabilizes completely.