Stephen Reed's Million Dollar Logistic Model

[jyakulis]

Looks like a dogecoin analysis with real maths and stuff.

[SlipperySlope]

My hypothesis is weakened a bit with this chart which shows transaction quantity relatively surpassing market cap in the summer of 2012, without a major new bubble.

That was Satoshi Dice running it's network transaction quantity "stress test" I think you'll find ...

I see now. For this reason and to filter out other non-economic transactions, Blockchain excludes the 100 most popular addresses when calculating the data series that I follow.

[marcus_of_augustus]

My hypothesis is weakened a bit with this chart which shows transaction quantity relatively surpassing market cap in the summer of 2012, without a major new bubble.

That was Satoshi Dice running it's network transaction quantity "stress test" I think you'll find ...

I see now. For this reason and to filter out other non-economic transactions, Blockchain excludes the 100 most popular addresses when calculating the data series that I follow.

yeah, that was the TXS data series I used ... didn't satoshi dice generate random addresses on demand?

[wachtwoord]

My hypothesis is weakened a bit with this chart which shows transaction quantity relatively surpassing market cap in the summer of 2012, without a major new bubble.

That was Satoshi Dice running it's network transaction quantity "stress test" I think you'll find ...

I see now. For this reason and to filter out other non-economic transactions, Blockchain excludes the 100 most popular addresses when calculating the data series that I follow.

yeah, that was the TXS data series I used ... didn't satoshi dice generate random addresses on demand?

No they had a set of vanity addresses depicted the wager one wanted to take.

[cuddaloreappu]

With this article claiming bitcoin transaction is increasing day by day but the price dropping every day, can we come to conclusion that metcalfe law does not have any relation with bitcoin price?

http://www.cio.com.au/article/556378/mobile-payments-grow-60-8-by-2015-capgemini/

[SlipperySlope]

With this article claiming bitcoin transaction is increasing day by day but the price dropping every day, can we come to conclusion that metcalfe law does not have any relation with bitcoin price?

http://www.cio.com.au/article/556378/mobile-payments-grow-60-8-by-2015-capgemini/

I would accept that this observation weakens the Metcalfe Law hypothesis with regard to Bitcoin network effects. But as Peter_R has shown in his charts, there is considerable variability in the data series, although over time the correlation is significant.

I continue to wait for the 7-day smoothed number of transactions excluding the 100 most popular addresses to exceed 80000. That would be an all-time-high. And if bitcoin price is still depressed then that would be stronger evidence against the hypothesis.

[oda.krell]

Here's an observation, not sure if it is new to you or not...

(by the way, as I said before, your work is much appreciated Stephen. I've been critical about aspects of it before, and this comment won't be different,
but I think there's a good reason for someone to take the 'devil's advocate' role once in a while)

The observation is that, if we ignore the "spikes" into a higher range of transactions, one could argue there is an overall slowing down of adoption (as measure by transaction). The Metcalfe's law based price models wouldn't necessarily pick this up initially, because transactions *are* still rising, but it is (at least to me) conceivable that rate of growth is behind earlier expectations, and this reflects in the current price stagnation (as in: the markets pick up slower than expected adoption than the models do).

Here's the slow-down I have in mind, if viewed from the following point of view: Let's look at "transaction eras" only in terms of powers of 10, and only after the no. of transactions doesn't fall back into the previous order of magnitude.

Arbitrary definition? Maybe. Anyway, here's the transaction graph if parsed like that:



Any opinions on this?

[SlipperySlope]

The observation is that, if we ignore the "spikes" into a higher range of transactions, one could argue there is an overall slowing down of adoption (as measure by transaction). The Metcalfe's law based price models wouldn't necessarily pick this up initially, because transactions *are* still rising, but it is (at least to me) conceivable that rate of growth is behind earlier expectations, and this reflects in the current price stagnation (as in: the markets pick up slower than expected adoption than the models do).

Here's the slow-down I have in mind, if viewed from the following point of view: Let's look at "transaction eras" only in terms of powers of 10, and only after the no. of transactions doesn't fall back into the previous order of magnitude.

Any opinions on this?

As stated in the original post, my high price of $1 million is simply a guess. I could get a better fit on the logistic model with the data series to-date by assuming a high price of $2500. But that implies that we are near or have passed the adoption midpoint - which is hard to believe.

Alternatively, I am intrigued by the suggestion that the logistic model is a better fit to market capitalization data than to price data, because market cap takes into account the supply of bitcoin that meets the demand of the marginal new adopter.

I shall prepare another model using bitcoin market cap, but I would very much like to wait until the new year or a bubble, whichever occurs first because bubble peaks are easy to recognize and bottoms much more difficult. The right hand side of the model graph is hand fit to balance the central tendency and it is not clear yet where that region is for the bubble that peaked in November 2013.

[oda.krell]

The observation is that, if we ignore the "spikes" into a higher range of transactions, one could argue there is an overall slowing down of adoption (as measure by transaction). The Metcalfe's law based price models wouldn't necessarily pick this up initially, because transactions *are* still rising, but it is (at least to me) conceivable that rate of growth is behind earlier expectations, and this reflects in the current price stagnation (as in: the markets pick up slower than expected adoption than the models do).

Here's the slow-down I have in mind, if viewed from the following point of view: Let's look at "transaction eras" only in terms of powers of 10, and only after the no. of transactions doesn't fall back into the previous order of magnitude.

Any opinions on this?

As stated in the original post, my high price of $1 million is simply a guess. I could get a better fit on the logistic model with the data series to-date by assuming a high price of $2500. But that implies that we are near or have passed the adoption midpoint - which is hard to believe.

Alternatively, I am intrigued by the suggestion that the logistic model is a better fit to market capitalization data than to price data, because market cap takes into account the supply of bitcoin that meets the demand of the marginal new adopter.

I shall prepare another model using bitcoin market cap, but I would very much like to wait until the new year or a bubble, whichever occurs first because bubble peaks are easy to recognize and bottoms much more difficult. The right hand side of the model graph is hand fit to balance the central tendency and it is not clear yet where that region is for the bubble that peaked in November 2013.

Good points. Would like to see the market cap model very much.

The point of my post (and graph) above was a slightly different one, though. Aimed more at Peter R.'s models, now that I think of it (since he is the one who uses 'no of tx' as a proxy for adoption in a Metcalfe based model).

What I had in mind is: if Bitcoin adoption is, against earlier optimistic assumptions, neither accurately captured by your logistic model nor by a constant exponent exponential growth model based on a constant rate of growth, then all the current models could be missing something that the market / price discovery (perhaps) is picking up already: adoption continues, but the growth rate of adoption declines over time.

Your model would "miss" it because the growth function is hardcoded into it (the S-shape), Peter R.'s model would "miss" it, for a while at least, because the coefficient that relates price/mcap and adoption proxy is a global value, and will take time to adjust to a lower value.

Do you see the point I'm (clumsily) trying to make here?

[SlipperySlope]

The point of my post (and graph) above was a slightly different one, though. Aimed more at Peter R.'s models, now that I think of it (since he is the one who uses 'no of tx' as a proxy for adoption in a Metcalfe based model).

What I had in mind is: if Bitcoin adoption is, against earlier optimistic assumptions, neither accurately captured by your logistic model nor by a constant exponent exponential growth model based on a constant rate of growth, then all the current models could be missing something that the market / price discovery (perhaps) is picking up already: adoption continues, but the growth rate of adoption declines over time.

Your model would "miss" it because the growth function is hardcoded into it (the S-shape), Peter R.'s model would "miss" it, for a while at least, because the coefficient that relates price/mcap and adoption proxy is a global value, and will take time to adjust to a lower value.

Do you see the point I'm (clumsily) trying to make here?

Yes, and thank you for the helpful clarification.

Mathematically, the logistic model has the property of decreasing exponential growth, which is most obvious on a log graph as we near full adoption. It is only a falsifiable hypothesis that a logistic model can explain bitcoin prices. My reason for choosing this model was to fit the obvious constraint that exponential price growth must eventually end. Perhaps we are at that point now, but I believe not based upon the steady improvement in Bitcoin transactional infrastructure. http://www.bitcoinpulse.com/

There is at least one mathematical theory of price bubbles that could be used to elaborate this logistic model, but I hesitate to combine them for fear of unsound overfitting given the additional number of parameters whose values must be set. The bitcoin logistic model has only two parameters: the maximum price and the full adoption duration.

[oda.krell]

The point of my post (and graph) above was a slightly different one, though. Aimed more at Peter R.'s models, now that I think of it (since he is the one who uses 'no of tx' as a proxy for adoption in a Metcalfe based model).

What I had in mind is: if Bitcoin adoption is, against earlier optimistic assumptions, neither accurately captured by your logistic model nor by a constant exponent exponential growth model based on a constant rate of growth, then all the current models could be missing something that the market / price discovery (perhaps) is picking up already: adoption continues, but the growth rate of adoption declines over time.

Your model would "miss" it because the growth function is hardcoded into it (the S-shape), Peter R.'s model would "miss" it, for a while at least, because the coefficient that relates price/mcap and adoption proxy is a global value, and will take time to adjust to a lower value.

Do you see the point I'm (clumsily) trying to make here?

Yes, and thank you for the helpful clarification.

Mathematically, the logistic model has the property of decreasing exponential growth, which is most obvious on a log graph as we near full adoption. It is only a falsifiable hypothesis that a logistic model can explain bitcoin prices. My reason for choosing this model was to fit the obvious constraint that exponential price growth must eventually end. Perhaps we are at that point now, but I believe not based upon the steady improvement in Bitcoin transactional infrastructure. http://www.bitcoinpulse.com/

There is at least one mathematical theory of price bubbles that could be used to elaborate this logistic model, but I hesitate to combine them for fear of unsound overfitting given the additional number of parameters whose values must be set. The bitcoin logistic model has only two parameters: the maximum price and the full adoption duration.

Alright, playing around with my idea some more...

Extrapolating from the interpretation of the graph I posted above, we get something like: the first factor 10 increase takes 12 months, the second 18, the third 24 months, etc.

In other words, to apply n times the factor g increase of the starting value, we require n-th triangle number time steps.

Which leads to the formula:

f(0.5*(t^2+t)) = s*g^t

or equivalently:

f(t)=s*g^(0.5*(sqrt(8t+1)-1))

where s is the starting value and g the growth factor.

Now, where that one^[1] falls in terms of functional growth, I'm not sure. Doesn't seem to fit the definition of exponential growth anymore, but doesn't just grow linearly either... At first I thought it would be another example of bounded growth (similar to your logistic function then), but plotting it, it very much looks like it is still exponentially growing (just as a slightly compressed looking curve, compared to "regular" exponential growth) ...

^[1] O(c^sqrt(n))

[Minor Miner]

Wouldn't the number of transactions increase with difficulty (and network hashrate) just because people have to mine at pools and the pools are paying thousands of small miners with every block instead of hundreds?

[SlipperySlope]

Wouldn't the number of transactions increase with difficulty (and network hashrate) just because people have to mine at pools and the pools are paying thousands of small miners with every block instead of hundreds?

I consider mining transactions to be economic, but of lesser importance than using bitcoin for purchases or earned income. I suppose that network difficulty is arguably unrelated to transaction volume, and that the correlation you observe is merely a coincidence. I could argue that vertically integrated industrial mining leads to fewer miners and thus fewer transactions required to pay them.

I suffered through a steep increase in mining difficulty the week in June-July 2010 when I first downloaded bitcoin and began CPU mining on my then-awesome quad core AMD server. Within a few hours I solved my first block, but the next one took a week and that was it for solo CPU mining. I learned of Bitcoin from the widely read Slashdot blog article, and that same article was also read by many system administrators who proceeded to install the software on the hundreds and thousands of computers that they managed. According to the Blockchain.info data series, the number of daily transactions back then was about 200-300 and did not match the sudden difficulty increase from 24 to 182 - a factor of 7.5x.

I will be speaking on a panel presentation on the subject of mining algorithms at the Hasher' United Conference in Las Vegas this month. I wonder what mining equipment vendors' answer will be to the question of the relative proportion of small miners vs large miners over time.

[Minor Miner]

Wouldn't the number of transactions increase with difficulty (and network hashrate) just because people have to mine at pools and the pools are paying thousands of small miners with every block instead of hundreds?

I consider mining transactions to be economic, but of lesser importance than using bitcoin for purchases or earned income. I suppose that network difficulty is arguably unrelated to transaction volume, and that the correlation you observe is merely a coincidence. I could argue that vertically integrated industrial mining leads to fewer miners and thus fewer transactions required to pay them.

I suffered through a steep increase in mining difficulty the week in June-July 2010 when I first downloaded bitcoin and began CPU mining on my quad core AMD server. Within a few hours I solved my first block, but the next one took a week and that was it for solo CPU mining. I learned of Bitcoin from the widely read Slashdot blog article, and that same article was also read by many system administrators who proceeded to install the software on the hundreds and thousands of computers that they managed. According to the Blockchain.info data series, the number of daily transactions back then was about 200-300 and did not match the sudden difficulty increase from 24 to 182 - a factor of 7.5x.

I am not suggesting it accounts for all transactions nor all of the transaction growth but If there are 100,000 miners (small miners), all mining to pools, that is a lot of transactions each day (just the pool sending the fractions to workers).  I would love to see someone be able to pull out all the sends that are just paying people their rewards and see what the amount of real transactions are.   Above someone was saying that the dice transactions were removed from their data, so it is likely not a herculean task to subtract out all the pool payouts too (or maybe the number is small and does not matter to the overall growth).   

[mmortal03]

Wouldn't the number of transactions increase with difficulty (and network hashrate) just because people have to mine at pools and the pools are paying thousands of small miners with every block instead of hundreds?

I consider mining transactions to be economic, but of lesser importance than using bitcoin for purchases or earned income. I suppose that network difficulty is arguably unrelated to transaction volume, and that the correlation you observe is merely a coincidence. I could argue that vertically integrated industrial mining leads to fewer miners and thus fewer transactions required to pay them.

I suffered through a steep increase in mining difficulty the week in June-July 2010 when I first downloaded bitcoin and began CPU mining on my quad core AMD server. Within a few hours I solved my first block, but the next one took a week and that was it for solo CPU mining. I learned of Bitcoin from the widely read Slashdot blog article, and that same article was also read by many system administrators who proceeded to install the software on the hundreds and thousands of computers that they managed. According to the Blockchain.info data series, the number of daily transactions back then was about 200-300 and did not match the sudden difficulty increase from 24 to 182 - a factor of 7.5x.

I am not suggesting it accounts for all transactions nor all of the transaction growth but If there are 100,000 miners (small miners), all mining to pools, that is a lot of transactions each day (just the pool sending the fractions to workers).  I would love to see someone be able to pull out all the sends that are just paying people their rewards and see what the amount of real transactions are.   Above someone was saying that the dice transactions were removed from their data, so it is likely not a herculean task to subtract out all the pool payouts too (or maybe the number is small and does not matter to the overall growth).   

It would also be interesting to see, given the theory that everything is consolidating into massive mining farms. Payouts from mining pools to different addresses may decline with the trend toward mining centralization.

[SlipperySlope]

Above someone was saying that the dice transactions were removed from their data, so it is likely not a herculean task to subtract out all the pool payouts too (or maybe the number is small and does not matter to the overall growth).  

When Satoshi Dice used dust transactions to indicate wager results, Blockchain.info developed the simple algorithm of discarding transactions that involved any of the 100 most popular addresses each day - Satoshi Dice of course being high on that list.

https://blockchain.info/popular-addresses

When I was mining for BTCGuild on my GPU rigs a couple of years ago, I suppose that the origin pool payer address was the same for each miner. It might be harder today if the pools are using unique payer addresses to enhance anonymity.  Looking over my daily payout last spring from LeaseRig.net, I do not see any address reuse.

Any miners on this thread know if their daily pool payouts originate from the same address from day to day?

[BombaUcigasa]

Extrapolating from the interpretation of the graph I posted above, we get something like: the first factor 10 increase takes 12 months, the second 18, the third 24 months, etc.

Why are coinbase transactions included? In the first year many of the coins have not moved but the transaction speed is around 100.

Further, you can exclude first time coinbase output transactions (pool payouts) as a part of the base system and not part of the peer transactions.

[Minor Miner]

Above someone was saying that the dice transactions were removed from their data, so it is likely not a herculean task to subtract out all the pool payouts too (or maybe the number is small and does not matter to the overall growth).  

When Satoshi Dice used dust transactions to indicate wager results, Blockchain.info developed the simple algorithm of discarding transactions that involved any of the 100 most popular addresses each day - Satoshi Dice of course being high on that list.

https://blockchain.info/popular-addresses

When I was mining for BTCGuild on my GPU rigs a couple of years ago, I suppose that the origin pool payer address was the same for each miner. It might be harder today if the pools are using unique payer addresses to enhance anonymity.  Looking over my daily payout last spring from LeaseRig.net, I do not see any address reuse.

Any miners on this thread know if their daily pool payouts originate from the same address from day to day?

it seems to be a different address each payment. 

[cuddaloreappu]

When I read into metcalfe law it states

"Metcalfe's law states that the value of a telecommunications network is proportional to the square of the number of connected users of the system"

 You were modelling with number of transaction previously , and have decided now to model with the market cap since you say
 "market cap takes into account the supply of bitcoin that meets the demand of the marginal new adopter".

Buy my basic question here is if every new user who is running a wallet represent the nodes in the network, then is not the number of users a better variable to run the model than no.of transactions or market cap? and this model fits with metcalfe law better than no.of transactions or market cap right!

It would be really difficult to accurately predict the number of users across globe using bitcoin but am I right in what I say?

So why not have a model like this?

[BombaUcigasa]

Buy my basic question here is if every new user who is running a wallet represent the nodes in the network, then is not the number of users a better variable to run the model than no.of transactions or market cap? and this model fits with metcalfe law better than no.of transactions or market cap right!

It would be really difficult to accurately predict the number of users across globe using bitcoin but am I right in what I say?

So why not have a model like this?

Because it's false. New users don't install the full wallet and don't keep relay nodes online. There are not 2 million blockchain wallets out there for nothing. New users use Coinbase, Circle, exchanges, cold storage, mobile wallets, etc. None of these are network nodes.

My question remains. Why are coinbase transactions included? Why are first-moved-coins pool-payouts transactions included? These are not actual usage, they are the results of coin issuing.