Predicting mining productivity (BOUNTY)

[woodrake]

Apologies in advance for what is probably a very n00bish question, but I am trying to calculate the likely range of future productivity of my mining rigs. I am also attempting to quantitatively assess the impact of the coming tens of thousands (or hundreds of thousands) of ASICs that are likely to be deployed in coming months.

There is good historical data on both total BTC network hashrate and difficulty here, but my question is how do those two variables contribute to the productivity of a rig (ie. hashes/BTC)?

Total network computation appears to have been rising by about 0.5% - 1.0% per day for some time, but from what I can see mining productivity has not be falling that fast.

Difficulty in the last two months has gone from ~6,000,000 to ~12,000,000 in the last two months, which is a little more than 1%/day ( (6,000,000 * (1.01^61))) = 11,000,000). It is very close though, suggesting that the two are directly linked.

So, the questions:

1) Is mining productivity (hashes/BTC) directly proportional to difficulty, and if not how can you calculate hashes/BTC from difficulty?

2) Is difficulty directly proportional to total network hashrate, and if not would is an increase of x% in total network hashrate affect difficulty?

Thanks in advance for any pointers!

Kate.

Bounty: To the first person who gives me a full and complete answer including explanations where appropriate I will give a 0.1BTC bounty.

[crazyates]

1) Is mining productivity (hashes/BTC) directly proportional to difficulty, and if not how can you calculate hashes/BTC from difficulty?

2) Is difficulty directly proportional to total network hashrate, and if not would is an increase of x% in total network hashrate affect difficulty?

1) Yes. It's all basically luck based, but it does average out to some pretty predictable numbers. IIRC, it works out that about 71MH/s will earn you 1 share per minute (U:1.0/m). 710MH/s will earn you 10x shares per minute (U:10.0/m. Remember that these are diff=1 shares that are submitted to a pool, and not block solvers. A block solver is any share who's difficulty is over the current network difficulty, which currently is ~12.2million. Thus, it would take you an average of 12.2million shares to get a block solver. If the network difficulty was 100million, it would take you about 100million shares to eventually get one that was high enough. Now statistics says that each share has the same chance of being a block solver (1 in 12.2million), but we're talking averages here, so we can predict them a lil better.

2) Also yes. The difficulty is recalculated every 2016 blocks, so that the next 2016 blocks will take exactly 14 days (assuming no network growth or shrinkage). If we find all 2016 blocks in 13 days, the difficulty will go up by ~7%. If we find them in 7 days, the difficulty will go up 100%. This can be affected by strings of luck (both up or down), but obviously the Network Hashrate will be the most important factor.

Those answer you questions?

[kevindeangelis]

Hi, I just created a site last week that might be able to help you out a little - www.WhereToMine.com
Basically, you select your currency, enter your sha and/or scrypt hash rates, and it will show estimated earnings for various coins.
Is that what you were looking for?

[woodrake]

1) Yes. It's all basically luck based, but it does average out to some pretty predictable numbers. IIRC, it works out that about 71MH/s will earn you 1 share per minute (U:1.0/m). 710MH/s will earn you 10x shares per minute (U:10.0/m. Remember that these are diff=1 shares that are submitted to a pool, and not block solvers. A block solver is any share who's difficulty is over the current network difficulty, which currently is ~12.2million. Thus, it would take you an average of 12.2million shares to get a block solver. If the network difficulty was 100million, it would take you about 100million shares to eventually get one that was high enough. Now statistics says that each share has the same chance of being a block solver (1 in 12.2million), but we're talking averages here, so we can predict them a lil better.

2) Also yes. The difficulty is recalculated every 2016 blocks, so that the next 2016 blocks will take exactly 14 days (assuming no network growth or shrinkage). If we find all 2016 blocks in 13 days, the difficulty will go up by ~7%. If we find them in 7 days, the difficulty will go up 100%. This can be affected by strings of luck (both up or down), but obviously the Network Hashrate will be the most important factor.

Those answer you questions?

Pretty much I think.

To be sure I have understood: does this mean that if total network hashrate is increasing at 1% per day then the mining productivity for a particular rig (or per hash) is also falling by roughly 1%/day?

Or, to put it another way, if a 10 GH/sec ASIC rig is producing 0.40 BTC/day today then in 30 days (assuming 1%/day increase in total network hashrate) it will be producing 0.297 BTC/day ( 0.4 / ( 1.01^30 ) ) and in a year it will be just 0.011 BTC/day ( 0.4 / ( 1.01^365) )?

That would of course assume that the recent acceleration in hashrate growth is exponential rather than linear, which one could argue remains to be seen. If it is linear then the year-on numbers are 10x better.

Kate.

[crazyates]

1) Yes. It's all basically luck based, but it does average out to some pretty predictable numbers. IIRC, it works out that about 71MH/s will earn you 1 share per minute (U:1.0/m). 710MH/s will earn you 10x shares per minute (U:10.0/m. Remember that these are diff=1 shares that are submitted to a pool, and not block solvers. A block solver is any share who's difficulty is over the current network difficulty, which currently is ~12.2million. Thus, it would take you an average of 12.2million shares to get a block solver. If the network difficulty was 100million, it would take you about 100million shares to eventually get one that was high enough. Now statistics says that each share has the same chance of being a block solver (1 in 12.2million), but we're talking averages here, so we can predict them a lil better.

2) Also yes. The difficulty is recalculated every 2016 blocks, so that the next 2016 blocks will take exactly 14 days (assuming no network growth or shrinkage). If we find all 2016 blocks in 13 days, the difficulty will go up by ~7%. If we find them in 7 days, the difficulty will go up 100%. This can be affected by strings of luck (both up or down), but obviously the Network Hashrate will be the most important factor.

Those answer you questions?

Pretty much I think.

To be sure I have understood: does this mean that if total network hashrate is increasing at 1% per day then the mining productivity for a particular rig (or per hash) is also falling by roughly 1%/day?

Or, to put it another way, if a 10 GH/sec ASIC rig is producing 0.40 BTC/day today then in 30 days (assuming 1%/day increase in total network hashrate) it will be producing 0.297 BTC/day ( 0.4 / ( 1.01^30 ) ) and in a year it will be just 0.011 BTC/day ( 0.4 / ( 1.01^365) )?

Kate.

Pretty much. It will earn the same 0.4BTC/day for the first 10-12 days, and then drop to say 0.35 / day for the next 10-12 days.

What you're looking for used to be a lot easier when pools used PPS (Pay-Per-Share) a lot. For example, recently the OzCoin PPS rate was 0.00000217 BTC/share submitted. After the difficulty recalculate, it went down to 0.00000200 BTC/share. This new rate will last until the next difficulty recalculation, and then it will (most likely) go down even more. I don't use PPS, as I use DGM, but it illustrates the point.

Remember that a lot of the stuff you might be looking for has already been done. http://bitcoin.sipa.be/ has some good charts, where they estimate the network hashrate based off the rate of solved blocks at any given difficulty. They also do a good job at helping you discern between true growth and just a string of good luck. And finally, the bottom two charts show the daily growth per day. I would say 1% is a good estimate.

[crazyates]

woodrake,

The bottom line is that the earnings cannot be predicted reliably because the rate at which difficulty changes cannot be predicted.
Most calculators assume constant rate of increase or no increase at all.  But difficulty increase function is undefined.  Linear? No.  Parabolic? Maybe. Exponential? Possibly.  It is probably somewhere in between.

That's only partially true, and it depends on how far into the future you're trying to look. I can give you a pretty good estimate of what my earnings for tomorrow are going to be. The same for the next week. I can take a prediction of the diff recalculate, and predict what I'll be making for the next 2 weeks after that. One month prolly isn't too far to predict about what you'll be making. 6 months? Now that's a lot harder to tell, as there are way more variables than just "assume 1% growth per day" or "extrapolate the next diff recalc".

[woodrake]

Pretty much. It will earn the same 0.4BTC/day for the first 10-12 days, and then drop to say 0.35 / day for the next 10-12 days.

What you're looking for used to be a lot easier when pools used PPS (Pay-Per-Share) a lot. For example, recently the OzCoin PPS rate was 0.00000217 BTC/share submitted. After the difficulty recalculate, it went down to 0.00000200 BTC/share. This new rate will last until the next difficulty recalculation, and then it will (most likely) go down even more. I don't use PPS, as I use DGM, but it illustrates the point.

Remember that a lot of the stuff you might be looking for has already been done. http://bitcoin.sipa.be/ has some good charts, where they estimate the network hashrate based off the rate of solved blocks at any given difficulty. They also do a good job at helping you discern between true growth and just a string of good luck. And finally, the bottom two charts show the daily growth per day. I would say 1% is a good estimate.

Thanks for your explanation, I've a much better understanding now. It does not seem realistic to me that the growth will continue to be exponential since there are human factors (eg. how quickly ASIC rigs can be deployed) so I will use a combined approach, attributing some of the current growth rate to a compound element and some to a fixed element.

Anyway, you've certainly earned the bounty. I have sent you 0.1 BTC to the address on your footers (TID e7cc6796b639ead412827238da9512836eed55f4327d1478f890b71224b9c3e6). I would be grateful if you would give me a trust point in exchange, but of course do not feel obliged.

Kate.