12.3 Miner hashrate distributions 14th May 2013

14th May 2013

Recommended reading: 
12.1 The pre-ASIC network hashrate distribution
12.2 Pool and network miner hashrate distributions

Changelog:

• Since Blogger has limits on reproducing large images, the Pool user account hashrate empirical cumulative distribution function (Figure 1) has been broken up into sections which, when clicked, will open a larger image than before.
• New section containing:
• a comparison of the proportion of user account hashrates that make up the combined pools, pre-ASIC and currently.
• an estimation of how much of the network hashrate is due to user accounts with various hashrates.
• a table of the plot data to allow independent investigation.

0. Introduction

Well, it doesn't look like I'll be able to post an update weekly as I'd hoped. However I am updating the data weekly (on Sundays) and so when I do post an update there will be no weekly data lost. In these update posts I won't be discussing any changes in detail. If you have questions about any of the results, please post a comment.


1. Pool user account hashrate empirical cumulative distribution function

This set of plots illustrates the changes in various pools' eCDFs over time. I collect data in January, and since then have begun to collect more data from the start of April onward.

The eCDF describes in order, the number of variates at a given value of variate. We assume this describes some sort of underlying probability distribution function.

2. The density of user accounts at various hashrates, and the density of user account hashrates, by pool.

The next set of charts describe:

1. User account density: the number of users accounts contributing a particular hashrate to a pool. Scale is proportional to the number of user accounts.
2. User hashrate density: the amount of hashrate contributed to the pool by a particular amount of hashrate. Scale is proportional to the total pool hashrate

In these charts the scale is not comparable by pool. So, for example, the user account density of the Bitclockers' violin should not be read to indicate that Bitclockers had the same number of users as BTCGuild on 2013-01-27, or for the user hashrate density plot that bitclockers had a greater hashrate than BTCGuild on the same date. However the difference between the scale of the pre-ASIC BTCGuild violin and the April violins does indicate a significant change in hashrate.

3. Combined user account hashrate empirical cumulative distribution function

These plots combine data from all pools except 50BTC.com and Bitclockers - these had such unusual hashrate distributions compared to other pools I had to classify them as outliers or recording errors. The interesting thing about these eCDFs is how uninteresting they are - although changes in the pool eCDFs are clear, changes to the combined eCDF (and by extension, the network) is less obvious. If I plotted the eCDFs over each other the differences would be more apparent, but even then they overlay each other fairly closely. The only clear difference is how far the upper tail extends, as ASICMiner increases, decreases and increases hashrate.

4. The density of user accounts at various hashrates, and the density of user account hashrates, all pools combined.

Note that the scale of the following plots is unrelated to hashrate of number of miners, so scale comparisons cannot be made. This is done on purpose as I hope to add more pools over time, and adding a pool would make the combined hashrate or combined number of users increase. Thus scale is not comparable across time, so I've removed it altogether - however the shape of the densities can be compared. 

5.  Changes in user account proportions of the network hashrate
I created this section after wondering how the proportions of the network attributable to various hashrates have changed over time.

Although much of the increase in the network hashrate is attributable to one actor, ASICMiner, it is less clear how much of the increase has been attributable to, for example, GPU miners at 1 Ghps or 10 Ghps. Have the numbers of the user accounts also increased significantly, and have they also increased the hashrate significantly?

This analysis can help answer some interesting questions:

• What is the estimated network contributors' average weekly capital expenditure?
• What is the total electricity usage of mining, and what is the average electricity use per network contributor?  

The following plots and table have a few limitations:

1. I have to extrapolate from the included pool user accounts to the network, so this estimate is likely to be a little different from the actual network hashrate totals.
2. The pools included are not always the same from week to week, a source of error when comparing from week to week.
3. Sources from pools not listed and from solo-mining are not included, so these data cannot be used to detect increases in the network hashrate due to (for example) renegade ASIC manufacturers testing their equipment on the mainnet.

Figure 6: shows a comparison of the proportion of user account hashrates that make up the combined pools, pre-ASIC and currently.
Figure 7: is an estimation of how much of the network hashrate is due to user accounts with various hashrates.
Table "User hashrates proportion of the network" consists of the data from figure 7, without summation.

Since these are new charts, I'll record a few observations:

• Figure 6: The pre-ASIC and current user hashrate totals are quite different. All of the binned user account hashrates have increased their totals significantly, indicating many new miners. The big spike just prior to 100Ghps is probably Avalon miners.
• Figure 7: It was interesting to note that even hashrates binned at 0.01 and 1 Ghps have increased along with the network, although not nearly as much as at higher hashrates.
• Table: Increases in total hashrates at various bins since January:
• 0.1 Ghps bin has increased by a total of 330 Ghps
• 1 Ghps bin has increased by a total of 3000 Ghps
• 10 Ghps bin has increased by a total of 2700 Ghps
• 100 Ghps bin has increased by a total of is 13000 Ghps
• 1000 Ghps bin has increased by a total of is 18800 Ghps
• 10000 Ghps bin has increased by a total of is 29000 Ghps  

6. To do

1. Add an automated fitting (and test of fit) of a truncated Pareto II distribution to the combined user hashrate at each date.
2. Add table of data - total, median and mean hashrates per pool and combined, users accounts per pool, and estimated number of user accounts across the network.
3. If you can think of anything else interesting to include, please post in the comments and I'll do my best to add your suggestion.

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