More uncle statistics
The Complexities of Ethereum Mining: Uncovering the Truth Behind Uncle Statistics
As the Ethereum blockchain continues to grow and evolve, the dynamics of mining have become increasingly complex. One of the most fascinating aspects of this complexity is the phenomenon of "uncles," or orphaned blocks that fail to be added to the main chain. In this article, we'll delve into the world of uncle statistics, exploring the trends, patterns, and implications that emerge from a comprehensive analysis of the first 280,000 blocks of the Ethereum blockchain.
The Scatter Plot: A Visual Representation of Uncle Rates
The scatter plot below reveals a few primary trends that are worth noting. Firstly, uncle rates are remarkably low compared to other blockchains, with an overall uncle rate of 7.41% (or 6.89% if inclusive). This is not significantly higher than the uncle rates observed in Bitcoin during its early days, when CPU and GPU mining dominated the landscape and transaction volumes were low.
**Uncle Rate by Block Number**
| Block Number | Uncle Rate |
| --- | --- |
| < 100 | 10.71% |
| 100-1000 | 9.71% |
| 1000-10000 | 8.71% |
| 10000-100000 | 8.89% |
| >= 100000 | 5.55% |
The Relationship Between Miner Size and Uncle Rate
When we segregate the statistics by miner size, we observe a clear trend: larger miners tend to have lower uncle rates. This is not entirely unexpected, as larger miners are more likely to have invested in improving their connectivity to the network. However, it's essential to dissect why this happens and to what extent it's a real effect rather than a statistical artifact.
Hypotheses Explaining the Relationship Between Miner Size and Uncle Rate
There are four primary hypotheses that can explain the observed relationship:
- Professionalism Disparity: Larger miners are professional operations with more resources to invest in improving their connectivity to the network. In contrast, smaller miners are often hobbyists on their laptops, which may not be well-connected to the internet.
- Last-Block Effect: The miner that produced the last block "finds out" about the block immediately, gaining an advantage in finding the next block.
- Pool Efficiency: Very large miners are pools, which are likely more efficient than solo miners due to their ability to spread blocks and benefit from a weaker version of the last-block effect.
- Time Period Differences: Pools and other very large miners were not active on the first day of the blockchain, when block times were fast and uncle rates were high.
The Last-Block Effect: A Partial Explanation
The last-block effect can account for about 40% of the decrease in uncle rates from 7.1% to 5.5% for miners above 10000 blocks. However, it's essential to note that this effect is not the sole cause, and other factors are at play.
Pool Efficiency: A Slightly More Efficient Mining Pool
Interestingly, the two non-pools have uncle rates of 8.1% and 3.5%, respectively, which is not much different from the 5.4% weighted average stale rate of the three pools. This suggests that pools are slightly more efficient than solo miners, but the finding should not be taken as statistically significant.
The Efficiency and Inefficiency of Pooled Mining
Pools are likely well-connected to the network and do a good job of spreading their own blocks. However, the delay in getting work from a pool after creating a block should slightly increase one's stale rate. It's likely that these forces roughly cancel out.
Measuring the Genuine Inequality in Connectivity
To check how much of the disparities seen is due to genuine inequality in connectivity and how much is random chance, we can perform a simple statistical test. The deciles of the uncle rates of all miners that produced more than 100 blocks are:
[0.01125703564727955, 0.03481012658227848, 0.04812518452908179, 0.0582010582010582, 0.06701030927835051, 0.07642487046632124, 0.0847457627118644, 0.09588299024918744, 0.11538461538461539, 0.14803625377643503, 0.3787765293383271]
A Random Model: Half of the Effect
The deciles generated by a random model where every miner has a 7.41% "natural" stale rate and all disparities are due to luck or misfortune are:
[0.03, 0.052980132450331126, 0.06140350877192982, 0.06594885598923284, 0.06948640483383686, 0.07207207207207207, 0.07488986784140969, 0.078125, 0.08302752293577982, 0.09230769230769231, 0.12857142857142856]
A Normal Distribution Model: Close but Not Perfect
A simple model where "natural" stale rates are random variables with a normal distribution around a mean of 0.09, standard deviation 0.06, and hard minimum 0 yields:
[0, 0.025374105400130124, 0.05084745762711865, 0.06557377049180328, 0.07669616519174041, 0.09032875837855091, 0.10062893081761007, 0.11311861743912019, 0.13307984790874525, 0.16252390057361377, 0.21085858585858586]
Conclusion
The effects of genuine inequality in connectivity are not very large, especially when divided by 8 after the uncle mechanism is taken into account. The disparities are much smaller than the disparities in electricity costs. The best approaches to improving decentralization moving forward are arguably highly concentrated in coming up with more decentralized alternatives to mining pools. Perhaps mining pools implementing something like Meni Rosenfeld's Multi-PPS may be a medium-term solution.
Forward-Looking Thoughts
As the Ethereum blockchain continues to evolve, it's essential to address the complexities of mining and the disparities that arise from it. By understanding the underlying dynamics and developing more decentralized alternatives to mining pools, we can create a more equitable and sustainable blockchain ecosystem.
Source: https://blog.ethereum.org/en/2015/09/25/more-uncle-statistics
