Unveiling Uncle Statistics in Ethereum | Ethereum Foundation Blog


The Initial 280,000 block phase of the project has yielded some interesting results from the Ethereum blockchain. By compiling a list of block and uncle coinbase addresses; raw data is available Here for blocks and Here for uncles, giving us access to various useful information such as outdated rates and the connectivity between different mines or pools.

First, here is the scatterplot:

We can clearly see the major trends. With 20,750 uncles in 280,000 blocks, we get a total uncle ratio of 7.41%. If we factor in all blocks, we get a rate of 6.89%. This is similar to the numbers of Bitcoin in 2011, when its mining ecosystem was comparable to Ethereum’s. Still powered by GPU and CPU, with low transaction volumes.

Note however, that this doesn’t mean miners won’t make 93.11% less revenue if they have infinitely many connections to everyone else. Ethereum’s Mechanical uncle is the best way to determine the average loss. Poor connectivity affects only 0.9% of the population. These two factors will cause losses to increase: first, the mechanical uncle doesn’t take into account transaction fees, only base block rewards; second, larger blocks will result in longer propagation times.

Secondly, we see that larger miners tend to have lower uncle prices. This is something we’d expect, but it’s important to understand both how it happens and if it is a real effect or just a statistical artifact. Small samples can produce more extreme results.

Number Mined Blocks Uncle Average Rate
<= 10 0.127
10-100 0.097
100-1000 0.087
1000-10000 0.089*
>= 10000 0.055

* Arguably due to one outlier, the result is highly distorted. The point at 4005 blocks is probably a broken miner with 0.378 unclerate. Without this miner, the overall uncle rate is of 0.071, which is more in line with the general trend.

There are four main hypotheses that can explain these results.

  • Inequality in Professionalism– Bigger miners can invest more in their network connectivity to increase their efficiency, while smaller miners may not have the best internet connections.
  • Last Block Effect: The miner who mined the last block can find the next one quicker than waiting for it through the network.
  • Pool Efficiency: Mining workers are more productive when they are together in a pool than when working individually.
  • Time Period Differences: Very large miners weren’t present during the first two days, when block times were extremely quick and uncle rates were very high.

Evidently, the final block effect doesn’t tell the whole story. If the cause was 100%, we would see a decrease in efficiency. Miners mining 28,000 blocks (10% of all blocks) would receive a 7.2% uncle rate and those mining 56,000 blocks would see a 6.4% uncle rate. Because miners who mined more than 20% of the blocks would have accounted for 20% of all blocks, they would be eligible to receive a 20% decrease in the uncle rates from 8% down to 6.4%. It would not make any difference whether miners mined one block or 100 blocks. However, in reality, the decreases in stale rates as a result of increasing sizes appear almost perfectly logarithmic. The disparity hypothesis for professionalism is more consistent with this curve. The time period difference theory can also be supported by the curve. However, it is important to note that there were only 1,600 uncles, and 8% of all uncles were involved in the chaos of high uncle rates’ first two days. That means that the first two days alone account for almost half of the entire uncle rate.

An investigation of the uncle rate statistics has revealed some interesting results. The positive sign is that miners at small and mid-sized scales are more professional than larger-scale miners. This is due to the fact that they receive financial rewards for their hardware.

The jump from 7.1% to 5.5% for all miners over 1000-10000 blocks is also noteworthy. The effect of the final block may be as high as 40%, although this should be taken with caution due to the small sample size. The most efficient mining pool is not the largest (nanopool) but suprnova.

When it comes to inefficiencies, the deciles of miners who produce more than 100 blocks can be calculated. The lowest number is 0.01125703564727955 and the highest is 0.3787765293383271. This shows that there is a degree of inequality in how well-connected miners are.

The key to achieving efficiency and inefficiencies is to look for more decentralized alternatives to mining pools. Multiple PPS may be a temporary solution to this problem. Ultimately, electricity costs have a smaller impact on decentralization than mining pools.

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