Statistical Confidence in Mining Power Estimates for PoW Blockchains

Abstract

The security of blockchain systems depends on the distribution of mining power across participants. If sufficient mining power is controlled by one entity, they can force their own version of events. This may allow them to double spend coins, for example. For Proof of Work (PoW) blockchains, however, the distribution of mining power cannot be read directly from the blockchain and must instead be inferred from the number of blocks mined in a specific sample window. We introduce a framework to quantify this statistical uncertainty for the Nakamoto coefficient, which is a commonly-used measure of blockchain decentralization. We show that aggregating blocks over a day can lead to considerable uncertainty, with Bitcoin failing more than half the hypothesis tests (α = 0.05) when using a daily granularity. For these reasons, we recommend that blocks are aggregated over a sample window of at least 7 days. Instead of reporting a single value, our approach produces a range of possible Nakamoto coefficient values that have statistical support at a particular significance level α.