Variance is the varying frequency of achieving a reward. Variance is inherent to the probabilistic nature of mining and cannot be eliminated.

As a matter of consensus, different hash power among miners implies rewards will be earned by some more frequently than others. With 10% hash rate one might expect to be rewarded 10 times more frequently than with 1%. Actual results are unpredictable and can vary significantly. But it is sufficient here in both cases to assume proportionality. In this example one miner receives a reward every 100 minutes and the other every 1000 minutes. Assuming identical rewards per block, the magnitude of the reward is also proportional to hash power.

Consider then that a tiny miner might have to wait years before any reward. There is also the possibility that a mine is misconfigured and can never succeed. Despite being rewarded proportionally, a smaller miner is faced with a deficiency in relation to the larger miner. It must improve cash flow to receive a fraction of the reward more frequently. For these reasons miners discount returns for variance. Smaller miners will convert their mines to grinds and pay an aggregating miner for reduced variance. Avoiding this aggregation is the rationale behind P2Pool, but because distributed variance reduction is less efficient, pooling dominates.

This variance-based pooling pressure is a consequence of singular difficulty as required by consensus rules. Small miners must compete at high difficulty despite low hash power, which magnifies inherent variance. The proximity premium is another pooling pressure caused by consensus.

The defense that Bitcoin intends to raise is market defense against anti-market (state) forces. To do this hash power must be distributed broadly among people so that it becomes difficult to co-opt. However pooling pressures inherent in the consensus work against this objective. As such the characteristic is termed a flaw, though no way to eliminate the flaw has been discovered.