# Which is the better estimator for future mining intervals, the 10 minute protocol target or the observed, historical average?

The Bitcoin protocol is designed so that the network difficulty is periodically adjusted so that new blocks are mined on average every 10th minute. However, looking back the last 10 years, it appears the observed, average mining interval is 567.35 seconds. I calculated this by subtracting the timestamp of block nr. 573,795 with the timestamp of block nr. 0 and dividing by 573,794. I know block timestamps aren't that accurate, but this error should be negligible.

Bitcoin mining can be modeled as a Poisson process with certain simplifying assumptions. If I've done the math right, the 95 % confidence interval of a Poisson process with λ = 1.0575 (historical average nr. blocks mined every 600 seconds) and n = 573794 (current nr. of historical block intervals) allows for an actual mining interval no higher than 568.1 seconds, an error bound which is a long way from the 600 second block interval predicted by network difficulty.

I'm aware of at least one reason why there's a discrepancy, and that's the 2016 block difficulty adjustment interval. This was discussed and answered in a relation question here. But is this the only reason why historical block intervals are shorter than the mathematically predicted block intervals? If we experienced a long period of consistent decline in network hash rate, would we see a similar, opposite effect, where the observed block intervals consistently exceed 600 seconds?

Bottom line question is... for block intervals in the future, is it best to assume the target block interval of 600 seconds, or an interval that is slightly lower or higher than this? If so, how much? This has implications, e.g., for designing predictive time series models in finance.

• Just one comment. Although it doesn't make a difference of more than a second, it is prudent to start from block 1. This is because the first block was mined on Jan 9, almost six days after the genesis block. – Ugam Kamat Apr 30 '19 at 16:22
• For the first year of its existence the difficulty went below the minimum value effectively. – Anonymous Apr 30 '19 at 16:33 