What is the formula for inferring hash rate from difficulty and block frequency?
Better Late than Never. I was asking myself the same question...I thought the hash rate of the network came from Full Nodes observation on Miners...I was wrong.
I was looking for this answer on Bitcoin.org, but it's on Blockchain website: https://www.blockchain.com/charts/hash-rate. Look at the methodology at the bottom of the page.
Formula is Hash rate = (Difficulty*2^32)/(intervals in seconds between 2 blocks.
Theoretically you know this to be 600 seconds. So the tell it as H = 2exp32 D/T..
For the second part of your answer, this is from my own inference, but within a day, we can expect a persistent shorter time of resolution per blocks, as hash speed in the long run accelerates at about 400% per year (from technological efficiencies and Mining Nodes being added), meaning about 0,45% per day. Look at Network Difficulty over time, and you see that it continuously increases Difficulty, neutralizing efficiencies, to maintain block resolution time around 10 minutes. If it did not do so, reversibility would increase making reliability of security vulnerable, weakening users confidence, whom would either seek trust signals or defect . On this you can read Nakamoto's introduction of his white paper.
Many factors may affect the slowing of the Networks Hash rate. The most important is not from technology when Hash slips, but from defections (permanent or temporary) of miners associated with Price of the Bitcoin usually.
With blockchain.com latest charts (data from March 18 2021)I can infer the average time of block resolution from the same formula. By doing T = (Difficulty*(2^32)/Network Hash Rate. (21.6TH*4,294967296)/157.6EH = 588.65 seconds or 9'48&quot;.
I am new to this, a week or so, and am not and won't be either an investor, nor miner...but I am always very curious, like estimating the number of Miner Nodes, a statistics I cannot find anywhere.
They are about 70 Million lightweight Nodes (mostly wallets), Between 8,000 to 12,000 Full Nodes...but how many Mining Nodes? At Least 1,1 Million to up to 6 Million depending of the formula you create (or I create). If someone has the answer to this, please go ahead.