I have been saying that a 10% increase in Difficulty results in a 10% reduction in productivity of a miner. I think it is a good approximation. But not accurate when dealing with larger increases.
If Difficulty went up 100%, the productivity of a miner would not go down by 100%, since that would result in zero productivity. It goes down by 50%.
So what is the correct way to explain the percent drop in productivity when a Difficulty goes up by X%
I know, I'm clearly not a math major, but I can understand a formula when it is presented to me