I stopped tracking it some time after I got to over 30 different dig site ratios (and still counting).
Okay, wasn't expecting to be that far off. Tbh, I'm still in the situation that I dig each and every site because there are still artifacts that I would like to have but haven't found yet. Hence, I don't really care about the percentages of a specific digging site, I just take what I got.
Run my equation on the 8 hour 100% Common site to see why I picked 1000 hours.
Ah, I see. You wanted a specific baseline. At the same time I appreciate the formula more now and I still doubt that this exact formula would appeal to other players. It's still (pretty) arbitrary.
A lot of stuff in Idle is rounded for display. It could be a 1.4% chance at an Epic behind the scenes, or exactly 1% (as displayed). That makes a big difference in the value of that dig site.
After I missed to divide one number by 100 and was about to say, that the difference is neglectable, in the right circumstances such a .4% change can more than double the site's value given your formula. But in this edge case the base value is only about 10% of the 100% Common variant, so a .4% higher chance ups the value to about 25% of the Common digging site. So, either a .4% higher chance doesn't change the value much and the site already was more valuable than your baseline or .4% make a difference but the base value was far worse to begin with and you are far better off selecting the 100% Common site than the one where you can't be sure about the exact numbers.
AND: This heuristic would be rounded, too. So, no guaranty that you would actually be able to spot the difference in the rounded value.
I admit that I was wrong with assuming that there can't be so many different ratios. But it's still a very niche statistic that wouldn't necessarily give you more information than you currently have by just looking at the ratios. And a digging site with a value five times of the 100% Common baseline can still "reward" you with a poor artifact and therefore actually being worth five times less. Your formula would work for hundreds or even thousands of digging sites. But that would take you several years. And you could still have bad luck. Have you actually ever FOUND an epic artifact in the wild where you weren't guaranteed to find one (so, no buying for coins or upgrading)? I have yet to encounter one.