The poor job education institutions do (in my relatively limited but not so completely limited experience) worldwide with not properly explaining the role and execution to statistics to non-math majors irks me consistently. A fair few non-math-inclined people do get the basic functions, but a large enough group don't to allow, in the US at least, marketing to specifically target people's ignorance of odds to sell various gambles.
*Note* I'm simplifying this to a point which will probably annoy the numbers people. You can comment on that, or not, as you choose, but I'm noting here and defending it with: I think the simplification is worth the easing of situation explanation.
If the odds of finding a SoJ from NM Andy comes out to 1 out of 31 unique rings, then that means the ratio would be preserved if someone does not find one until their 248th ring, as long as someone else finds 8 within 31. (248+31)/9 = 31; 9/9 = 1.
Of course one person doesn't have to be alone in performing these numbers; several people finding fewer SoJs from more unique rings from NM Andy and several people finding more SoJs from fewer unique rings from NM Andy add together to form the ratio. In brash but fairly true terms, at least here, individual results do not alter or rely on the ratios. Pick a target and do a run (or pick a unique item type with multiple outcomes and start finding them) and all statistics can do is add a number to an instances column and tick yes or no whether the desired outcome occurred. That's the ugly part of statistics: it can make absolutely zero assurances of when a thing will happen. However, it's also the glory of statistics because it gives rise to what statistics can do: tell you how likely your performance was, or how likely your desired outcome is, from a supposed mean.
As such, statistics's usefulness really comes down only to large numbers. 31 NM Andy rings mean nothing in terms of finding an SoJ, statistically speaking; your findings mark only an imperceptible and momentary flux as they pile in among all the other numbers from all the other runners everywhere. Before you'd be able to call anything about good or bad luck and have it mean anything, you'd have to have a reasonable sample size, which in this case would be several hundred unique rings from NM Andy, and even then all you can determine from looking at the ratio likelihood is what your variance from that is, and then assign a personal subjective decision upon it.
Of course variance is expected, even when dealing with huge numbers. That is to say if you had 31,000 unique rings from NM Andy the expected value of the SoJs would be 1,000, but if you had 930 or 1,070 instead it would not represent any sort of cataclysm or anything, just a shift that happens because, again, statistics only determines likelihood across large numbers of instances and any single instance can vary fairly drastically with no harm done to the numbers, unless that shift becomes a trend.
In other words, if you haven't found an SoJ in 31 unique NM Andy rings, it's no worries. And if you haven't found one in 100 rings, then it's no worries, as far as looking at the statistics goes. Which means, quite frankly, unless someone feels willing to put a ton of time and effort into whatever the endeavor (like buying a lot of lottery tickets or playing a lot of hands of poker or farming a lot of unique rings from NM Andy) then looking at the statistics means essentially nothing for them, unless they know enough about statistics to take comfort from any "bad luck" they might perceive.
Guess I could actually play through the game solo though. Has been a while.
It was just the math possibility due to drop percentage.
