It's hard for many to set aside envy. You know the type. .. the person who bitches every time someone gets a ring.. or gets a hit from Explosives or hits a big one in mining... and then bitches because when you do said things to chase a HOF (shouldn't ever).. their ped cards are depleted... not realize the fell into the gamblers' trap.
No one's claim that there are lucky avatars is founded by math. It is proclaimed by feelings, envy, and jealousy. All which are not scientific methods for which to make hypotheses. It is methods of undisciplined people with perception bias
I'm afraid your claims aren't any more founded by math & scientific methods than anyone else's. Everyone's perception is biased, yours included. Not all "unlucky avatars" are undisciplined or envious/jealous. As some have stated here, the longer you play, the more things (supposedly) balance themselves out. This is NOT always the case, though.
There are players who complain (perhaps erringly, during a bad spell for example) that they are "unlucky". Then suddenly loot improves, for a spell. Good for them. However, there are a distinct minority of avatars here, who have played a LONG time, but never had an uber, a loot over 1K TT value, for example. I challenge you to find another avatar that has in the neighborhood of 100K skills or level 50 in their main profession who has NEVER had an uber--in ANY profession. Yes, there are certainly players who've reached those levels
in a faster period of time, but 100K skills is 100K skills, REGARDLESS of how long it took...
I remember years ago someone put up a poll of who else reached level 50 or something in that neighborhood who never had an uber, and there was only 1 other person besides me who met that infinitesimally-possible level of "bad luck". I've made bets with disciples that they'd uber before I did, even though I'd played 6 years and they were bald-faced n00bs. I have yet to lose one of those bets (cuz I've never ubered).
I also "grew up" playing this game with similarly-skilled and similarly-progressing hunters and we compared the frequency and speed at which each of us hit our first globals, or first uber, relative to our primary hunting skills, and the results THROUGHOUT our development were very different. Yes, there was some math involved, not mere perception. Some of you say "then HUNT more"; well to that I reply, "So how many ubers did YOU have by the time you reached 100K skills/level 50?"
For example, my in-game friends at the time both had their first global (or more than one) by the time they reached 400 in laser sniper. I didn't get one until I'd hit 800, which as you know, takes more than twice as long to reach than 400. Maybe 3 times as long. By the time I'd had my first global, they'd each had 5 or 6. We hunted the same amount, mostly the same mobs, and were playing more or less the same amount of time. One of those friends looted an Imp MK2 from a Longu. Over a decade later and I still haven't had a loot over 1K TT value, in hunting, mining or crafting.
I have several blog entries that reveal some very interesting observations of my hunts over the years; feel free to read through them. There's a lot more going on than "perception bias".
The bottom line is, until you have played the game as long as the most-unfortunate-few among us have, and experienced what WE have, you can't pretend to know what you're talking about or have the answers or revelations that we've had.