This info is for a legendary, but you can adjust it for regular Pokemon by just... doing it less, I guess.
Gen 1-3:
If you’re playing anything before the DS , the RNG basically stays the same every time you soft reset.
So if you reset and do the exact same thing, in the same timing, same menu presses, same animations, same everything else, you WILL keep getting the same outcome.
That means if your ball fails once, it’s always going to fail unless you do something to mess with the RNG, like waiting a second or moving differently before throwing, like having two Pokemon and using a different lead.
Gen 4–7
Once you hit the DS era, the game starts using the system clock to seed RNG when you start it up.
That means every time you boot the game (not just soft reset, but actually close and reopen), you get a different random seed depending on the time down to the second.
but it’s way less likely to be perfectly identical. And also, it just takes a lot longer than other games.
Gen 8–9
Now, for anything on the Switch, Sword/Shield, Brilliant Diamond/Shining Pearl, Legends Arceus, or Scarlet/Violet,
RNG is tied to the console’s internal clock and constantly ticking in the background, no matter what.
Even the smallest delay can and most likely will, shift the RNG.
So you CAN get a new outcome just by waiting a moment before throwing your ball or doing something slightly different before you do.
Z-A Specifically
Because Z-A uses a more modern RNG system, so each time you reset, you can be getting a new random number check. Also, the game saves shiny Pokemon, even if you load another area or even if you close the software (don't do that though, could maybe go wrong) so use that as you will.
So, TL;DR, your ball can theoretically succeed, given your catch rate, even if you’ve failed hundreds of times.
Even though you’re getting new RNG rolls, the odds remain the same each attempt. You mentioned your calculated chance was about 10%. So multiple failures aren’t outside normal. In fact, it's almost always gonna happen once or twice.
Sorry for sounding like an AI, I'm always either really technical or really casual. There is no in-between for me.
But I hope this helps you, even if it took me around a day, sorry again.
(Wow, really living up to the Canadian stereotype by saying sorry this much. Now I just need to start saying "Eh" and add poutine to my diet and I will be fully Canadian XD)
