Have you ever caught a Pokemon with pure "Dumb Luck?" By this, I mean catching a normally hard-to-catch Pokemon rather easily. Examples would be catching a legendary with a Poke Ball at full health, finding a shiny legendary in a small number of tries, or quickly finding a Pokemon in an area where it has only a 1% encounter ratio. One dumb luck catch I had was in Crystal, when I was actually attempting to encounter Raikou for the first time (he was not in my Pokedex as seen yet), I found him on the first encounter of the first patch of grass I tried. And what more? I caught him in a regular Poke Ball on that encounter without doing anything to him. The odds of that catch being successful are 0.4%, so I'd call that dumb luck.