Playing through Ultra Moon, ran into a wild Level 18 Magby at Wela Volcano Park. What I hadn't realized until partway through this battle was that Magby has a catch rate of only 45, which is on par with the box legendaries for the past three generations. Anyways, I get it down to red health (about 15-18% I think) and paralyzed with my Pikachu. I throw a Poke Ball. It breaks out. No big deal, I'll just switch to chucking a Great Ball at it. It broke out of that one too. In total, I used one Poke Ball, my only Ultra Ball, and eight Great Balls on a red-health, paralyzed Magby before I caught it on the eighth one. I used the Dragonfly Cave calculator afterwards to figure out my approximate odds of this happening, and here's what I found:
- One Poke Ball had about a 33.5% chance of catching, so a 66.5% chance of it failing. No biggie.
- One Great Ball had about a 45.5% chance of catching, so a 54.5% chance of failing.
- The Ultra Ball had a 56.4% chance of catching, so 43.6% chance of failing.
Multiplying the odds of one Poke Ball miss, one Ultra Ball miss, seven Great Ball misses and one Great Ball successful catch together, the odds of this exact sequence happening were about 0.19%. Honestly, considering its box-legendary catch rate, I'm not too mad about this one, considering the circumstances.
Later on in this run, my Torracat was switched into a trainer's Cleffa in Malie Garden. During this run, Sweet Kiss from the Cleffa hit twice (75% for each hit), Torracat hit itself both times in confusion (33% per turn), Sing hit on the first try (55%), and Fire Fang missed on the first try (5%) for about a 0.17% chance of that sequence happening.