How high is the odds of seeing a 100% Raid boss?
I've personally only saw it once and it's a mawile. Yet i heard endless stories about the 100% legendary catch on twitter. What is the exact odds of getting one and are they as common as they say?
Answers
Well as people posted already there is a 1 in 216 shot for each raid you get a 100%. But you could be an unfortunate soul like me and have never seen a 100% legendary out of 265 attempts. I've done over 100 regular raids also and to my knowledge have not seen a 100 there either but I admit that I don't always remember what the 100% for each species would be so I could have thrown at one and missed it (I know I've never caught one at least).
If you've done 216 raids, your expected value is exactly 1 perfect. A quick calculation shows that if you do 216 raids, you have about 1/3 chance of getting no perfects, 1/3 of getting 1 perfect, and 1/3 of getting 2 or more perfects in those raids.
For your case, simply take (215/216)^{no_of_raids_done} to find your chance of getting no perfects in that number. For 271 raids, that translates to 28.44 %. So if you and three friends had all done 271 raids, on average, one of you wouldn't get any perfects. Not lucky, but not stupidly unlucky either.
It averages out when you do enough raids, but it could take a while.
First week of normal raidbosses I got a 100% Tyrannitaur, that got away. First day with legendary raids I got a 100% Articuno. That was way over what you would expect.
Then I did not get anything above 96% until last day of Ho-Oh, when I got a 98%. Way below the curve by then.
Then I had a lucky streak after New Year with 2 100% and 3 98%.
Out of a total of 1200 raids I am now probably just a bit under average.
The inverse of 6 cubed, or once every 216 raids, which is 0.0046296 or 0.46296%. That is a bit less than one-half of one percent.
Now your question was of "seeing" a 100% raid boss" and that is different and higher than "catching" a 100% raid boss, which is the real goal. You might see perfection, but then, alas, not catch it.
I've been quite lucky. Only 194 total raids of all levels, and I've seen three 100s. I caught a perfect Raikou and a perfect Groudon, however the perfect boosted Tyranitar got away because I didn't know it was perfect until I had 3 balls left. I was throwing pinaps and wasn't concentrating as much as I could have. Now, I'm left with what could have been. Still, I've been quite lucky overall.
