Shiny Rarity?
Excusing the fact that my GF just gotten a 100 IV Latios recently, she just gotten a shiny Ho-Oh. Maybe i know how rare are they for raid bosses? Because I AM NOT AT ALL JEALOUS. ):
Answers
Yesterday we had three Ho-Oh raids with seven accounts on each raid. We got a total of two shinies, I got a 93% and the guy who only did the first raid got a 98%.
Granted, that's still a small number (2/21) but we'd have been pretty lucky if shinies only come up one time in fifty. Maybe we could do a study from the other end - have a few hundred people report their raid rate, capture rate, and number of shinies. That way we could zero in on a number with reasonable confidence. The main wrinkle, of course, is that the catch rate is 100% for shinies, and much less otherwise, so we need to add in the ones that got away. How many shinies do you have, and how many Ho-Oh's have you seen (not caught, seen.) Personally, I have one shiny, and have done 15 raids (thirteen total catches, and one fail where the game crashed and didn't let me catch - Ho-Oh has always seemed easy to catch to me, or maybe I'm lucky).
The other issue, of course, is collector bias. If someone wants a shiny, they will raid until they get one, and then decrease their frequency for that species. However, this won't affect the rate at all, just the data pool.
There's nothing unusual about being pretty lucky. In your case of 21 tries, there was a 35% chance that one or more shinies appear if the rate is 1/50.
Like you said, the relevant data is total Ho-Ohs seen and the number of shinies seen. Whether anything was caught is entirely unnecessary for determining the shiny rate.
Shiny Raid Bosses are exceptionally common - all you have to do to get a Shiny raid boss is to do the raid you decided to skip. You thought to yourself "If I get off the bus to go do that Mawile raid, I'll have to wait 30 min for the next bus and I won't have time to cook a good dinner. So I'll skip that raid." at the time, but that's the raid that your Shiny was at. So all you have to do is to go back in time and do it that raid, and BAM! Shiny Raid Boss. Every time.
(no, I haven't done 10 Ho-oh raids in the past 3 days to try to finally get that Shiny Ho-oh before Ho-oh vanishes again, and no, it's not true the number of shiny Ho-oh's that popped from those raids for ALL participants can be counted on the digit located between my knees and my belly button, and no, I didn't catch 300+ Omanyte and 300+ Kaubto without getting a single Shiny for each (not to mention 300+ Meditite and 300+ Wailmer previously), and no, I'm not getting irrationally pissed off with Niantic's Shiny Drop rate, why do you ask? What do you mean by "Too Much Sarcasm. WAAYYY Too Much." and "Snark Overdose? You're Proving It's Possible." and "We Get It, You Hate The Niantic "R"NG." and "It's Called PASSIVE Aggressive, You Dolt. PASSIVE." and "STFU Already, Geez."??)
