Has anyone else been this unlucky with shiny legendaries?

I have had 93 Dialga encounters since the shiny became available, but only have one shiny. The odds of this happening with a 5% shiny rate are 0.9%.

Because I traded all Dialga from last year each one counts as two in my Pokédex, and I know that I only did one Dialga raid before the shiny was released, so I subtracted the number of recent Dialga that are untraded and the one from before the shiny was released, (143-42) and divided the answer (101) by two to get the number of Dialga that I caught + traded, and because there can’t be half of a Dialga it gets rounded to 51. Add the number of untraded Dialga, excluding the one from before shiny, to the number of traded Dialga to get 93 Dialga encounters.

Multiply the odds of not getting a shiny (0.95, with 1.00 equaling 100%) by the number of encounters minus 1 because of the ONE shiny, to get the odds of getting only one in 93 encounters (0.95 to the power of 92), which equals 0.008924, or a 0.9%, not 9%, but 0.9% chance of this happening.

While it is scientifically possible for this to happen, and would likely happen to one or two people if every player encountered this many, it seems unlikely that the chance has actually been 5% for a shiny.

Edit: all Dialga from 2021 were transferred after being traded, the Dialga from 2019 is untraded, and I didn’t do Go Fest 2020, so I don’t have any Dialga from that time.

Well… My third dialga was a shiny (all in all 1 of 18)… and my most caught legendary, landorous, was never shiny (55 caught, but I honestly do not know how many times it could have been shiny, was it shiny the last two times? then maybe 35). but to be honest, i don’t see the point… About 100 caught is not THAT many, as you hinted by yourself - and you GOT a shiny!
The chances are about 4 percent. Perfectly fine if you ask me.

Maybe I miscalculated, but afaik, the formula (Bernoulli) would be [93!/(1!92!)](1/20)*(19/20)^92

Which equals roughly 4.1 percent. think of a 20* dice. You’ll get mostly 5 times the perfect 20 if you roll 100 times… But also 4, 3, 2, 1 and of course 6, 7, 8 and 9 times 20 would be that rare. The 1 is completely in the “ok” range

Edit: indeed I think I made a mistake. For just one “event” of course you don’t need the above complicated calculation (it’s for two or more) so yours should be ok as well and somehow mine overestimated it, maybe someone finds the mistake, my brain is in Sunday mode…
The bottom line is the same with 1 percent anyway: that’s completely in the “normal” range which we would expect