89%+ Magikarps

I have caught around 650 and have only found 3 at 89+. Two of which are 89 on the dot (both hatched) and my 91 (found in the wild) which was evolved in the a B/HP gyro. Sounds pretty reasonable compared to your findings. Best of luck

Caught 539
Found:
3 x 96%
1 x 98%
Lost count of the 89%s because I transfer the less than level 20 away. (But I've got 3 of them right now)

Caught 100 or so Magikarps, got 10 with 82%+. 1 96%, which I evolved into a B/Twister Gyarados.

I've caught 53 karps and hatched 1 since Saturday. Nice little nest in a park up the street from me. 3. Worth saving out of those. .. 171 cp level 29 87%, 144 cp level 25 87%, and of course a level 20 82% at 108 cp. I have 3 others from a while back... 2 93%, 163 and 119 cp and 1. 91% 157cp. Sitting on 812 candy at the moment and gonna go back today for a few hours for the double candy, and rest of the week and next week for some more. .. I have 3 gyarados now. Levels 35, 32, and 26... 84,89,and 98%.... b/dp on first 2, and b/hp on 98%. I've caught 453 total.

There's about a 0.65% chance of catching something with 39/45 or better IVs (86.67%).

Another way to ask the question is what are to odds of each IV being either 13, 14 or 15 (which would be 39/45 or better in sum). That's easy to calculate as the odds of that occurring are (3/16)^3 or about 0.65%.

Of course, this is for a caught mon. When you hatch them, the odds are much better--(3/6)^3 or 12.5%.

TLDR; - If you're at a 1% catch rate of mon over 89%, you're doing pretty well.

For egg catches, IV is always 10 or greater per stat and follows a bell curve distribution.
https://pokemongo.gamepress.gg/node/18331

I remember seeing a similar distribution for wild catches, however IV could be anywhere from 0-15 with a bell distribution centered around the middle (can't remember if it was 10 though)...

CAUGHT 1859
GOT 7 perfect IV (100IV)