Out of desperation I let a raid buddy take a shot, she caught my first Moltres for me, 87 IV
He still hates me, had many great shots, won't stay in the damn ball. Plus got hit with an error
That was my best one yet too.. sigh, WHY WON'T YOU LET MEEE CATCH YOU YOU BASTARD
They really want me to buy more passes don't they
Side note it does often seem like the damage you contribute to the battle has some influence on the Pokemon you can catch, but I still dunno for sure