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I recently gave out a full box of 3 IV breeding leftovers and got remarkably few true shitmon. The only bunny I got had its HA. I've gotten quite a few 3-4 and even got a 5 IV Riolu.
And while stuff like 0IV Torrent Froakies are shit to me, they're not as bad as a Bidoof. I can't decide if I should recycle or release those, though, because while a new player would be ecstatic, it's worthless to the people actually giving out useful stuff.