From my experience, 25k - One Party character piece, 30k+ Full Party Character piece. Believe if you keep it around 15k and up, you'll score an infinite cosmetic item over a coin reward all the time. I could be wrong, but that's just my experience with Infinity time.... which I hate with all my heart and soul for the amount of time put into it.
You do NOT get a full party character from 30k+ shards. Prior to the first patch it was possible to get two rewards, but after the patch, you only get one. Like most have said, just die when you get to 26K shards for your best chance to get a party character piece.
