One thing you may not know about Piper is that she is always on the lookout for a good game of chicken. She is pretty sure she rocks at it. I'll concede at least that she has nerves of steel. You could throw that ball at her and she wouldn't flinch...she would just try to stare it into submission until it hit her in the face. Then she would give a quick, indignant hiss, move a foot away and act like she had won. She also employs this method with Remy. It's amazing to see a snot-nosed, sticky-fingered toddler barreling at a cat and the cat staring him down without batting an eye. The wisdom of her tactics (or tactic, it's pretty straightforward) is sometimes questionable (I can't count the number of times I have stepped on her not realizing that we were engaged in a game of chicken) but her persistence is remarkable.
By the way, I did not throw that ball at her face. But Remy might have.