In Battletech, the further you move in your turn, the more of a Dodge Bonus you get during the enemy’s turn. You could do something similar for PP.
There’s a dodge trait that reduces damage by 25%, when in close quarters. While it’s far from a clean solution, you could potentially just do something like that. Shots have a chance of missing, or inflict less damage.
It is a bit annoying to get no advantage to sprinting, as far as dodging bullets goes, so I think this touch might be worth adding. It’ll mean the little fast aliens aren’t so effortless to deal with, if they get a dodge bonus.
Missing in this case would be hitting for no damage. That and hitting for less damage are both unfortunate work arounds, since there are no dodging animations or such.
Of course, it would be trivially easy to make it so the bullets do miss. If the character “dodges” all the bullets, then the circle would be made just large enough that the bullets can miss, and any part of the circle that overlaps the character would be off limits.
It could look funny, but so does characters getting shot in the head all the time, or having bullets hit characters but do 25% less damage because they “dodged.”
It worked pretty well in Battle Tech, is all I can say. I think it can work fine here. Though, rather than a straight -25% damage per shot, I’d prefer to have a random roll for that, so your maximum potential damage isn’t reduced.