Originally Posted by Infernalbargain
Here's something about Dead Shot that makes it quite nice for crit-fishing. If any of the attacks in the Dead Shot crit, the whole thing crits if you confirm, so improved crit would be a significant damage increase at high levels. At 11th, having improved crit changes your crit threat chance from 1-(19/20)^3 = 14.2625% to 1-(9/10)^3 = 27.1%, so it's like you're crit range increases with your BAB (34.39% with improved crit, 18.549375% without at 16th). All of a sudden you're effectively wielding a 14-20 / x4 weapon. This gets juicier if you allow haste etc. to give you extra attacks in your Dead Shot.
You'd want Improved Critical and Critical Focus in my book, anyways, for Grit renewal purposes, since Keen is melee only. Just be aware of the confirm penalty that's part of Dead Shot, which is what makes Critical Focus important for countering.