Ah ha! I finally figured out what this skill does. I noticed that a Third Eye Ganger evaded just 2 damage with a Dive for Cover attack, when normally they avoid 4-8. So it seems to give an invisible negative Evasion Power debuff to your opponents.
(Looks like the chained ghoul has this skill as well, or at least the flag that gets set by having this skill. That's probably how you can get the "… but you evade no damage" against him.)
Still collecting some data but it looks like it gives about -2 (possibly more with other conditions?).
Data:
Third Eye Gangers (evade 4-8 originally):
- You punch the thug for 16 damage, but he ducks behind cover, which absorbs all but 14 damage. [-2]
- You punch the thug, throwing the whole weight of your body behind it and dealing 22 damage, but he ducks behind cover, which absorbs all but 20 damage. [-2]
- You punch the thug for 9 damage, but he ducks behind cover, which absorbs all but 6 damage. [-3]
- You punch the thug for 14 damage, but he ducks behind cover, which absorbs all but 11 damage. [-3]
- You punch the thug for 9 damage, but he ducks behind cover, which absorbs all but 4 damage. [-5]
- You close on the thug, then jab him for 13 damage, but he ducks behind cover, which absorbs all but 10 damage. [-3]
- You punch the thug for 9 damage, but he ducks behind cover, which absorbs all but 3 damage. [-6]
- You punch the thug for 10 damage, but he ducks behind cover, which absorbs all but 4 damage. [-6]
Lake serpent (evade 6-10 originally):
- You punch the lake serpent for 6 damage, but the lake serpent is already underwater. The water absorbs all but 2 damage. [-4]
- You close on the lake serpent, then jab her for 14 damage, but the lake serpent is already underwater. The water absorbs all but 9 damage. [-5]
- You punch the lake serpent for 9 damage, but the lake serpent is already underwater. The water absorbs all but 2 damage. [-7]
- You punch the lake serpent for 5 damage, but the lake serpent is already underwater. The water absorbs all of the damage. [-5 or more]
- You punch the lake serpent for 7 damage, but the lake serpent is already underwater. The water absorbs all but 3 damage. [-4]
- You punch the lake serpent for 8 damage, but the lake serpent is already underwater. The water absorbs all but 4 damage. [-4]
- You punch the lake serpent for 5 damage, but the lake serpent is already underwater. The water absorbs all of the damage. [-5 or more]
- You close on the lake serpent, then jab her for 14 damage, but the lake serpent is already underwater. The water absorbs all but 8 damage. [-6]
EDIT: thinking about this some more, it seems it's not just a evasion power debuff - the Third Eye Ganger reduces 4-8 to 2-6. That should be 2-4 if it was just -2 Evasion Power; more likely it's applied flatly after the damage is calculated, much like reactive defense.
From the chained ghoul discussion:
The ghoul loops chain around you, creating a vicious trap dealing 21 damage, but you tumble out of the way, avoiding no damage.
Cinematic dodge is only 2 Base Defense, so this could be just a -2 to it.
Further edit: Mag points out this exact idea a couple months ago. I feel less clever now. :(