Assassin's shrouds

Do the shrouds still do damage even if the attack misses. That's the way I read it. I just don't know if I'm right.

Dragon Magazine 379 pg 19

At-Will ✦ Shadow
Free Action (Special) Close burst 10
Target: One enemy you can see in burst
Effect: You subject the target to your shroud. If any of your
shrouds are already on the target, you subject it to an additional
shroud, up to a maximum of four. The shrouds last
until you use this power against a different enemy or until
the end of the encounter.
B efore you make an attack roll against the target, you
choose to invoke either all your shrouds on it or none of
them. If you invoke your shrouds, the attack deals 1d6
damage per shroud, minus one shroud if the attack misses,
and all your shrouds then vanish from the target. This damage
roll never benefits from bonuses to damage rolls, and is
in addition to the attack’s damage, if any.
Level 11: 1d6 + 3 damage per shroud.
Level 21: 1d6 + 6 damage per shroud.
Special: You can use this power only on your turn and only
once per turn.

Yes, the shrouds still do damage if you miss with the chosen attack, they just deal 1 shroud less damage than they would if you hit.

ie: If you have 4 shrouds on an enemy and choose to use them as part of your next attack you deal an extra 4d6 damage if you hit, or 3d6 if you miss.

Yes they do.

1) Before you make the attack, you announce how many shrouds you are expending (X).
Then you make the attack:
2a) If the attack hits, deal damage for the X shrouds.
2b) If the attack misses, deal damage as per X-1 shrouds.