Projectile supports comparision

Let's compare performance of available projectile supports on a single projectile skill without additional mods.
We will compare DPS in 3 situations:
single target - obvious
multiple targets - extra arrows have ~50% chance to hit
crowd - extra arrows will most likely hit
Additionally, I will add a more subjective parameter "reliability" - how little performance depends on conditions, like area layout and monsters disposition.

Pierce
Single target - 100%
Multiple targets - 150%
Crowd - 200%+ (no limit)
Reliability - low

Fork
Single target - 100%
Multiple targets - 150%
Crowd - 200%
Reliability - low

Scattershot
Single target - 64%
Multiple targets - 128%
Crowd - 192%
Reliability - medium

Chain
Single target - 50%
Multiple targets - 150%
Crowd - 150%
Reliability - high

As we can see, Pierce is slightly better than Fork. Both are highly situation dependent.
Scattershot is slightly weaker against mobs, but theoretically it's compensated with a higher liability. Terrible against rares. Gets worse with additional arrows. Great with AOE skills.
Chain loses to its competitors. Its aim-bot makes it equal to other supports only in low to medium density situations. Gets worse with additional chains.

Chain is useful when your projectile inherently has Pierces All Targets. Staggering Palm /Lightning Slam projectiles carry this quality. The pierce nullifies Fork entirely and allows projectiles that would have whiffed another chance to find a target.