[{quoted}](name=Ariel the Cruel,realm=NA,application-id=3ErqAdtq,discussion-id=9AIKyutG,comment-id=00080000,timestamp=2017-09-21T05:17:00.719+0000)
Relic's shield doesn't benefit from Ardent.
And the reason ADC's are taking relic is because Relic is a stronger defensive start than doran's+1pot.
450g
+80 health
+5 damage to minions (decent CS'ing doesn't need this)
+20 heal over 10 seconds after taking champion damage (=2/sec; 10 health regen)
+1 pot (150 health)
350g
+75 health
+2 gold per 10
+2.5 health regen (execute average)
+3 pots (450 health)
or + 1 bead (50% health regen - 1.25 on Soraka [lowest in game])
So right out the gate; relic is cheaper, refunds it's self, and offers better average health regen.
Then we add the bonus heal and gold for the support (which, let's be honest, most non-LCS ADC's don't even notice or care about).
But the benefit don't stop there. Relic can be upgraded for passable game-long defensive stats (by ADC standards).
850g (+500)
+175 health
+50% health regen
+2gold per 10
+8.3 health regen (execute average)
+255-340 passive shield (quest)
(For comparison, BT shield caps at 50-350.)
EDIT:
Looking at the value of Doran's heal...
lvl 1 Oriana has the lowest AD in the game at 40.368.
The highest armor in the game is lvl 18 Rammus with curl at 197.6228. (0.33599576376541044570510055009226 damage multiplier)
That means the 1 AA will deal about 13.56 damage. You profit 5.5 health in this effectively impossible scenario if you suffer only 1 Auto attack.
So Doran's heal is more trade mitigation than effective regen.
Added note, as it is LCS, A major contributor is the gold funneling into support. Since, as the shout casters have mentioned a few times, First censor wins lane.
EDIT:
Original quote was before Targon start was standard meta.