Optimized ADC vs. Anti-ADC-Itemized Tank
Even for a hypothetical, optimized ADC (that is not specialised in tank busting), it takes quite a bit to kill a tank that has dedicated his build towards surviving an ADC's damage.
First, what our hypothetical optimized DPS autoattacker (HODA)? Let's simply take the highest of base AD@18, base AS and AS/lvl of all ADCs.
AD@18: 113.5 (Draven) Base AS: 0.679 (Draven/Twitch) AS/lvl: +4%/lvl (Caitlyn) MS: 335 (Sivir, Quinn, Lucian, Kai'sa)
Items:
.
Hoda only uses auto-attacks, and doesn't have a further steroid in his kit (since he has superhigh base stats). He also uses Precision primary and Sorcery secondary (+6 AD/+9%AS), is 40 min in for Gathering Storm (48 AD), Legend: Alacrity (18% AS), Cut Down (+10% damage) and has Celerity (2 AD)
With his items, that amounts to 439.5 AD, 160% increased AS for a total AS of 1.7654, 100% Crit with 1.5x bonus damage, and 30% increased damage against targets with 2000+ more max HP. Energized will stack at a rate of 15/attack, meaning it procs every 8 attacks and thus averages 50 magic damage per attack.
Thus, final DPs of Hoda: 2521.653225 physical + 97.07 magical
Our tank has 2200 base HP, 100 base Armor and 58 base MR at level 18. His items:
. Resolve primary with Inspiration secondary (130 HP), Conditioning (8 Armor/MR) and Overgrowth (40 min = ~480 minions/lane, 12% increased HP).
Despite both giving Cold Steel, the combination of Randuin's and Thornmail is effective. With the high Armor of this build, Hoda's Lifesteal will be completely negated. Sunfire could also be replaced with Dead Man's Plate without affecting the final outcome.
HP: 4205 x 1.12 = 4709.6 Armor: 438 (319.7 against Last Whisper) MR: 66 Our tank also takes 20% less damage from critical strikes, 10% less damage from auto-attacks and reduces the attack speed of his attacker to 72.25% of its normal value.
Thus, let us adjust Hoda's stats and DPS to our tank: AS: 1.2755015 DPS: 312.548 physical + 56.122 magic, total 368.67
4709.6/368.67 = 12.8 seconds
Our anti-ADC-itemized tank thus survives 12.8 seconds of continuous pounding from Hoda the optimized AD.
Bonus: How effective is Hoda's Lifesteal and Fleet Footwork?
Hoda has 38.5 MR. His FF heals for 252.48 per proc, or 31.56 per attack. His 20% Lifesteal gives 49 HP back per attack, resulting in a heal of 80.56 per attack, or 48.336 after Grievous Wounds.
Thornmail, with that build, returns 68.8 damage, reduced to 49.319 damage after Hoda's resistances.
Thus, both Lifesteal and Fleet Footwork are completely negated. If he hits his abilities, the tank should be able to kill Hoda in the 12.8 seconds it takes Hoda to kill him.
This is just to serve to show that dedicated anti-ADC itemization is enough to enable enough of a survival against even a optimized ADC, provided he is not a dedicated tank killer (Kog and Varus, for instance, would kill the tank way faster).
For a cost comparison, the ADC's build costs 18.3k gold, while the tank's build costs 15.35k gold.