I was under the impression you don't build thornmail until you have the health to allow it to do significant damage. Should you ever build thornmail first?
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If you're ever building Thornmail, build it first.
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From my Dominion/Treelines experiance:
Thornmail is pure cancer as a first major purchase.
It's pretty tame as a 3rd major purchase regardless of the circumstances, and kind of meh in Abyss.
Increasing your defense via damage reduction isn't really that different from HP as to the high HP value comment.
While HP is usually a more cost-effective stat early, the cost-effective difference is pretty negligible when you're facing off against a pure physical or pure magical champion in regards to countering them with the appropriate stat.
HP comes more into play when you're trying to do things vs. mixed damage or against an entire team.
100 armor is x2 EHP.
On top of the base ~30 armor at level 6, you need ~130 armor to double your HP.
You need ~1000 HP to double your EHP at level 6, and the highest HP item is the 2500 Warmogs, where the 2100 Thornmail is 100 armor.
In short - Riot doesn't punish champions for attempting to straight counter-build their opponents without getting HP first.
For Thornmail in particular:
100 armor from Thornmail effectively doubles your HP against physical damage.
the 30% damage reflection applies Prior to any damage mitigation. So with 50% damage reduction, you'll effectivly deal 60% of how much damage an opponent actually deals to you with Thornmail.
And if they just built a damage item that increases their HP by 0%, and you have twice their effective HP, you can litterally AFK kill them.
with a first purchase.
The counters to Thornmail are life steal along with enough %armor penetration to bring the reflected damage you need to cover with life steal to a manageable level, as well as enough MR to reduce the reflected damage to a manageable level.
Or just a 5v5 fight where phys auto-attackers can choose to not target you and smack someone else, leaving the ability-relaint champions to deal with you.
Late-game any AD champion worth their salt is going to have a decent chunk of life steal and armor penetration, and possibly sources of MR from something. Several supports offer sudo MR or actual MR buffs, melee champions get a decent chunk of MR from bases, and generally Thornmail late will reflect, like, 10% of an opponent's actual damage back to them after life steal.
It will effectively prevent them from life-stealing Off of you, which is a small victory, but it won't do much beyond that late-game. And that's only if auto-attackers focus you, which is more the reason Omen and Sunfire are purchased frequently - nobody has to focus you to utalize the passives of those items.
Thornmail's more of a duelist-tank item.
TLDR:
thornmail late-game stops lifesteal from doing things. If auto-attackers focus you.
thornmail early-game nets AFK kills.
If you want Thornmail, you want it early.