Frozen Heart vs Randuin's Omen vs Thornmail: Which Armor Item

Patch 26.19

Buy Randuin's Omen if you just need to stay alive. Buy Frozen Heart into champions who attack fast, or if you keep running out of mana. Buy Thornmail when you're the one trading hits with auto-attackers, because it wins more of those fights than either of the others.

What each item gives you on Patch 26.19

All three give the same armor. Randuin's adds health and takes the edge off critical strikes, Frozen Heart adds mana and ability haste and slows the attack speed of everyone near you, and Thornmail hurts whoever hits you and cuts their healing.

Staying alive: Randuin's, unless they attack fast

Randuin's 350 health does most of the work here. It's ahead even against attackers with no crit at all, and its crit reduction adds a little more against the carries who stack it. Frozen Heart's aura only wins when the damage comes from a high attack speed and on-hit effects rather than big crits: against Warwick, Vayne, Kai'Sa, Fiora and Teemo, it keeps most tanks alive longer.

Attacker	Ornn	Malphite	Rammus	Nautilus
Jinx	Randuin's	Randuin's	Randuin's	Randuin's
Caitlyn	Randuin's	Randuin's	Randuin's	Randuin's
Kai'Sa	Frozen Heart	Frozen Heart	Frozen Heart	Frozen Heart
Vayne	Frozen Heart	Frozen Heart	Frozen Heart	Frozen Heart
Yone	Randuin's	Randuin's	Randuin's	Randuin's
Yasuo	Randuin's	Randuin's	Randuin's	Randuin's
Master Yi	Randuin's	Frozen Heart	Thornmail	Frozen Heart
Warwick	Frozen Heart	Frozen Heart	Frozen Heart	Frozen Heart
Fiora	Randuin's	Frozen Heart	Frozen Heart	Frozen Heart
Sett	Frozen Heart	Frozen Heart	Frozen Heart	Randuin's
Zed	Randuin's	Randuin's	Randuin's	Randuin's
Ahri	Randuin's	Randuin's	No kill in 30s	No kill in 30s
Syndra	Randuin's	Randuin's	Randuin's	Randuin's

Which item keeps each tank alive longest against that attacker's standard three-item build. "No kill in 30s" means that attacker can't finish the tank at all, so neither choice matters.

Trading back: Thornmail

Most tanks don't just stand there. Once you're hitting back, Thornmail's reflect punishes every attack the other side lands, and it wins 78% of the duels against the 450 marksman and fighter matchups here. Its anti-heal is a bonus on top, and it matters most against Fiora, Naafiri, Briar, Warwick and Sylas.

Attacker	Ornn	Malphite	Rammus	Nautilus
Jinx	Thornmail	Thornmail	Thornmail	Thornmail
Caitlyn	Randuin's	Randuin's	Thornmail	Thornmail
Kai'Sa	Thornmail	Thornmail	Thornmail	Thornmail
Vayne	Thornmail	Thornmail	Thornmail	Thornmail
Yone	Thornmail	Thornmail	Thornmail	Thornmail
Yasuo	Thornmail	Thornmail	Thornmail	Thornmail
Master Yi	Thornmail	Thornmail	Thornmail	Thornmail
Warwick	Thornmail	Thornmail	Thornmail	Thornmail
Fiora	Thornmail	Thornmail	Thornmail	Thornmail
Sett	Thornmail	Frozen Heart	Thornmail	Thornmail
Zed	Thornmail	Thornmail	Thornmail	Thornmail
Ahri	Randuin's	Randuin's	No kill in 30s	No kill in 30s
Syndra	Randuin's	Randuin's	Frozen Heart	Randuin's

Which item leaves the tank better off at the end of a one-on-one fight, both sides able to die.

Mana: Frozen Heart

Frozen Heart is the only one of the three with mana and ability haste, and for a tank who lives on their spells that's usually the reason to buy it. Casting everything on cooldown, it stretches how long a tank can keep going before the mana runs out: K'Sante 91 to 104 seconds; Malphite 47 to 56 seconds; Nautilus 59 to 71 seconds; Ornn 105 to 120 seconds; Rammus 68 to 87 seconds; Sion 70 to 82 seconds.

Against mages

None of these three is the item to buy into magic damage (a magic resist item is the real answer there), but if the choice comes up anyway, Randuin's health wins more of those duels (52%) than Thornmail does (30%).

How these were worked out

Every item and champion number comes from the Patch 26.19 game files. Each tank holds the first two items of a standard build plus one of the three, at level 13, against every champion in the game holding a standard three-item build. Each fight is played out a fiftieth of a second at a time from eight starting points and averaged.