Math behind thornmail and misconceptions regarding lifesteal

Figured I'd repost this here since I see people questioning thornmail's effectiveness and counters a lot. Item values probably have changed slightly but the math stays the same regardless

Original Post

http://forums.na.leagueoflegends.com/board/showthread.php?t=4140983

Thornmail is calculated before mitigation, whereas life steal is calculated after mitigation; this single fact changes a lot. Thornmail becomes stronger the more armor you have, and because of this, the amount of lifesteal someone needs to simply break even with the damage thornmail deals to them is absurd.

Example: Say (hypothetically) an Amumu with thornmail has 100 armor with thornmail's passive and an ashe is autoattacking him who has 0 MR. (This is hypothetical to show the point). Assume ashe crits amumu for 1000 before mitigation.

With 100 armor, he takes 50% less damage, so he takes 500 damage and thornmail deals 300 (30% of 1000). Ashe would need 60% Lifesteal to match that With 200 armor, he takes 2/3 less damage, so he takes 333 damage and thornmail still deals 300. Ashe would need need 90% Lifesteal to match that. With 300 armor, he takes 75% less damage, so he takes 250 damage and thornmail still deals 300. Ashe would need 120% lifesteal to match that.

Now you can account for someone who has MR, since thornmail's damage is magic. Squishy carries (melee or ranged) typically have somewhere between 40-85 MR based on runes and masteries and items like GA or QSS or what not, a bit more for melees.

At 40 MR, the damage from thornmail is reduced to 5/7. Using the same example from above, thornmail deals 300 * 5/7 = 214 damage back to a 40 MR ashe.

At (Amumu's) 100 armor, she'd deal 500 damage and would need 43% lifesteal. At 200 armor, she'd deal 333 damage and would need 64% lifesteal to break even with thornmail At 300 armor, she'd deal 250 damage and would need 85% lifesteal to break even with thornmail.

At 85 MR, ashe would take 54% reduced damage down to 162 from thornmail. Using this MR value: She'd need 32% lifesteal to BREAK EVEN with thornmail at 100 armor She'd need 49% lifesteal to BREAK EVEN with thornmail at 200 armor She'd need 65% lifesteal to BREAK EVEN with thornmail at 300 armor.

But Wait, now take into account if ashe doesn't get a QSS/GA right away and instead goes for last whisper! Now she's back to 40 MR but the armor values change due to LW.

100 armor goes to 65 armor, ashe deals 606 damage, thornmail deals 300*(100/140) = 214 damage, she needs 35% lifesteal to match thornmail's damage 200 armor goes to 130 armor, ashe deals 438 damage, thornmail deals 214 still, she needs 49% lifesteal to match thornmail's damage. 300 armor goes to 195, ashe deals 339 damage, thornmail deals 214 still, she needs 63% lifesteal to break even with thornmail's damage.

Now assume end game, when the carry has their MR item of choice and has 85ish MR along with a Last Whisper. Thornmail here deals 162 damage again but the armor values are adjusted due to LW.

At 100 Armor, (so actually 65 Armor), Ashe deals 606 damage, she needs 27% lifesteal to break even. At 200 Armor, (so actually 130 Armor), Ashe deals 438 damage, she needs 37% lifesteal to break even. At 300 Armor, (so actually 195 Armor), Ashe deals 339 damage, she needs 48% lifesteal to break even.

As you can see, the lifesteal values someone needs to even match thornmail's damage are ridiculous in all scenarios. As you can also see, Thornmail becomes much more effective the more armor the wearer of it has in all scenarios. Thornmail is most effective against targets without mixed damage on hit type skills, such as ashe, draven, miss fortune, tryndamere. It is a lot less effective against champions with mixed damage on hits, such as Irelia, Jax, Vayne etc. For these guys, Omen and Frozen Heart are more effective due to the AS slow, but everyone knew that already. Thornmail is most effective at high values of armor, meaning it is a heavy resist building tank/fighter item, not a carry item that wants a bit of defense to last.

Tl;dr Thornmail is not countered by lifesteal. The life steal values an autoattacker would need to simply break even with thornmail's damage return is ridiculous and completely unrealistic in a 5v5 game. At realistic values of life steal , thornmail deals way more than the life steal benefits the autoattacker. Also, thornmail becomes much, MUCH more effective the more armor the wearer has. MR counters thornmail better than lifesteal does