Actually, I think the equation is Thornmail vs. Lifesteal + ArPen + MR.

Thornmail returns 30% of damage (prior to mitigation) as magic damage.

Lifesteal (Bloodthirster fully stacked) returns as HP 25% of damage (after armor mitigation).

How much of Thornmail's damage does lifesteal counter? Combined with your base MR, most of it. But to fully mitigate Thornmail, you probably need some ArPen and more MR.

Examples (assumes your champion has 30 base MR at level 18 and your opponent has 75 base armor at level 18):

**With a Bloodthirster (100 AD + 25% lifesteal)**

Say you have 100 base damage + 100 bonus AD from BT. Thornmail will hit you with 60 magic damage. Accounting for your 30 base MR, you take 60 * [1 - (30 / 130)] = 46 damage from TM (before lifesteal).

Your target has 175 (75 base + 100 from TM) armor or 64% mitigation. This means you only do 72 damage to him. 200 * [1 - (175 / 275)] = 72

You get 25% of this back as lifesteal (18Hp) so total damage to you is 46 - 18 = 28

So, if my calcs are correct, with only 25% lifesteal, for 200 AD you would do 72 damage to your enemy and take 28 damage yourself.

**With Merc Treads (30 MR) and Last Whisper (40 AD, 40% ArPen, no lifesteal):**

- 140 AD * [1 - (105/205)] = 68 damage to enemy.

- (.3 * 140) = 42 * [1 - (60/160)] = 26 damage returned.

Almost the same as the lifesteal example.

**With Bloodthirster (100 AD, 25% Lifesteal) , LastWhisper (40 AD, 40% ArPen) and Merc Treads (+30 MR):**
- 240 * [1-(105/205) = 117 damage to enemy.

- (.3 * 240) = 72 * [1 - (60/160)] = 45 - (29 lifesteal) = 16 damage returned.

So you can see why Thornmail is so efficient. To fully (mostly) mitigate a 2000g item, takes 6500g worth of offensive items (but many of which AD carrys would have anyways).