### At what point does life steal counter Thornmail?

I may be totally off here, this is just what I believe should happen based off of what I understand, feel free to correct what's wrong.

So let's assume the adc and enemy tank have zero armour or MR. One auto attack deals 100 damage, so thornmail would return 30. I believe lifesteal should also simply be a percentage of your damage, so you would need 30% to heal 30, effectively canceling the thornmail.

So now resistances. The armour of the enemy won't affect how much damage you take, but it will affect how much they take and how much you heal. Thornmail damage is calculated before resistances, so keeping the previous basis, you still take 30 magic damage. Let's assume their armor negates 50% of your damage. They take 50 damage and you steal (let's say you have 30%, which is far more than you would normally have), 15 hp. So overall, you dealt 50, and received a net 15 damage.

Now go back to zero resistance except let's say your MR negates 50%. You will take 15 damage, but heal 30. So net gain 15.

So specific numbers. Pretty hard to say because there so many percents involved, it would always be relative per game. Also I'm on mobile so I can't really do hard math right now (or ever). But the theory would be since you take 30% of your total damage, and you'll steal X% of actual damage, you would have to have more life steal than the percent damage you take. So if you took the full 30%, you'd have to have at least 30% if you did 100% damage, the less damage the enemy takes, the more life steal you need over 30% (this excludes critical hits. You could take into account the average DPS due to crits actually nevermind, I think crits would just be a new total damage so nevermind I'm stupid).

So it's impractical to attempt to get enough lifesteal to counteract the damage. What you need is MR to make it realistic. The more you can reduce that 30%, the less life steal you need. If you have about 66% magic damage reduction, you'd be probably close to break even.

Now don't think this doesn't mean you can't kill someone with thornmail, it just adds to their DPS while decreasing yours. It still comes down to who out DPS's the other (taking into account total health). Best bet would be to have your casters help focus thornmail users though.

tl;dr - Get MR to counter thornmail. The percent lifesteal has to be greater than the percent damage you take. Exact numbers are hard. Math is hard.

Let me know if I'm stupid and wrong