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Magic Penetration and its effects on Effective Health

Verandure··6 votes·1,361 views

A short analysis of items which reduce the effective health of a target (or targets) with respect to magic damage. I apologize, in advance, for the math -- the boards do not have a good format for equations.

Ways to reduce effective health of the target:

Ehp = Hp*(100+MR)/(100 x Total Damage Modifier)

Magic Penetration, Magic Resistance Reduction, Damage Amplification

  • Void Staff
    • Ehp=Hp*(100+0.65MR)/(100)
  • Sorcerers Shoes
    • Ehp=Hp*(100+(MR-15))/(100)
  • Liandry’s Torment
    • Ehp=Hp*(100+(MR-15))/(100)
  • Abyssal Scepter
    • Ehp=Hp*(100+(MR-20))/(100)
  • Devastating Strikes (3/3)
    • Ehp=Hp*(100+0.94MR)/(100)
  • Greater Mark of Magic Penetration (9/9)
    • Ehp=Hp*(100+(MR-7.83))/(100)
  • Greater Quintessence of Magic Penetration (3/3)
    • Ehp=Hp*(100+(MR-9.03))/(100)
  • *Deathfire Grasp
    • Ehp=Hp*(100+MR)/(100x1.20)

Wit’s End isn’t being considered due to the reference frame of my analysis being that of a common mage rather than an auto-attack reliant champion.

Assuming: 21/-/- Masteries Pen reds, armor yellow, mr blues Sorc shoes

Which is the most effective at reducing the effective hp of a target? (Remember: reduction is calculated before percentage penetration, which is calculated before flat penetration.)

  • Sorc Shoes + Devastating Strikes (3/3) + Greater Mark of Magic Penetration (9/9)
  • Ehp=Hp*(100+(0.94MR-(15+7.83)))/(100)=Hp*(77.17+0.94MR)/100
  • Liandry’s Torment
    • Ehp=Hp*((77.17-15)+0.94MR)/100=Hp*(62.17+0.94MR)/100
  • Abyssal Scepter
    • Ehp=Hp*(77.17+0.94(MR-20))/100=Hp*(58.37+0.94MR)/100
  • Void Staff
    • Ehp=Hp*(77.17+0.65x0.94xMR)/100=Hp*(77.17+0.611MR)/100
  • Deathfire Grasp
    • Ehp=Hp*(77.17+0.94MR)/(100x1.2)=Hp*(77.17+0.94MR)/120

Break Even Point

Abyssal Scepter > Liandry's Torment Void Staff > Liandry's Torment when target's MR is greater than 45.593 Deathfire Grasp > Liandry's Torment when target's MR is greater than 13.649 Void Staff > Abyssal Scepter when target's MR is greater than 57.143 Deathfire Grasp > Abyssal Scepter when target's MR is greater than 37.904 Void Staff > Deathfire Grasp when target's MR is greater than 74.632

All champions have 30 base MR and some build up to 52.5 by leveling. MR Blues (which are standard on most rune pages) give 12 MR. Nearly every champion in the game will have, at least, 42 MR and may have up to 64 MR without abilities or items.

This means Deathfire Grasp is the most effective at reducing effective health when the target has 42 MR:	(DFG > AS > LT > VS)
At 64 MR; Deathfire Grasp is, again, the most effective at reducing the effective health of the target: (DFG > AS > VS> LT)

The lowest possible value of MR bought, on Summoner’s Rift, is 25. This means that; with the assumptions made, a single null-magic mantle purchase makes the order (DFG > VS > AS > LT) for champions without MR per level, and (VS > DFG > AS > LT) for champions that have MR per level.

Deathfire Grasp [had] only a 4 second window in which it reduces a single target’s effective hp, Abyssal Scepter requires you to be within 700 units (Max Rank Switcheroo! Fishbones auto attack range), and Liandry’s Torment is simply the least effective at all feasible values of magic resistance the enemy may have. 

Abyssal Scepter: 2440g
Deathfire Grasp: 3100g
Void Staff: 2295g
Liandry's Torment: 2900g

This is solely looking into the effective health reducing mechanic of each of these items. It is clear that Liandry’s Torment is meant to help against health stacking with its percent current health passive, it’s clear that Abyssal Scepter is meant to be a defensive item with a slot-efficient damage increase, and it’s clear that Deathfire Grasp [was] meant to help secure kills for burst mages by inflating their burst rotation (while not being oppressive on sustain damage mages).

Even with all that in mind, though, Void Staff is far and beyond the safest and most effective purchase of these four items for increasing your damage against tanks, bruisers, and anybody come late game. It’s comparatively cheap, gives a decent chunk of AP, has an easy build path, and has no downtime. 

    There is very little reason for the other penetration items to exist (rest in peace; Deathfire Grasp) when the values of MR that make Void Staff efficient are so low when it's bought in tandem with Sorcerer's Shoes. Removing Deathfire Grasp does; however, give flat penetration a tiny amount of wiggle room to be effective (Liandry's Torment is still virtually worthless for reducing a target's effective health).

5 Comments

balbraaksel3 votes

Liandry's Torment isn't a usual AP damage item, it deals % current health DoT meaning the more health someone has the more damage it does. It particularly can do a lot of damage to tanks, however they usually also have high MR, so if you build Liandry's Torment you should always pair it up with a Void Staff.

I personally prefer the have the Haunting Guise, then Void Staff, then Liandry's Torment.

Thank you for the enlightening calculations :)

Verandure1 votes

Thanks for reading!

I would definitely agree that Liandry's Torment is an oddball item. Personally, I love the item due to its synergy with DoT casters and Rylai's Crystal Scepter. The "Burn build", as it's called, offers an interesting build diversity for casters.

I certainly believe Liandry's Torment is a good damage item. This analysis only deals with how the items stack up at reducing the effective health of a caster's target rather than which item is better at helping you reduce that health to 0.

Verandure1 votes

As an aside; I'd like to also point out that Deathfire Grasp was severely gated by its cost. The window of effectiveness is typically early and mid game, unless your target rushes any sort of MR, and Deathfire Grasp is difficult to rush unless you're already ahead. It may have seemed like Deathfire Grasp was having enormous effects on damage output, but it is not due to the damage amplification portion of the passive (which is in-line with penetration in terms of reducing a target's effective health).

A 15% max health, unavoidable nuke was more likely the cause of its purported safety. From max health, Liandry's Torment would need 7 seconds of its passive to be active on the target to achieve the same amount of damage. If the target isn't at max health, it would take even longer. Out of anything, I truly think throwing such a strong nuke onto an active meant to amplify damage was where the imbalance came from.

A burst mage can 100-0 (or even more) most "squishy" targets in a single burst rotation. Deathfire Grasp doesn't do much, for them, because their kit already includes enough damage to be considered overkill on a single target. What Deathfire Grasp does; however, is make the mages that aren't balanced around 100-0 burst rotations able to 85-0 burst a champion after its use -- mages that don't have significant cooldowns to gate their abilities.

xLegendary Troll1 votes

Liandri's torment is a trap item. Go into a custom game and play against an intermediate nasus. Build Void staff and Liandries and wait for him to finish his spirit visage. Turn on ap damage and you'll find out it does 0-2 DoT

I'm not even joking. I tried "increasing" the Dot by activating DFG and the highest I got it to burn is 4 per tick. Waste of an item. Brand's passive does around 14-30 per tick. Huge difference

Verandure1 votes

And, as always, a lot of work gone into a post only for it to be ignored because it doesn't have an accusatory or complaining title.

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