League Of Legends How every on-hit item works with Katarina’s ultimate By: CS_Emerald

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Tl;dr at the bottom

Hello there. I’m Katastrophical, Master peak Katarina OTP with close to 3mil mastery and i love finding new mechanics/combos for Kat or going in-depth on her mechanics and item interactions.

For some reason, different items still have different ways of interacting with Katarina’s ultimate. Due to all the Pre-Season-Craziness it can be hard to keep an eye on what works and what doesn’t, so i thought it would be helpful to write a sort of guide on which items work well with Katarina’s R and which don’t.
Some of these interactions may change in the future, this post is accurate for Patch 10.23.

As a reminder, we expect every item with 0 CD On-Hit effects to proc exactly 3.75 times (15 times at 25% efficiency), but some small variation is to be expected, because League doesn’t calculate with exact numbers (81 may in reality be 81.47 without the game showing it to you, for example).

For this test, Katarina is level 6 (71 base AD), has no damage enhancing runes whatsoever, and always uses exactly one item. Let’s go!

(Reminder: I am ONLY testing the effect these items have on Katarina’s ultimate ability, Death Lotus.)

1) THE WORKING-AS-INTENDED ITEMS

—–Blade of the ruined King:—– (PROCS 3.75 TIMES, WORKING AS INTENDED, MATH BELOW)

Stats:
111 AD, 0 AP, R damage total: 375(AP) + 146(AD) = 521.

Description:
Every attack, Bork deals 10% of the enemies current health as physical damage.

Test:
Ulting a 20000HP dummy (high number to minimize error) with 0 Armor/MR yields 6249 damage dealt by Botrk.

By solving

20000*0.9^x=20000-13751

we get x=3.5556

Conclusion:
Doing the same calculation again for a 30000HP dummy, we get x=3.5717, which leads me to believe that we’re approaching x=3.75. Keep in mind that the other Bork passive reliably procs on the third utlimate tick, further skewing x downwards together with the 521 base damage.

—–Nashors’s Tooth:—– (PROCS 3.75 TIMES, WORKING AS INTENDED, MATH BELOW)

Stats:
71 AD, 100AP, R damage total: 660(AP) + 0(AD) = 660.

Description:
Every attack, Nashor’s deals 40 magic damage.

Test:
Ulting a 1000HP dummy with 0 Armor/MR yields 150 damage dealt by Nashor’s.

x=150/40=3.75

Conclusion:
Nashor’s applies its damage 3.75 times, which is 15 times at 25% efficiency.

—–Wit’s End:—– (PROCS 3.75 TIMES, WORKING AS INTENDED, MATH BELOW)

Stats:
101 AD, 0 AP, R damage total: 375(AP) + 112(AD) = 487.

Description:
Every attack, Wit’s End deals 34 magic damage (at level 6).

Test:
Ulting a 1000HP dummy with 0 Armor/MR yields 128 damage from Guinsoo’s.

x=128/34=3.7647

Conclusion:
Accounting for rounding errors, Wit’s End very likely applies its damage 3.75 times, which is 15 times at 25% efficiency.

—–Black Cleaver:—– (SHREDS ARMOR IN 1.00s, MISSING HP% DAMAGE REDUCED BY 90%, MATH BELOW)

Stats:
111 AD, 0 AP, R damage total: 375(AP) + 134(AD) =509.

Description:
After attacking an enemy champion 6 times, each consecutive ability or attack deals 5% missing health damage, at 40% efficiency for damage over time abilities.

Test:
Ulting a 1000HP dummy with 0 Armor/MR yields 27 damage dealt from Butcher, the first 6 ult ticks fully stacking the Carve passive and the last 9 ticks applying the Butcher damage.

These 9 Butcher ticks do 2 2 2 2 2 2 3 3 3 damage to the dummy, with an extra 5 damage the moment full stacks are applied (this is because not only attacks, but also abilities proc Butcher, meaning Katarinas R itself procs Butcher once at 25% damage, separately from the on hit effects of its dagger ticks).

Conclusion:
Butcher damage gets reduced to 25% from Katarinas ult, and again to another 40% from the Butcher passive for damage over time abilities, leaving only 10% of the original damage.

—–All Spellblade Items (Essence Reaver, Divine Sunderer, Sheen, Lich Bane, Trinity Force):—–

Every Spellblade item procs exactly once at the start of your R, dealing 25% of its normal damage and going on Cooldown normally. YOU SHOULD PREVENT THIS! Do not open a combo with your R if you have any of these items, as you will lose 75% of its damage output. This especially hurts if you’re using Lich Bane, which has a 2.5s cooldown.

2) THE MAYBE-NOT-WORKING-QUITE-AS-INTENDED ITEMS

—–Guinsoo’s Rageblade:—– (PROCS 3.75 TIMES, DOES NOT GIVE DOUBLE HITS, MATH BELOW)

Stats:
71 AD, 0 AP, R damage total: 375(AP) + 0(AD) = 375.

Description:
Every attack, Guinsoo’s deals 40 physical damage.

Test:
Ulting a 1000HP dummy with 0 Armor/MR yields 525 damage dealt i total, which leaves us with 150 damage from Guinsoo’s.

x=150/40=3.75 

Conclusion:
Guinsoo’s applies its damage 3.75 times, which is 15 times at 25% efficiency.
The second Guinsoo passive (“Every third attack applies your On-Hit effects twice”) does NOT work with Katarina’s ultimate.

—–Titanic Hydra:—– (PROCS 3.75 TIMES, CLEAVE DAMAGE IS APPLIED ONLY IF ENEMIES STAND CLOSE TO EACH OTHER, SEEMINGLY AT RANDOM, MATH BELOW)

Stats:
115 AD, 0 AP, R damage total: 375(AP) + 150(AD) = 525.

Description:
Every attack, Titanic hydra applies an additional 26 physical damage, creating a shockwave that deals 84 physical damage to enemies behind the target.

Test:
Ulting a 1000HP dummy with 0 Armor/MR yields 98 damage from Titanic Hydra.

x=98/26=3.769

However, this is where the item gets weird:

As soon as enemies stand behind one another and get hit by the Cleave AOE, the damage gets wonky.

Ulting 2 or 3 enemies that are not close to each other yields exactly 622 damage per enemy, as expected.

Ulting 2 people standing behind one another, we would expect the enemy further away to take more damage due to the Cleave passive: “a shockwave that deals 84 physical damage to enemies behind the target

And if the second enemy is standing just outside the ultimate range, this actually does happen: The first target will normally take 622 damage with the target behind it taking 325 damage, which is 84 (Cleave damage) applied 15 times at 25% efficiency, just as expected.

If however both enemies stand within ult range, the damage increases in an inconsistent way.

Over 20 different ults, these are the average damage values for the close target (T1) and the far target (T2), where T2 stands withing Cleave range of T1 (or: right behind it)

T1: ~852.8 damage
T2: ~685 damage

This is surprising, because apparently the closer enemy takes more damage?

The total average damage dealt to these two enemies is around 1537, which is roughly the normal damage of 622 (times two) plus 293, which is close to the 325 damage we would expect the Cleave passive to do.

I assume that, similiar to Kraken, the Cleave damage gets distributed almost randomly, with Hydra sometime proccing Cleave on one target, then on the other. This is an issue that arises when several enemies get hit with Katarinas ult daggers at the same time: Only one target at a time will Cleave enemies behind it.

If we ult 3 people standing in a row, these are the average damage values for the close target (T1), the middle target (T2) and the far target (T3):

T1: ~734 damage
T2: ~820 damage
T3: ~683 damage

As random as this seems, again this is roughly equal to normal damager per targt (622*3) + 325 (normal Cleave damage), which gets randomly distributed, in reality that number is at 371 here.

Conclusion:
Every enemy takes at least the normal Titanic Hydra on-hit damage, and most of the time a bonus damage of roughly Cleave-damage*15*0.25 will be distributed seemingly randomly among enemy targets, but only if they stand close to each other, sometimes doing more Cleave damage total, sometimes less.

3) THE DEFINITELY BROKEN ITEMS

—–Ravenous Hydra:—– (PROCS ONCE AT THE START, DOING FULL DAMAGE AGAINST 2 ENEMIES AND 50% DAMAGE AGAINST 3 ENEMIES)

Stats:
136 AD, 0 AP, R damage total: 375(AP) + 217(AD) = 592

Description:
Attacks and abilities deal up to 81 damage to other enemies near target hit.

Test:
Ulting a 1000HP dummy with 0 Armor/MR yields exactly 592 damage, Hydra doing 0.

Let’s put 2 identical dummies next to each other and try again.

Ulting two 1000HP dummies on top of each other with 0 Armor/MR yields exactly 673 damage per dummy, Hydra doing 81. Looking at the ult in practice tool, you can see that Hydra damages both dummies once at the start (fulfilling the “abilities deal damage” – part) at 100% damage, but doesn’t damage the dummies on consecutive dagger ticks at 25% damage (not fulfilling the “attacks deal damage” – part).

Putting 3 identical dummies right on top of each other yields 244 total damage done by Ravenous Hydra, which is 244/81 = 3 procs at 100% damage.

Conclusion:
Enemies cannot get hit with more than one Hydra AOE in Kats ult, even if more than two enemies are standing next to each other.
I consider this interaction as probably not working as intended.

—–Kraken Slayer:—– (PROCS 5 TIMES, EFFICIENCY NOT REDUCED TO 25%, TRUE DAMAGE DISTRIBUTED UNEVENLY AGAINST SEVERAL TARGETS, MATH BELOW)

Stats:
131 AD, 0 AP, R damage total: 375(AP) + 215(AD) = 590.

Description:
Every third attack, Kraken deals an additional 78 True Damage.

Test:
Ulting a 1000HP dummy with 0 Armor/MR yields 390 damage dealt from Kraken.

x=390/78=5

Conclusion:
Kraken applies its damage 5 times total, which means it procs on every third ult hit, without getting it’s damage reduced to 25%.

Keep in mind that Kraken can have uneven distribution of its true damage due to every third total dagger proccing the true damage, as opposed to every third dagger per enemy. This means that, if you ult 3 people, one champion could get hit by Krakens true damage 11 times, the second enemy 4 times, and the third enemy 0 times. Predicting the targetting of Kraken against moving opponents curently seems impossible.

Thanks for reading! If you have any questions, please go ahead and write a comment.

Stream Link: https://www.twitch.tv/katastrophical_lol
Discord for more Katarina discussion: https://discord.gg/GJAvDuA

Tl;dr: Spellblade items, Bork, Nashors, Black Cleaver and Wits End work as intended, Ravenous Hydra and Guinsoo’s are weird in a bad way, Titanic Hydra is weird in a good way, Kraken is broken in a very good way.

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