League of Legends

Liandry’s vs Luden’s [LEC] – Which one should Abbedage have bought? Let’s do some math!

Hello everyone!

As some of you may know, yesterday G2 and S04 played a Bo5 series, and for game 5 Abbedage, who was playing Azir, bought Luden's Tempest instead of Liandry's Anguish as a Mythic item, which raised some criticism in the post-game thread, and on Twitter. Even the guy himself tweeted after the game.

With that said, I decided to run some numbers and see how much of a difference either Mythic would make at the later stages of the game, keeping the rest of his build but swapping the Mythic item. (TL;DR at the end)

I wanted to keep things more or less realistic, without getting too lost on details, so before anything else I checked (in between the item builds, levels, and the hovers and camera pans on the different players) the stats of each of G2's champions near the last teamfight of the game:

HP and Magic Resist for each G2 champion (may have minor differences to the actual game)


Afterward, I did the same thing for the Azir relevant stats, namely AP, Flat Magic Penetration, % Magic Penetration.

  • Build 1 (Actual Abbedage build) – Luden's Tempest, Rabadon's Deathcap, Void Staff, Zhonya's Hourglass, Sorc Shoes, Oblivion Orb
  • Build 2 – Liandry's Torment, Rabadon's Deathcap, Void Staff, Zhonya's Hourglass, Sorc Shoes, Oblivion Orb

Azir's combat stats (AP value assumes two AP runes)

We can already see that, aside from some of the passives associated with the two Mythic Items, the Luden's build has a higher flat magic penetration than the other one.

With that said, I decided on two trades to compare the two builds:

  • A longer trade: 5 auto-attacks (with 3 sand soldiers), 2 Q's, 1E, 1R – For purposes of Liandry's burn I assumed the trade went for 8 seconds, which burns for a total of 12 seconds because it remains burning for 4 seconds after the trade ends). For purposes of Luden's, with the new reduction of the passive cooldown, I assumed that in those 8 seconds, the Luden's damage would proc 3 times. (To summarize – 12 seconds of burn for Liandry's, and 3 Luden procs)
  • A shorter trade: 2 auto-attacks (with 3 sand soldiers), 1Q, 1E, 1R – 4 seconds of trade duration (8 secs of burn) and 1 Luden's proc.
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Having both the trades and the combat stats for all champions involved, I calculated the modifiers to the magic damage, according to the Magic Resist (after Flat and % Magic Penetration), and the Liandrys Bonus damage according to the champions' bonus health:


Since both builds have the same AP numbers, the raw damage from both trades will be the same. The difference makers will, therefore, be the difference in magic penetration between the two builds, and the difference in the passive applications (Luden Procs vs Liandry's Amplified Damage and Burn). The graph below shows the calculated damage (post magic reduction, considering the passives of both items – which means, the real damage the champions would take in that trade). It also shows the HP of each Champion:

Damage dealt to each champion with both builds, for the long and short trade

Some takeaways from the graph:

  • The results show that the only champion against which building Liandry's is more powerful is Sion (and the difference is not insanely significant)
  • Admittedly, the damage numbers of the long trade result in overkill for all the other 4 champions, so one can argue that you might as well buy Liandry's, since the combo will kill the other 4 champions anyways.
  • For the shorter trade, both Gragas, Volibear and Sion would survive. For Gragas and Voli in particular, both builds achieve nearly similar damage outputs.
  • The favoring of Luden's has a few reasons:
    • Low magic resist numbers – with higher MR levels, especially on the champions with higher HP, the added flat magic reduction would be slightly less impactful.
    • Low HP values and Low Bonus HP values on Lucian and Seraphine – This impacts both the burn damage (Torment) and the amplification of magic damage (Agony). Combine that with the low MR of those champions, and Luden's value is amplified.
  • The main takeaway for me is that even though, for practical terms, you could argue that Liandry's would be better for dealing with Sion in longer teamfights, the difference is not that significant.
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Things that weren't considered in this analysis but should be noted because they impact the teamfights:

  • The Liandry's burn grants the application of Grievous Wounds for longer periods of time.
  • The Liandry's build has 55 ability haste, compared to 40 from the Luden's one (considering Transcendence rune at lvl 18) – in a 8-second trade you could maybe squeeze in an additional Q with the Liandry's build (so, 3 Q's as the CD becomes 3,9 secs) but the relationship of the graph would remain the same (only favored for Sion).
  • Luden's gives bonus MS when proccing the passive.
  • Luden's procs hit 3 additional champions (so added damage that wasn't considered here).
  • EDIT: Because people are arguing in the comments over the application of the Grievous Wounds with the burn: the normal application of grievous wounds lasts for 3 seconds, so Azir would have to be 3 seconds without doing damage during the trade for the burn application of the GW to be relevant (in a beneficiary way for Liandry's). The period post-trade (or when Azir stops hitting for a long time) is where the burn can actually be useful because it extends the burn for 4 plus seconds).

TL;DR: It isn't that clear-cut that if Abbedage built Liandry's instead of Luden's the results would be significantly different.

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Bonus:

For the long trade (8 seconds with 2Q's, 5AA, 1E, 1R – 12 sec burn or 3 Luden procs) I created a chart that lets you know which item would be more useful in the build, according to the enemy's HP and MR. For the purposes of calculating the bonus HP (for the Agony passive), I had to assume an arbitrary number for the base HP, which I set as 1900. The area with two colors is the range in which the damage between the two builds with the full combo varies between -50 and +50 for either side.

Liandry's and Luden's sweet areas according to enemy's MR and HP

EDIT: Bonus 2:

Someone asked for a comparison with the old Luden (before 11.6) where there was Magic Resistance Shred but there was no damage Amplifier!

So here's the graph, with the shred roughly averaged across the trade duration.

Thank you for reading! If you have any suggestions or want different trades compared, let me know and I can give it a try!

Another Edit: Thank you so much for the awards everyone!

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