![Liandry’s vs Luden’s [LEC] – Which one should Abbedage have bought? Let’s do some math!](https://thinkofgames.com/wp-content/uploads/https://digilord.nyc3.digitaloceanspaces.com/server.digimetriq.com/uploads/2021/03/word-image-4843.png "Liandry’s vs Luden’s [LEC] – Which one should Abbedage have bought? Let’s do some math! 17")
As some of you may know, G2 and S04 played the Bo5 series yesterday, and in game five Abbedage, playing against Azir, bought Luden’s Storm instead of Liandry’s Torment as a mythic item, which drew some criticism in the post-game thread and on Twitter.
Even the man himself tweeted after the game.
In doing so, I decided to do some calculations and see what value a particular myth would have in the later stages of the game, keeping the rest of my design but replacing the mythic element. (TL;DR at the end)
I wanted it to be more or less realistic without losing too much detail, so I mainly checked (between item builds, levels and skirmishes and cameras on different players) the stats of each of the G2 champions near the last team fight of the game :
HP and magic resistance for each G2 champion (may have minor differences from the real game).
Then I did the same for the corresponding values of Azir, namely: AP, flat magic penetration, % magic penetration.
- Building 1 (current abbey construction) – Luden’s Storm, Rabadon’s Death Blanket, Empty Staff, Jonja’s Hourglass, Zork’s Shoe, Power of Oblivion.
- Building 2 – Liandri’s Torment, Rabadon’s Death Shell, Empty Wand, Jonja’s Hourglass, Zork’s Shoe, Orb of Oblivion.
Asir’s combat stats (AP value implies two AP runes)
We can already see that, apart from some passives related to the two mythic elements, Luden has a higher flat magic penetration than the others.
With that in mind, I decided to make two swaps to compare the two builds:
- A longer deal: 5 auto-attacks (with 3 sand soldiers), 2 Qs, 1E, 1R – For the purposes of Lindry’s Burn, I assumed the deal lasts 8 seconds, which burns for a total of 12 seconds, because it burns for 4 seconds after the deal ends). For Luden’s purposes, with the new passive cooldown reduction, I assumed Luden’s damage is reduced by a factor of 3 during those 8 seconds. (Summary: 12 seconds burned for Lindrey and 3 procs for Luden).
- A shorter trade: 2 auto-attacks (with 3 sand soldiers), 1Q, 1E, 1R – 4 seconds trade duration (8 seconds burn) and 1 Luden proc.
Since I have the trade and combat values for all participating champions, I calculated the modifiers for magic damage based on magic resistance (per Plat and % magic penetration), and Liandry’s damage bonus based on the champions’ health bonus :
- Magic damage multiplier due to magic resistance, for each Azir building.
- Lindry’s Agony magic damage bonus – I assumed it increased incrementally, not linearly, according to the wiki. Not 100%. I’m sure it’s the right thing to do.
Since both constructions have the same number of PAs, the gross damages of both offers are the same. The difference will be the difference in magic penetration between the two builds, as well as the difference in passive uses (Luden’s procs vs. Liandry’s Boosted Damage and Burn). The table below shows the estimated damage (after mage reduction, taking into account the passives of both items – so the actual damage the champions do in this deal). It also shows the HP of each champion:
The damage done to each champion by both constructs, for both long and short trades.
Some conclusions from the diagram:
- The results show that the only champion Lindree is building against is Zion (and the difference isn’t crazy significant).
- It’s true that the amount of damage from the long trade leads to an overbid for the other 4 champions, so you could argue that you might as well buy Liandrys since the combo will still kill the other 4 champions.
- For the shortest exchange, both Gragas and Volibear and Zion will survive. Especially with Grahaz and Will, both builds get almost identical damage results.
- There are several reasons for Luden’s benevolence:
- Low Magic Resistance – At higher MR levels, especially for champions with higher HP, the extra flat magic reduction would be slightly less impressive.
- Low HP and low HP bonus on Lucian and Seraphina – this affects both burn damage (Torment) and magic damage increase (Torment). Combine that with the low MRT of these champions, and the value of Luden is reinforced.
- The main conclusion for me is that while one can argue from a practical standpoint that Leandri can handle Zion better in longer teamfights, the difference is not that significant.
Elements that were not considered in this analysis, but should be because they affect team fights:
- With a Lindrie burn, you can apply for Serious Wounds for an extended period of time.
- Lindri’s build has 55 rush abilities, compared to Ludens’ 40 (given the transcendence rune at lvl 18) – you could put an extra Q into an 8 second deal with Lindri’s build (so 3 Q in CD becomes 3.9 sec), but the graphics ratio would remain the same (and only favor Sion).
- Luden’s gives a bonus of MS when preparing passives.
- Luden’s profiles hit 3 other champions (so the extra damage doesn’t count here).
- EDIT: Since people in the comments are discussing Severe Wounds’ burn application: the normal application of Severe Wounds lasts 3 seconds, so Azir has to do 3 seconds of no damage while acting to make GW’s burn application relevant (as a beneficiary of Liandry’s). In the post-hit phase (or when Azir doesn’t hit for an extended period), the burn can be really useful, as it extends the burn by 4 seconds or more).
TL;DR : It is not certain that the results would have been significantly different if Ebbedage had built Lindrie instead of Luden.
Bonus:
For the long swap (8 seconds with 2Q, 5AA, 1E, 1R – 12 seconds burn or 3 procs of luden) I made a table to see which item would be most useful in the build depending on the HP and MR of the opponent. To calculate the HP bonus (for the agony passive), I had to take a random number for base HP, which I set to 1900. The two-color area is the area where the damage between two full combos varies between -50 and +50 for both sides.
Lindry and Luden soften zones based on the opponent’s MR and HP.
EDIT: Bonus 2:
Someone asked for a comparison with an old Luden (pre 11.6) where there was a Magic Resistance patch, but no damaged amp!
So here’s the chart, with a portion roughly averaged over the duration of the transaction.
Thanks for reading! If you have any suggestions or want to compare different quotes, let me know and I’ll give it a try!
Another overview: Thank you all for the prizes!
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