14 April 2015 - 10:17
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Luden's Echo versus Rabadon's Deathcap (Crocodile Juniors full analysis)

The item Luden's Echo is on the live servers for a while now and it received a lot of negative feedback.
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The item Luden's Echo is on the live servers for a while now and it received a lot of negative feedback. According to the opinions of some E – sports authorities, Luden's Echo does not have a place in most champion builds or it might only be an option as a very late purchase in the game. I read a lot of babbling about the new item without any true evidence and I ask myself: why has it to be like that?

We have all the neccessary formulas and statistics to make fair comparison between items, so that we can actually calculate their effectiveness and see for sure how strong an item is. I sat down to do this analysis, so I can know exactly what Luden's Echo is worth and I am going to share it with you.

I start with the item itself, its statistics and its unique passive:

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So first of all, the item costs 3100 gold, gives you 120 ability power, 7% of movement speed and an unique passive.

Is this a fair price by Riot?

Like with all other items, you can calculate their gold efficiency by finding the gold value of each of their raw ingredients and then adding those together.

1 ability power has the gold value of 21.75 at the moment, therefore 120 ability power equals the gold value of 2610. 1 movement speed costs 13 gold, but Luden's Echo gives you 7% of movement speed. This actually means, that those 7% movement speed can give you more or less, depending on your base movement speed.

Luden's Echo is an item for magic damage dealers and it gets therefore also statistically seen mostly approached by mages, who have an average movement speed base of 330.

Many of those mages are immobile and rely on shoes and its upgrade, which adds 65 movement speed on top of the 330, capping at 395. Now you apply the 7% movement speed of Luden's Echo and you gain 27.65 bonus movement speed.

27.65 movement speed equals 359.45 gold.

The statistical gold value of Luden's Echo is 2969.45 in total for most mages and it has a gold efficiency of 95.7%. Its passive has to be worth atleast 130 gold to make this item 100% gold efficient.

This is the case for many final upgraded items in League of Legends like for example Blade of the Ruined King, Randuin's Omen or Void Staff. Their passive effects should be meaningful for the player to make up for the small gold inefficiency.

I can tell you already that Luden's Echo passive makes this item more than 100% gold efficient in pretty much every scenario, but I am going to look at the passive more closely right now.

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There are several parts about Luden's Echos passive that we can seperate.

There is the condition, that you have to charge it by moving around or spellcasting. The obvious conclusion of this is, that mobile champions with low cooldowns profit from the passive in a way, that they are able to charge it very quickly.

When you have fully charged it, you apply its passive with the next spellcast, provided it deals magical damage. At this point, champions who are able to apply Luden's Echos passive from a far distance away benefit in a siege scenario, I am looking at you long range mages!

And then of course, there is the proc (proc from "Programmed Random OCcurrence", meaning the actual functional part about Luden's Echos passive) itself, which deals 100 + 0.15 ability power (AP) magic damage and is AoE (AoE stands for Area of Effect and it means, that Luden's Echos passive damages several enemies).

Every champion benefits from bonus damage but you can make the argument that the AoE increases your waveclear and teamfight damage output.

The proc consists out of two damage instances:

Static 100 base damage, which scales with magic penetration

and

the bonus AP ratio of 0.15, which scales with ability power.

The static part assures a decent power boost when you build Luden's Echo early in the game. I can imagine a strategy working around the 100 base magic damage:

Games in League of Legends scale with a certain game flow. What I mean with this is, you can chill in your base but the damage of the minions and the turrets is going to ramp up over time. Every champions ability scales with a certain algorythm, same goes for the items. Go to the wiki and check out the ranks of the spells, their damage, their utility and so on scales from rank to rank with a set number.

You won't find an ability that for example begins with 60 base damage at rank 1, then goes up to 105 base damage at rank 2 and then suddenly jumps at 250 base damage at rank 3. But if you would, wouldn't that be a pretty significant boost in power?

Yes, it would be indeed. This is also referenced as "power spike", but it is not as drastically as shown in my example.

However, you will gain a power spike when you finished an item for example and in the case of Luden's Echos static 100 base damage, its power spike will be more recognizable when you buy it as early as possible. Given that you play one of the rare champions that can afford a very early Luden's Echo, you are then ahead of the game flow curve and can abuse this to pressure your enemies and take objectives.

Now back to Luden's Echos second damage instance - the bonus AP ratio of 0.15.

It enhances Luden's Echos late game strenght, when you usually have a lot of ability power.

Isn't this interesting? Luden's Echos passive synergizes with the early and late game at the same time. I like this aspect of the item.

So overall, the item itself looks really solid!

However, this doesn't mean anything so far.

If you want to rate items or champions in League of Legends, you have to compare them with the champions or items they compete with.

In the case of Luden's Echo, this item was ment to replace the old DFG ("Deathfire Grasp"). Luden's Echo is one of the three available 120 ability power items and therefore, it directly competes with Zhonya's Hourglass and Rabadon's Deathcap.

But I can already exclude the Zhonya's Hourglass as it satisfies the need of an item with a lot of ability power, coupled with the usage of a defensive passive.

Rabadon's Deathcap though, can be seen as the offensive counterpart to Zhonya's Hourglass and because Luden's Echo is an offensive item as well, the question arises now:

What is better, Rabadon's Deathcap or Luden's Echo?

I am going to answer this question for several areas but before I start, I want to talk shortly about itemization:

There are two ways you itemize, you either itemize for the most effectiveness of your champion or you itemize as a counter to an enemy champion or even several enemy champions at the same time.

Pretty much every champion has to build for his own effectiveness at the beginning in a game, I am talking about their ressources in general. Most mages are mana gated and their first choice of item purchase helps to reduce this limitation. It is very often either a Morellonomicon or an Athene's Unholy Grail, but it can also be a Tear of the Godess or a Catalyst the Protector.

Boots of Speed are a neccessarity for most champions during the early game and it is common that they upgrade them during the beginning of the midgame. In the case for mages, they mostly upgrade their shoes into the Sorcerer's Shoes, as they provide the cheapest mid game powerspike in the game.

Now, that those elementary needs are satisfied, the option of counter itemization arises. I'll stick to the mages here, as they most likely build Luden's Echo. If they face an AD assasine like Zed for example, Zhonya's Hourglass might be the better  choice for them, but if they feel save enough and just look out for more burst damage or more over all DPS, should they go for Luden's Echo or should they better go for Rabadon's Deathcap instead?

 

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versus

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In a direct comparison, Rabadon's Deathcap and Luden's Echo share the same amount of ability power, but they have different passives and Luden's Echo has also 7% of bonus movement speed going into its favour.

That said, 7% bonus movement speed is a sheer utility value and therefore hard to evaluate. It is situational but the bonus movement speed can make the difference between getting caught or being able to escape or getting in range for an attack or not getting in range for an attack and so on. However, the major different aspect are the unique passives.

Rabadon's Deathcaps passive gives you an ability power multiplier of 30%. The gold efficiency of this item increases when you have a lot of ability power, as it adds 30 bonus ability power for every 100 ability power.

The formula is:

Spell - AP - ratio * AP * 1.3 = Spell Damage

But not only damage, also ability power based utility spells like shields are affected by Rabadon's Deathcaps multiplier, which makes this item so great on champions like Lulu for example.

The areas where I want to compare Rabadon's Deathcap and Luden's Echo are: poke, burst, damage per second.

 

Poke

 

It is time to siege a turret with your allies down. You are grouped up in front of your enemies, who try to hold their spot and sustain under their turret. None of the two parties have great tools to engage the fight, but they are capable of some long range skillshots.

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A poke war begins.

In this situation, we do not care about how long it takes to fully charge Luden's Echos passive as we can simply do this by walking in a circle, neither are we interested in the answer of the question, which item (Luden's Echo or Rabadon's Deathcap) would be more effective during damage rotations.

Everything what now matters is the single spellhit damage.

As you can already imagine, Luden's Echo is most likely going to win this simply due to its 100 bonus magic damage.

But how does the actual comparison look like?

With Luden's Echo, you add a 0.15 bonus ability power ratio on top of your spells ability power ratio and 100 bonus damage when you proc the passive.

With Rabadon's Deathcap, you multiply the ability power ratio of your spell with its passives multiplier of 1.3 (30%).

I use Xeraths long range spell "Arcanopulse" as an example. This spell has an AP (ability power) ratio of 0.75 and does 240 magic damage at rank 5.

This spell has an AP ratio of 0.9 and deals 340 magic damage at rank 5 if it procs the passive of Luden's Echo.

This spell has an AP ratio of 0.975 and deals 240 magic damage at rank 5 if you have Rabadon's Deathcap.

Different scalings are working here.

You have a multiplicative gain with Rabadon's Deathcap and its actual increase depends on how high your spells AP ratio is.

AP - ratio AP - ratio * 1.3 AP - ratio gained
1.1 1.43 0.33
1.0 1.3 0.3
0.9 1.17 0.27
0.8 1.04 0.24
0.7 0.91 0.21
0.6 0.78 0.18
0.5 0.65 0.15
0.4 0.52 0.12
0.3 0.39 0.09

But you have a constant additive gain of 0.15 bonus AP plus the 100 base damage with Luden's Echo.

How much AP would you need with Rabadon's Deathcap to outtrade Luden's Echos linear scaling passive?

I did the calculations for the most common AP ratios and you can see it here:

AP - ratio   AP needed
1.0 = 666,67
0.9 = 740,740
0.8 = 833,33
0.7 = 952,38
0.6 = 1111,11
0.5 = 1333,33
0.4 = 1666,67
0.3 = 2222,22

Overall we can clearly see, Luden's Echo wins in a siege/poke - heavy environment.

 

Burst

 

There are the so called "burst mages" in this game and their sole job is to blow one target up with a single rotation of their cooldowns. They have most commonly one initiation spell that they rely on to hit, which then again allows them to set up their following burst.

Veigar is one of those burst mages and he needs to hit his "Event Horizon" ability, so he can hit his "Dark Matter" with a much higher reliability, as this spell comes with a delay.

Another example would be Lux. Her initiation spell is her "Light Binding". Given that she hits it, she is free to combo her skill shots onto the enemy, including her laser ultimate.

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Her ideal burst rotation would be:

Type Q + AutoAttack + E + R
Name Light Binding   Illumination   Lucent Singularity   Final Spark
AP - ratio 0.7   0.2   0.6   0.95

As you can see, there is an interaction of spells and autoattacks within one rotation, but autoattacks do neither charge, nor proc Luden's Echo.

Although Lux spells have fairly high cooldowns, therefore we can assume that Luden's Echos passive will be up again for her next spell rotation, given that she moves a bit to get the last missing charges.

Now, according to our item comparison, which spell rotation would do more damage in total?

To find the answer, we have to add all AP ratios within the rotation:

0.7 AP + 0.2 AP + 0.6 AP + 0.95 AP = 2.45 AP

2.45 is the total AP ratio of the rotation and it is 3.185 AP with the Rabadon's Deathcap passive. Luden's Echos total AP ratio would be 2.6 (2.45 + 0.15) + 100 bonus damage though.

Rabadon's Deathcap has 0.585 bonus AP ratio over Luden's Echo, but Luden's Echo still has the flat 100 magic damage going into its favour. Once again the question arises, at which point is Rabadon's Deathcap going to outtrade Luden's Echos linear scaling?

The formula for this is: 100/0.585 = 170.94

Lux's burst rotation is going to do more damage with Rabadon's Deathcap than Luden's Echo, when she has atleast more than 170 ability power.

 

Damage per Second

 

How does this work with DPS (damage per second)?

Now we need DPS - heavy mages like Karthus or Cassiopeia, champions who have low cooldown spells and can therefore deal constant magic damage.

I use Cassiopeia as the example for this: she relies on hitting either her Q - "Noxious Blast" or W - "Miasma" poison.

When she fulfills this condition, her E - "Twin Fang" cooldown gets reduced to only 0.5 seconds, allowing her to spam - cast this ability.

So, her main source of damage comes from her "Twin Fang" ability and her spell rotation starts with the poison set-up, followed by many "Twin Fang" casts and then furthermore mixing one of her poisons in, to keep the "Twin Fang" cooldown low.

Example rotation:

Q - E - E - E - E - E - Q

At this point we need to know how many charges your champion can get during his rotations through mobility only. If you do only kite or chase your target, you can assume that you will get atleast one charge, if not two actually.

An important note here: every position displacement counts towards gaining charges. This includes summoner spell "Flash", dash abilities, homeguard or even summoner spell "Teleport".

For once, I will calculate this as if Cassiopeia wouldn't move at all during her rotation, so she would need 5 spellcasts to fully charge her next Luden's Echo passive.

I do the same calculation I did before and add all AP ratios within the rotation:

Luden's Echo           Luden's Echo
100% 20% 40% 60% 80% 100%  
Q E E E E E Q
0.45 AP 0.55 AP 0.55 AP 0.55 AP 0.55 AP 0.55 AP  

3.2 total AP, 4.16 with Rabadon's Deathcap and 3.35 total AP with Luden's Echo.

Total AP difference: 0.81

Formula: 100/0.81 = 123.45

Only roughly 123 ability power is with Rabadon's Deathcap neccessary to outtrade Luden's Echo, but keep in mind that I did not include movement based gained charges.

So DPS wise it seem that Rabadon's Deathcap is the smarter first purchase, although it would need a lot more AP if your DPS champion is able to charge 1 or even 3 charges via mobility.

 

Conclusion

 

We can welcome a second very offensive item with 120 ability power next to Rabadon's Deathcap. You will need all three 120 AP items, if you aim to achieve the highest AP pool in the lategame and overall Luden's Echo scales greatly with a lot of ability power.

When it comes to the question, which of the two items (Rabadon's Deathcap or Luden's Echo) you should buy FIRST... well the answer of this question depends on several factors that I have mentioned in this article before.

Meaningful in this sense is the way you want to deal your damage (poke, bursty and so on) and also of course how greatly your champion synergizes with Luden's Echo (can he quickly gain charges through movements? How high are his AP - ratios? And so on.)

 

Synergies

 

At the end, I want to list some champions that have certain synergies with Luden's Echo:

AP Kog'Maw:

Besides the fact that he is immobile and therefore heavily evaluates bonus movement speed, Kog'Maw is one of the best, if not THE BEST long range sniper champion in this game. Given that he rushes Luden's Echo fairly early in the game, the 100 flat magic damage from Luden's Echo are going to HURT A LOT.

Twisted Fate:

Player like Jeong "Apdo" Sang-gil prefer to run movement speed quints on this guy and they do this for a good reason: Twisted Fate is all about quickly running into the range of his target to set up his initiation spell, the "Gold Card", then doing his damage and quickly disengaging afterwards. Twisted Fate loves the 7% MS (movement speed) from Luden's Echo and it scales greatly with the MS multiplier from Lich Bane as well. Not to mention that his ultimate gives him a free charge on arrival.

All long range mages (note: if you prepare for a siege!):

Luden's Echo won the siege/poke war in my analysis, this one here should be obvious.

Evelynn:

Stealthy assassin, who can open the fight with an immediate boost in burst from Luden's Echos passive. Her sudden openings coupled with an increased burst at the beginning should lead to many enemies flashing because they panicked in situations, where maybe it wouldn't even have been necessary to flash at the first point. #psychology abuses

Ahri:

Another magey assassin. She received a MS steroid a few patches ago, which lets her charge Luden's Echo passive very quickly, plus her ultimate gives her 20% charges for each dash.

Bard:

I like to run it on him when I have a good time. He has garbage AP ratios but can make great use of the flat 100 base damage. He is very mobile and spam casts a lot, you might want to try it out.

 

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This article was written during the time of LoL patch 5.7.

Leave me some feedback. You can follow me on twitter or facebook.

https://twitter.com/Crocodile_JrYT

https://www.facebook.com/pages/Crocodile-Junior/1597324280495696

You can also check out my Youtube channel

https://www.youtube.com/channel/UCzFadMnJt0mCBC7P1uq5lvQ

or just mail me at

croc123doc123@gmail.com

 

 

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