Luden's Echo and the numbers behind it.

First let me preface this with the fact that it's my first time doing this for league of legends. I kept talking with friends about the item and wanted to share what I've came up with. I've not did a lot of research into other works so don't hold it against me. I'm open to constructive criticism and will admit when I am wrong and give credit where it is due. Now lets jump into the post!

TL;DR: Luden's Echo has an extremely gold efficient passive(early to mid game). Coupled with low CDR abilities on champions + elixir of sorcery is one of the biggest spikes you can get. Great for wave clear and tower seiging. Late-game, the passive falls off drastically.

Luden's Echo and the numbers behind it.

First let us refresh everyone with the item: Luden's Echo 120 Ability Power 7% Movement Speed

UNIQUE Passive: Gain Charges upon moving or casting. At 100 charges, the next spell hit expends all charges to deal 100 (+15% AP) bonus magic damage to up to 4 targets on hit.

Recharge Rate: 20 Per Spell cast 6-10 per second of movement (no boots, may be tied into how far/fast you move?)

At first glance, this item seems to be awesome. Some people get it as their first item. Some people get it as a last item. We will explore the benefits of this item (mainly the passive).

Lets start with the fact that all champions start with a minimum of 30 Magic Resistance at level 1 (32.1 is the highest). Stat gain for "most" melees goes up to 53.4 at level 18. (Bard/Gnar/MaoKai/Poppy/Shen/Singed/Yasuo do not gain). 30 MR and 53.4 MR equate into 23.1 and 34.82% Damage reduction. Standard**(1)** Magic Resist glyphs give 1.34 each for a total of 12.06. Taking this into account level 1 players will have 42.06 Magic Resistance, for a total of 29.61% Damage Reduction.

Luden's Echo will do 119~ damage if it is the only item with ability power purchased (Includes bonus % from Masteries). The maximum this will do to a single**(2)** target will be 91.511 damage (0 Bonus MR on a champion 0 magic penetration).

Okay now that the basic math is taken care of lets venture into the land of theorycrafting.

The good thing about the passive on this item is that it replenishes fairly quickly and can hit up to 4 targets. Taking this into consideration it seems to start having some good output. In reality it's rare you will get good opportunities that this will hit 4 champions. Usually it's 1 champion + 3 minions or any combination of minions/champions. If you were to only attack and not move it would take 5 spell cast until it recharged. Moving while casting greatly lowers this.

As a first item you are gaining the poke/burst (however you want to look at it) as well as gaining movement speed. This is great for roaming/harassing. If you are using, for example, Katarina, you can have the passive charges up after a QWE combination (60/100 Charges and with the moving around you will be doing, by the time your combination is up again, you will have the charges). Effectively have a free 92 damage every 5-10 seconds. If you are not casting spells on a champion you will have 92 free damage every 10 seconds if you cast when it's off cooldown. We will call it an 11 second cool down for future reference (Travel Time + Reaction Time + 10 Seconds for it to recharge).

Every champion has different AP coefficients. In order to figure out the true gold value of this passive it would take a while (feel free to do this for your champions and it can be added). That being said we will use some generic AP coefficients. 20% AP 25% AP 30% Ap With the coefficients we can determine how much of a gold value this item gives in terms of damage. In order to get 92 bonus damage on a single target with a coeffecient of: 20% - 460 AP 25% - 368 AP 30% - 307 AP

Using these numbers we can determine that it would take 23 to 15.35 amplyfying tomes to increase your AP by that much to get the damage. At the highest coefficient the value of Amplifying Tome's would equal 6677~ the item cost 3100, making it very efficient.

In effect you are gaining 6677~ gold value every time you use the passive on this item.

Now let's begin to start adding some more Ability Power.

In order to gain an additional 100 damage on the item you would need 666.7 ability power. Masteries give 5% ability power so you would in essence only need 633.365, very easily doable late game.

As the game progresses, people gain more magic resistance and more health. The value of this item start to diminish for how much it actually does. Doubling the damage for it's passive cost more gold than it would be to buy AP + Magic Penetration + CDR.

Where this item shines

The item really shines with early game harass/burst. With the extreme cost efficiency of the item it is beneficial in almost every aspect. With the burst that it puts out early it can help secure those kills that almost get away. The movement speed increase on it allows for dodging / roaming better. Wave clearing/Tower seiging.

Where it lacks Make the effects more noticable.

Best coupled with Low CDR casters Elixir of Sorcery

(1) - Standard Magic Resist is the glyphs (blue) runes that most players run when versing an AP champion.

(2) - Single target is used as the least common factor when determining numbers as it is the lowest damage this will proc.