See that items. Cause of it your damage dealt build is weak.

Hipotesys:

If your build have no Lich Bane, then, ALWAYS have an build with it that deal more damage.

That is the hipotesys I will prove to you. But before lets up our intuition about the power of this item seeing 2 builds that I craft for us.

Note: It don't consider combos, only final match damage. It less consider the difficult of play. It also consider that you ALWAYS, will play correctly.

Taking this lets see the first build of this guide: an AP Ashe. It can dealt considerable damage as well even she has only the Enchanted Crystal Arrow that scale with AP. Lets see it dps.

You gain 475 AP from items, 42.39 from runes and 24 from masteries: its is a total of 541.39, applying the Rabadon's Deathcap and Archmage bonus we will got 541.39*1.25*1.05 = 710,5 AP.
Note that we got 35% reduction with this items plus 4% from masteries we have an total 39% CDR. It Down the Volley's CD to 2,44 and Enchanted Crystal Arrow to 48,8s

DPS = damage/CD

Each volley will 'proc' an Lich Bane's passive and each 2,44s you will deal to one target: 80 + 0,75AP + 98 (base ad): (80 + 0,75*710+98)*1,02( Havoc = 724

DPS = 724/2,44=296.

That's mean that in each second of battle against one target that build will deal 296 damage (reductible), more precise 724 from each 2,44 CD circle.

Its quite low to be competitive but is high considering that her constant damage have no ap's scales. That dps come only from Lich Bane. Ashe has a low AD base and Volley has a low base damage. Let's take it from another point considering the second build.

The second build at this guide is an AP Skarner. His ap is 487 from items + 65,25 (2175*0.3) from Seraph's Embrace = 552,25

Applying the Archmage and Rabadon's Deathcap we got 552.25*1.25*1.05=724 AP

The interesting of Skarner is he has no combo. Due energize he can frenetic spawn his skills, granting a Lich Bane proc every 2s. Each Lich Bane proc grant 724*0.75 = 543 Auto-attack bonuus damage.

In 8s it is equal to 2174 FREE DAMAGE from it, pretty insane no?

Note that build is not an AP rush like talons build, it give all that an AP Skarner need.

Now that our intuition about the power of this items are high we can prove the initial Hipotesys for an AP build.

All items excluding by Rabadon's Deathcap, Deathfire Grasp and full stacked Mejai's Soulstealer can be trade for an Lich Bane for more damage.

AP is you normal build AP
SS is the damage scale of one AP spells

EX: Skarner Scales will be 0.4 is the SS of Shattered Earth, 0.7 is the SS of fracture, 0 is the SS of Seismic Bastion (it don't deal direct damage to oponents)

If the item you will trade is Zhonya's Hourglass you will loss 40 AP and it give no CDR

So we got it: (it is our Hipotesys for Zhonya's Hourglass)

LBD = (AP-40)*SS + 0,75AP (is the damage of a skill with Lich Bane)
ND = AP*SS (is the damage of you skill without Lich Bane)

we want to prove that (AP-40)*SS + 0,75 > AP*SS

(AP - 40)*SS + 0.75AP > AP*AS .:. AS*SS - 40*SS + 0.75AP > AP*AS .:. 0.75AP > 40*SS .:. AP/57>SS

the less AP u can have with this trade is 80 (from Lich Bane) taking this we got

80/57>SS<1,4

So if you have only the 80 AP Lich Bane and no more AP (it consider any item and runes/mastery)) a skill who have an 1,4 scale will do more damage damage with zhonyas The highest scale skill of the game is Absolute Zero with a 2,5AP scale and we take equal damage with 143AP IF YOU ARE TRADING Zhonya's Hourglass FOR Lich Bane.

Any other trade will let your AP Equal or better and of course Lich Bane will increase you damage.

Also, you always can trade an item that don't give CDR, so CDR don't need to enter in that count.

And with this considerations we prove that ALWAYS have an AP Build with Lich Bane who deal more dps than you common build.

So that mean i always must build Lich Bane?

No. Have heros that don't have any synergy with it. An iconic example is Gragas, his damage come from ranged skills and he is a meele champion, so to apply the Lich Bane proc he must be in meele range. It will crush you play style.

I hope you enjoy this little explanatory guide. And of course we can't forgot the Trinity Force, the AD version for Lich Bane. See the topic below and know her power in talon. (but i don't prove it too, it spend a lot of time *-*)

Its a Talon build. It has 19% CDR and total 430,3 AD Bonus and 121 AD Base. (551 total ad)

He's CD's low to 3.24, 8,1, 8.1 and 44,55.

Lets see he's dps with this combo sequence (2s with each Skill)


This is talon CD Cicle, At the end of this sequence with this 19 CDR, Talon will have all his skills out of CD and can do this combo angain, it take 8s. knowing this, lets Calc the damage of this combo.

Noxian Diplomacy = 150 + AD*0.3 + 2,5 AD (TF Proc+AD normal) + AD(normal Auto-atack beteween the skills) 4(50 + AD)/6 (bleed damage in 4 s) so we have this in some steps: 183 + 4,46AD

Rake = 130 + 0,6AD + 2,5AD*1,1(mercy) + AD = 130 + 4,35AD

cutthroat = 2,5AD + AD = 3,5AD

The combo will deal 183+4,46AD (1º ND) + (3,5AD(CR)+183+4,46AD(2º ND))*1,15(CR Passive))+130+4,35AD(RK) = 523 + 17,964AD = 9898,164 (plus Havoc but it don't interest to us) damage in 8s (4 skills)

it give us 9898/8 = 1237 Damage Per second or 9898,164 on each 8s until u have no mana. It is 4,17 more damage than the first build. Pretty more interesting no? with that damage u can kill the most tanky enemy on a single combo. Sona need one Noxian Diplomacy to die. with 48% lifesteal you can kill the baron nashor at 60 min of game with less than 2 combo.

The damage from Trinity Force is 1,5*4 = 6AD, 1/3 of that combo that means (551*6)=3306, considering that from an item, that damage is very very high.