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• If the increased physical damage from the 35% amour penetration can be thought of as increased AD, the passive must increase damage by 23.89 points (860g/36g per AD = 23.89 AD), in order to be gold efficient. For this to occur, “Arm*(AD-44.367) > 6825.7”, where Arm is the targets armour. This can be rounded to “Arm*(AD-45) > 7000”, for ease of remembering. A graph of the unrounded equation can be seen below.

An example of this is a champion with Last Whisper and 110 AD auto-attacks an enemy champion with 100 armour, the Last Whisper is not efficient (100*(110-44.367) = 6563.3 < 6825.7).

However if another champion with Last Whisper and 120 AD auto-attacks the same enemy champion, the Last Whisper is now efficient (100*(120-44.367) = 7563.3 > 6825.7)

The equation can also be applied to physical damaging abilities that scale with 100% AD, (such as Ashe’s Volley) by substituting the AD value on the Y axis, for the physical damage that the ability will do. If Ashe with Last Whisper and 130 AD auto-attacks an enemy champion with 50 armour, Last Whisper is not efficient (50*(130-44.367) = 4281.65 < 6825.7). However if she uses level 4 Volley with 65+130=195 damage, Last Whisper is efficient (50*(195-44.367) = 7531.65 > 6825.7).

These examples assume no other form of armour penetration/reduction. Due to this, the graph should only be used as a guide, as in game, there may be other sources of pentration.

As a general rule, the higher your AD and the higher the targets armour the more efficient Last Whisper will be.

• Why are you saying this? Almost every player above level 20 knows that you buy Last Whisperer on any champs that have a lot of AD Dmg.

• These calculations show when it is efficent to have Last Whisper. It allows you to determine when you should purchase Last Whisper in a build order. If you are facing opponents with low armor, it is more efficient to purchase more AD items instead. This explanation was originally on the Last Whisper page, but was moved here, and replaced with a simplified version on the Last Whisper page.

• In a nutshell, whatever the enemy builds, if you build even some AD, Last Whisper will be efficient in the late game amirite?

• I always consider which champions I'll be attacking most, when determining my item build.  If I'm an ADC, and will be constantly hitting the front line, I build last Whisper as a 2'nd or 3'rd item (assuming the enemy tanks build armor).  If the enemies I'll be attacking don't buy armor, I will just go straight for Infinity Edge as a 3'rd item.

• It is not so easy to compare the efficiency of items as such tho. Say you bought a PD as first item (that is an assumption, I know it sucks in most cases), then getting IE will be immensely effective, whereas getting LW will just suck.

What this graph teaches us is that going for BT + LW should be a decent choice (look at Graves). You will need other stats than AD at some point anyway (attack speed, movement speed). Would a non-crit build be decent? Something like Boots/BT/BT/Botrk/LW/Defensive item for retarded life steal build?

• It's very difficult to generate a general efficiency curve for Last Whisper because it is based on so many variables.  It's heavily dependent on the opponent's armor values, on your AD, AS, crit chance, and abilities.

A common goal for creating an efficiency curve is to compare Last Whisper to alternative sources of armor pen in an item build such as BC or YG.  In this case, the whole situation becomes even more complicated.

• "The equation can also be applied to abilities that scale with 100% AD"
What no it doesn't. You don't account for so many factors, but let's start with an easy one, base damage on skills.

deals 20/40/60/80/100 + 100% AD damage, while 60/95/130/165/200 + 80% bonus AD damage. Ignoring the difference in AD scaling, LW is better for Graves, because the higher base damage is also reduced by armor.

Let alone that you must assume some ability-to-autoattack-ratio, say 3 normal auto attacks every Gnar boomerang or something, but Caitlyn can stuff way more autoattacks inbetween two of her Peacemakers. The cooldown is also relevant in this, and the amount of damage abilities. A Riven can stuff you full of Q damage but it resets the aa timer every cast.

These examples assume no other form of armour penetration/reduction and 0% crit chance. How realistic.

They also assume the enemy's armor isn't increased by enemy champions, be they self- or allied-targeted buffs, like one of these. While you can say "just put the result number in the graph", you then have to estimate some ratio of "damage at buffed target"/"total damage on target".

has 100% AD scaling but deals magic damage, it benefits from AD but not from the penetration.

You can then calculate this for a single target, but for the whole item to be efficient you have to estimate the amount of damage at every different of the enemy champions, and even then it's not that simple. If getting AD instead of a LW would kill the adc faster but the tank slower, is that a bad thing? If you plan to only attack the tank, sure. But an adc taken out one second earlier could result in your teammate being alive. Then again, is anyone able to sufficiently damage the tankier enemies? Should you take on that role?

TL;DR: No, the calculation isn't that simple, graph is nearly useless. Yes, LW becomes better as the game continues, /copy "As a general rule, the higher your AD and the higher the targets armour the more efficient Last Whisper will be". Its efficiency is also greatly affected by which champ abilities you have, as well as your teammates and the enemy team. But most of all, it's a difference in playstyle; do you attack the high-armor characters more or the weak ones? Can you change that? Can the enemy force you not to?

TL;TL;DR: Dumbly buying LW as an "Xth" item is 'bad' no matter the X. But buying it too late hurts a lot more.

• Rakanishu2199 wrote:
In a nutshell, whatever the enemy builds, if you build even some AD, Last Whisper will be efficient in the late game amirite?

Well, kinda. If the enemy builds armor, Last Whisper would be the best option. But if they are not, it is better to build items with more AD instead of armor pen.

• Modified the post to take into account the comments above. Clarified the paragraph about abilities with 100% AD ratios. Removed the comment about being dependant on crit chance, (as the efficientcy of Last Whisper is not dependant on this). Adjusted the example for the change in damage of Ashe's Volley.

The efficency of Last Whisper is not directly dependant on attack speed, crit chance, or crit damage, it is dependant on the damage of your physical damaging abilities and their AD ratios if applicable.

Remember that different enemies may have different armor values, use this graph individually for each enemy, or just for the ones you plan on damaging.

• LW is a DPS multiplier. Your DPS is a product of Attack Damage, Attack Speed, Crit variables, and enemy resistance. With LW, you could say DPS resembles:

DPS = AD * AS * Crit Chance * Crit Damage * Enemy Resistance * (armor red/pen)

LW is just as related to AD as any of the others when it comes to overall DPS. If you want to talk about gold efficiency, then you have to include all the variables.

For example, you can have 1000 AD and your graph would show armor pen to always be the most efficient option even when the opponent has low armor, when in reality, especially against low armor opponents, the most gold efficient option would be to buy some attack speed or crit.

All your graph does is look at a single dimension. You need a 6 or even 7 dimensional graph to really do it. It's too complex to ever be generalized as you are trying to do. If you want remotely accurate results you'd have to do it case by case every time.

• Blaisem wrote:

All your graph does is look at a single dimension. You need a 6 or even 7 dimensional graph to really do it. It's too complex to ever be generalized as you are trying to do. If you want remotely accurate results you'd have to do it case by case every time.

OP Wrote:
If the increased physical damage from the 35% amour penetration can be thought of as increased AD, the passive must increase damage by 23.89 points (860g/36g per AD = 23.89 AD), in order to be gold efficient.

It only looks at whether it'd be efficient in terms of gold/gold of AD.  It's also outdated and it only affects Bonus Armor now.