# League of Legends (LoL) Question: What is the opportune time to buy the new Last Whisper?

Posted in Items | Tags: Last Whisper Riven 4,440

#### What is the opportune time to buy the new Last Whisper?

I've done a TON of math on this. It seems that there is a pretty accurate time of ~ lv 5 and they have 50 bonus armor. Then I have to factor in all my abilities for Riven and her passive and how much the bonus armor percentage will increase percentage of damage dealt at further levels as base armor increases decreasing bonus armor's effectiveness and thus, LWs.

Here's all the work I've done on it so far. If someone could tell me if this is correct and/or their input on it all.

I'm just going to simplify this the best I can. In the early game, if you rush this item when they rush chain, you will deal 8.37% increased damage, assuming they have no armor runes... If they have armor runes (just yellows) you will deal 9.16% increased damage.

After you come back to lane again, Let's say you've picked up 25 AD. Those percentages skyrocket. That 9.16 turns into 10.955. That's just picking up a pick axe, let's say you get 40 damage and it becomes 12.1%.

The equation is AD x (100/100+(armor)) If your AD is 100, and they have no armor. Your attack will deal 100 damage

100 x (100/100) = 100

The reason these percentages increase, is that a percentage that was 8% damage at 100 damage, will scale up to 16% at 200

100 x (100/163) = ~8% difference with LW

200 x (100/163) = ~16% difference with LW

If I'm wrong on any of this math, please prove it to me, but if this works how I've put it, LW is an EXTREMELY strong item on its own right now, and just gets better as the game goes on.

Just now I played 2 custom games with a friend

One where I rushed LW

One where I rushed Pick axe LS

In both games I had LS as starting item

My friend had a total of 50 bonus armor

Results of first game (LW rush) 25 AD and 30% bonus armor pen

auto deals = 66 base (82) enhanced

57 w

62 q

Results of second game (AD rush) 35 AD

Auto deals = 66 base (83 enhanced

58 w

59 q

So, why does this make sense? the q has a 50% scaling with AD, so the % damage was worth more by far. The w has 100% AD scaling, meaning the AD was more worth it if its dealing less than 100 damage

Here's all the work I've done on it so far. If someone could tell me if this is correct and/or their input on it all.

## Math

I'm just going to simplify this the best I can. In the early game, if you rush this item when they rush chain, you will deal 8.37% increased damage, assuming they have no armor runes... If they have armor runes (just yellows) you will deal 9.16% increased damage.

After you come back to lane again, Let's say you've picked up 25 AD. Those percentages skyrocket. That 9.16 turns into 10.955. That's just picking up a pick axe, let's say you get 40 damage and it becomes 12.1%.

The equation is AD x (100/100+(armor)) If your AD is 100, and they have no armor. Your attack will deal 100 damage

100 x (100/100) = 100

The reason these percentages increase, is that a percentage that was 8% damage at 100 damage, will scale up to 16% at 200

100 x (100/163) = ~8% difference with LW

200 x (100/163) = ~16% difference with LW

If I'm wrong on any of this math, please prove it to me, but if this works how I've put it, LW is an EXTREMELY strong item on its own right now, and just gets better as the game goes on.

Just now I played 2 custom games with a friend

One where I rushed LW

One where I rushed Pick axe LS

In both games I had LS as starting item

My friend had a total of 50 bonus armor

Results of first game (LW rush) 25 AD and 30% bonus armor pen

auto deals = 66 base (82) enhanced

57 w

62 q

Results of second game (AD rush) 35 AD

Auto deals = 66 base (83 enhanced

58 w

59 q

So, why does this make sense? the q has a 50% scaling with AD, so the % damage was worth more by far. The w has 100% AD scaling, meaning the AD was more worth it if its dealing less than 100 damage

Ki Burst has scaling with 100% bonus AD

Broken Wings has scaling with 100% total AD

Hence why the damage ratios are skewed.

As for the math...

If your opponent has 100 armor, if you'd have done 100 damage, you'd do 50, since armor damage reduction is f(x)=(100/100+x){x>0}

As such, the damage you get from increasing AD will scale linearly, according to the function f(x)=x*damage multiplier

Here's a graph that'll help you visualize

Here's more math I did on it

At 500 bonus armor = 5.555 % increased

At 400 = 6.3

At 300 = 7.2%

At 200 Bonus armor = 8.4 % increase

At 100 bonus armor = 8.8% damage increase

At 90 bonus armor = 8.7 %

At 80 Bonus armor = 8.54 %

At 70 Bonus armor = 8.3

At 60 Bonus armor = 7.9 %

At 50 Bonus armor = 7.4% .

At 40 Bonus armor = 6.7

At 30 Bonus armor = 5.72

At 20 Bonus armor = 4.3 %

At 10 Bonus armor = 2.55 %

At 5 Bonus armor = 1.3%

Those are the percentages I found using the formula. This is what it increases your damage by. I figured 7-8.8% damage was better than 12.5 damage based on that math. Yet, this slows down your build overall and doesn't deal that much to champs without much bonus armor. Thankfully in considers runes, but that's not enough. 100 bonus armor is the best point that I could find, BUT, that doesn't mean that its not worth buying before that, right? This is partly because when you're level 5, your q should be dealing very close to 100 damage, but you don't want to get it first item because you don't have a big value of AD to work with in the first place. Its factoring in all her various ratios it makes it extremely hectic, as well as base armors for champions.

I mainly want a direct correlation between an increase in damage dealt, and a flat increase in attack damage. I want to know when the percentage is undeniably worth it. What base AD, vs what bonus (and base) armor. Its absurdly difficult work, and you can clearly see that I've spent plenty of time working at it.

I figure someone can help me explain it simply, yet I don't have the endurance to compare both of those since %damage and flat AD can be compared in so many ways.