Talk:Evelynn/@comment-96.255.148.48-20130318015543/@comment-4840597-20130512083025

Ok. C = current hp, H = max hp.

Dfg : Unique: Deals 15% of target champion's maximum health in magic damage and applies the debuff, Doom. Doom amplifies all magic damage that champion takes by 20% for 4 seconds. 60 second cooldown

So dfg damage = 0.15H

Ult: Magic Damage: 15% / 20% / 25% (+ 1% per 100 AP) of enemies' current health

Let d = the percentage damage dealt by the ult.

So ult damage = dC.

Situation 1 - Ult then DFG

Damage taken is dC (from ult), followed by 0.15H, thus damage taken is dC+0.15H

Situation 2 - DFG then Ult

Damage taken is 0.15H, followed by 1.2dC, thus damage taken is 0.15H+1.2dC.

The C used in both of these equations is different, so for situation 1, I will use a capital c - 'C', and for situation 2, I will use a lower case c - 'c'.

Secondly, I will redefine 'C'/'c' as being a multiple of H. So if the person is at 90% hp, C would be 0.9H. This percentage of hp will be equal to p.

Looking back at situation 1, the damage is dC+0.15H, which I will rewrite as dpH+0.15H. I can then rewrite this again as H(dp+0.15). This means the damage dealt to the target is equal to the percentage damage of the ult, multiplied by the percentage of health of the target, plus 15%. So a basic rank 3 ult will deal H(0.25+0.15)=H(0.4) = 40% of the target's max hp in damage, when using your Ult followed by DFG active, on a full hp target.

Then looking at situation 2, the damage is 0.15H+1.2dc. As I mentioned earlier, c is in lower case for this situation, this is to represent the target's lower hp. However, lets convert this c (which is the target's current health after DFG damage) into C (the target's initial current health. c is 15% lower than C, because DFG deals 15% of thier max hp. so we can rewrite 0.15H+1.2dc as 0.15H+1.2d(C-0.15H). Since as mentioned before, C is pH, this can be wrote again as 0.15H+1.2d(pH-0.15H), and again as 0.15H+1.2dH(p-0.15), and finally as H(0.15+1.2d(p-0.15)).

To compare these two situations I can use an inequality. So lets say I want to know when situation 1, using Ult then DFG will result in higher damage than using DFG then ult.

Thus, if the damage of situation 1 is higher than the damage of situation 2, then Ult -> DFG will be superior.

So if H(dp+0.15)>H(0.15+1.2d(p-0.15)) is true, then using Ult followed by DFG will result in superior damage.

[What follows is derivation of general rule]

H(dp+0.15)>H(0.15+1.2d(p-0.15)) {Divide by H}{H is +ve, if it was -ve, then they'd already be deader than dead}

dp+0.15>0.15+1.2d(p-0.15) {take away 0.15}'

dp>1.2d(p-0.15) {Divide by d}{d is also +ve, unless you suddenly heal them with your ult}

p>1.2(p-0.15){multiply out}

p>1.2p-0.18 {collect p terms}

-0.2p>-0.18 {Divide by -0.2}{-0.2 is -ve, therefore flip inequality sign}

p<0.9

Therefore: If the target is below 90% health, ult first, if not, dfg first.

Examples: Target with 1000/2000 hp.

Ulting first @ rank 3 ult, no AP => 1000*0.25=250 damage. The dfg follows up with 2000*0.15=300 damage, for a total of 550.

DFG first @ rank 3 ult, no AP => 2000*0.15=300 damage, 1000-300= 700 hp left, 700*0.25=175, 175*1.2=210, for a total of 510 damage.

Target with 2000/2000 hp.

Ulting first @ rank 3 ult, no AP => 2000*0.25=500 damage, DFG follows up with 300 damage, for a total of 800 damage.

DFG first @ rank 3 ult, no AP => DFG deals 300 damage, target left with 1700 hp. 1700*0.25=425, 425*1.2=510 damage, for a total of 810 damage.

Target with 1800/200 hp (90% hp left)

Ulting first @ rank 3 ult, no AP => 1800*0.25=450 damage, DFG follows with 300 damage, 750 total.

DFG first @ rank 3 ult, no AP => DFG deals 300 damage, target left with 1500 hp, 1500*0.25=375, 375*1.2=450, for a total of 750 damage. The same as when ulting first.

As such, if they are above 90% DFG first, if they are below 90%, Ult first. However the difference is arguably marginal. Also, from a gameplay PoV, using ult first is both easier and is a safer choice, as your shield is given faster. As well as this, using DFG while gap closing means the DFG will hit as you reach them, so while your DFG may not be boosting your ult damage on that target, it may keep the debuff on long enough for an extra hatespike and lichbane, which may result in more damage.

TL;DR

- If the target is above 90% hp, use your DFG first.

 - If the target is below 90% hp, use your ULT first.

 - If you dont care, use your ULT first.

 - It is likely that using ULT first may result in more damage as your DFG debuff will be on longer for your hatespikes/lichbane procs.