Hi, I'm InvertedDisciple a League of Legends theorycrafter. I've been trying to reach out to people in the pro community because I think most pros aren't itemizing optimally. But I haven't gotten much of a response so I decided to post a little bit of my math on reddit.
It appears to me most pros buy items based on what feels good instead of math. However calculating the optimal build can give you a substantial advantage. This math is about what the best 3rd item on MF is, assuming you want an offensive item as your third item.
This math is about crit MF but at the end I will also give you my quick thoughts on Manamune Lethality MF.
Scroll down for TL;DR
Level 15 Miss Fortune, third item damage math.
Most pros buy Essence Reaver, Berserker's Greaves, Infinity Edge and Firecannon on MF when they’re trying to build damage. In my example I will calculate which is better, Firecannon or Lord Dominik's.
Dominik's costs 2800 gold and Firecannon costs 2600 gold. In order to adjust for the gold cost difference I will add 8% AS to Firecannon since 8% AS is worth 200 gold making it so both items effectively cost 2800 gold.
The target enemy I'm using is a level 15 Kalista with no armor items or armor runes which means she has 74 armor, giving her 42.5% reduced damage from physical damage.
Vs Dominik's, her armor is reduced by 35% giving her 48 armor and 32.4% reduced damage from physical damage. To get the armor reduction multipliers we take 1-0.425=0.575 and 1-0.324=0.656.
Firecannon deals 120 magic damage roughly every 9 autos. Kalista has 37 MR giving her 27% reduction from magic damage. Once again we take 1-0.27=0.73 to get the MR reduction multiplier.
I will be calculating AA+Q DPS (4 sec combat duration), AA Q AA combo and ult damage.
Miss Fortune level 15
AD 292 247
AS 1.08 1.74 (with W) 1.33 1.99 (with W)
Crit 50% 75%
Armor reduction multiplier 0.676 0.575
Crit modifier +25% (from IE) +25% (From IE)
PTA flat damage 155 155
PTA percent modifier 11.29% 11.29%
Passive damage 294 247
Q damage 394 347
On hit 0 120 (roughly every 9 autos)
MR reduction multiplier 0.73 0.73
Auto attack DPS for 4 seconds + 2 Qs
Let's start with AA DPS for 4 seconds in 4 seconds you will also have time to Q twice. First lets see how many AAs both items can do in 4 seconds.
Dominik's with no W 1.08*4=4.32 AAs
Dominik's with W 1.74*4=6.96 AAs
Firecannon with no W 1.33*4=5.32 AAs
Firecannon with W 1.99*4=7.96 AAs
(AD*2*crit*crit modifier+passive+Q+PTA proc+((total autos-2)*AD*crit*crit modifier+Q)*PTA percent modifier)*reduction from armor
No W (292*2*1.5*1.25+292+392+155+((4.32-2)*292*1.5*1.25+392)*1.1129)*0.676=2557
With W (292*2*1.5*1.25+292+392+155+((6.96-2)*292*1.5*1.25+392)*1.1129)*0.676=3645
(AD*2*crit*crit modifier+passive+Q+PTA proc+((total autos-2)*AD*crit*crit modifier+Q)*PTA percent modifier)*reduction from armor+Firecannon on hit+(Firecannon on hit*PTA percent modifier only if total autos+Qs≤9)*Reduction from MR
No W (247*2*1.75*1.25+247+347+155+((5.32-2)*247*1.75*1.25+347)*1.1129)*0.575+120*0.73=2510
With W (247*2*1.75*1.25+247+347+155+((7.96-2)*247*1.75*1.25*+347)*1.1129)*0.575+(120+120* 1.1129)*0.73=3520
Dominik's deals more damage both with W and without it. In order to find out the damage difference on average though we need to calculate how often W is up.
Miss Fortunes W has a 12 sec base cooldown and we have 20% cdr from Essence Reaver meaning that W has a 12*0.8=9.6 sec cooldown. The cooldown is reduced by 2 seconds every time you proc your passive. You’ll most likely proc your passive at least once per W meaning the cooldown is effectively 7.6 sec.
The duration is 4 sec so if we take the duration and divide it by the cooldown we get the percent uptime of W. 4/7.6=0.526. Meaning W has 52.6 percent uptime and 47.4% downtime.
We can then multiply the Damage with W by 0.526 and the Damage without W by 0. 474 then add them together to get the average damage.
On average Dominik's deals 2.9% more damage.
When we look at ult damage The difference is much bigger. At rank 2 MFs ult has a 1050% AD ratio and each wave can critically strike for 20% bonus damage instead of 100% like a normal crit which means we need to divide our crit chance by 5 for this calculation. The formula for both items is.
AD*AD ratio*Crit/5*Crit modifier*Reduction from Armor
292*10.5*1.1*1.25*0.676=2850 (3257 with rank 3 ult)
247*10.5*1.15*1.25*0.575=2144 (2450 with rank 3 ult)
MF ult deals 32.9% more damage with Dominik's which I think is very meaningful especially when hitting multiple targets.
An example where this really mattered is this match between 100T and TSM https://youtu.be/FrLasCI8n5c?t=2445 if Cody Sun built Dominik's instead of Firecannon He would’ve killed Xayah with his ult and potentially won the game.
Or at least improve his odds of winning and at 44:08 he would've killed Xayah, Rakan and Jarvan faster with Dominik's which would mean that he might win the game.
AA Q AA combo
Now let’s look at the AA Q AA combo. Since Firecannon gives more AS it will be able to do the combo slightly faster, we can adjust for that by looking at the difference in AS and then multiplying Firecannons AA damage by the result.
No W 1.33/1.084=1.227
With W on 1.99/1.74=1.144
We can then use the same method as last time to get an average.
Now we have our AS adjustment multiplier. Now for the formulas.
(AD*2*crit*crit modifier+passive+Q+PTA proc)*armor reduction
(AD*AS adjustment multiplier*2*crit*crit modifier+passive+Q+PTA proc)*armor reduction+Firecannon passive*MR reduction
Dominik's deals 4.3% more damage even when adjusted for AS.
I'm using a level 15 Kalista with no bonus armor as my target.
The builds I'm comparing are Essence reaver, Berserker's, IE, Firecannon Vs Essence Reaver Berserker's, IE, Dominik's.
Since Dominik's costs 200 more gold I have added 8% AS to Firecannon in my calculation since 8% AS is worth 200 gold. Making it so both items effectively cost 2800 gold.
3rd item Dominik's deals 2.6% more damage on average than Firecannon with autos and 2 Qs (4 sec combat duration)
Dominik's deals way more damage with your ult 32.9% on average to be exact.
Dominik's deals 4.3% more damage on average with Q AA Q even when adjusted for the fact that Firecannon has more AS which allows it to do the combo faster.
Against targets that have more armor than a level 15 Kalista with no bonus armor the numbers for Dominik's are even better.
If any Pros/Coaches/Analysts etc find this stuff interesting feel free to DM me, This is just a small portion of the item math I've done and I'd love to work with pro players.
Quick thoughts about Manamune MF
I know a lot of people like to build Manamune on MF. From the math I've done Manamune is generally weaker than crit before it's fully stacked but stronger when fully stacked.
If you want to play Manamune MF this is the build i would recommend if you want full damage. Manamune, Berserker's, Duskblade, Dominik's, Ghostblade and IE.
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