Hi, I'm InvertedDisciple, back with some more math. So lately I've seen a few pros buying IE as their last/second last item on Senna. So I decided to do some math to see if IE was the best item to buy or if there was a better option. The item I'm going to compare it to is Dominik's.

The builds I'm comparing are.

https://preview.redd.it/3anwegg8iye51.png?width=673&format=png&auto=webp&s=d3b751f906c0beda8b4d2bc2fe010c55330ab280

Scroll down for TL;DR

In this math Senna is level 16 and she has 100 souls. The target I'm using is a level 16 Aphelios with no bonus armor. At level 16 Aphelios has 71 armor and Duskblade gives 20 armor pen meaning that vs the IE build Aphelios effectively has 51 armor and takes 33.8% reduced damage from physical.

With the Dominik's build Aphelios armor is reduced by 35% and then by 20 flat armor which means he effectively has 26 armor, giving him 20.6% reduced damage from physical.

Aphelios has 1804 health and Sennas passive deals 16% current health meaning it deals 8% max health on average so 1804*0.08=144

https://preview.redd.it/aslhqeifhye51.png?width=411&format=png&auto=webp&s=2393ed4e952088e9a84a2bbf49989cbb4c566415

Before we get into the damage math I need to talk about how crit interacts with Senna. Sennas crits deal 130% damage instead of 200% like a normal crit. IE increases Sennas crit damage to 146.25%. What this means is that Sennas crit multiplier with IE is

0.4625*crit/100+1=0.4625*1+1=1.4625

Dominik's

136*0.792=108

IE

136*0.662=90

Passive damage (soul proc)

Dominik's

144*0.792=114

IE

144*0.662=95

Dominik's deals 20% more damage with your passive.

Auto damage

Dominik's

(329*1.3+146)*0.792=454

IE

(364*1.4625+153)*0.662=454

Dominik's and IE deal the same amount of damage.

Q damage

Dominik's

(272+146)*0.792=331

IE

(286+153)*0.662=291

Dominik's deals 13.7% more damage with your Q.

W damage

Dominik's

445*0.792=352

IE

470*0.662=311

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Dominiks deals 13.2% more damage with your W.

R damage

Dominik's

779*0.792=617

IE

814*0.662=539

Dominik's deals 14.5% more damage with your R.

Now that we've looked at the damage math let's look at some other variables. IE gives 14 more healing on Q (+19 from lifesteal) and 14 more shielding on R. It also gives 8.75% lifesteal from your passive since you overcap your crit by 25%.

This means that your autos heal you for 364*1.4625*0.662*0.0875=31.

TL;DR

In this math Senna is level 16 with 100 souls and the target she is attacking is a level 16 Aphelios with 0 bonus armor, health and MR. Against targets with higher armor the numbers for Dominik's get even better.

Remember that even squishy champs like ADCs and mages often build some armor like Death's Dance or Zhonyas. In those cases the damage numbers will be even better than the numbers shown below.

Dominik's costs 600 less gold than IE

Duskblade proc deals 20% more damage with Dominik's

Passive soul proc deals 20% more damage with Dominik's

Autos deal the same amount of damage with both items.

Q deals 13.7% more damage with Dominik's

W deals 13.2% more damage with Dominik's

R deals 14.5% more damage with Dominik's

All out combo (all abilities and item procs+1 auto) deals 10.5% more damage with Dominik's

Q heals for 33 more with IE (14 from ad ratio and 19 from lifesteal) (20 vs healing reduction)

R shields for 14 more with IE

Autos heal for 31 health with IE due to Senna passive converting overcapped crit to lifsteal. (19 vs healing reduction)

Bonus math

In this part I'm going to show you what the difference between the two items is if I add 17 AD to Dominik's since 17 AD is worth 605 gold making it so both Items are worth almost the same amount of gold.

Autos deal 4.6% more damage with Dominik's

Q deals 16.5% more damage with Dominik's

W deals 16.4% more damage with Dominik's

R deals 16.9% more damage with Dominik's

All out combo (all abilities and item procs+1 auto) deals 13.3% more damage with Dominik's

Q heals for 25 more with IE (6 from ad ratio and 19 from lifesteal) (15 vs healing reduction)

R Shields for 6 more with IE

Autos heal for 31 health with IE due to Senna passive converting overcapped crit to lifsteal. (19 vs healing reduction)