Pre 8.11 Vs Post 8.11 Crit damage number crunch

I crunched some numbers with one of my Jax builds to see what kind of damage output an ADC may have against him pre patch 8.11 and post patch 8.11. I thought the changes i found to AD items was interesting, and thought that i would post this number crunching.

To begin with the jax build I used in this number crush uses the following items: titanic hydra, Sterak's gage, Trinity force, Spirit Visage, and Randuins Omen, i forgot to account for the +8 armor +5% bonus armor from the conditioning rune but after the number crunch i don't think it will account for too much of a difference. In this example I focussed on an adc going for tank buster getting both IE and Lord Dominik's Revenge. Lets begin:

Previously the crit damage of an ADC with both IE and LDR would have been as follows: 1.2(2.5)(Damage After Reduction [or DAR for short])(AD). Where 1.2 comes from LDR, 2.5 from infinity crit boost.

Now the crit damage of an ADC with both items would be like this: [.85(2)(DAR) + .15(2)]AD We are splitting the crit damage between the physical (85% of damage) and true damage (15% of damage)

Damage After Reduction is calculated by 1-[Ar-ArPen/(Ar-ArPen+100)] where, in this situation ArPen=35% bonus armor before Patch 8.11 or 35% total armor after Patch 8.11.

Now looking at what that would do against my jax build: Jax's base armor is 87 at lvl 18 with 147 total armor (60 bonus) and a total of 280.5 armor (193.5 bonus) using his ult.

Pre 8.11: Crit damage before Jax ults = 1.2(2.5)(.644) AD = 1.932 AD (Vs. 147 armor) Crit damage after Jax ults = 1.2(2.5)(.32) AD = .96 AD (Vs. 280.5 armor) I do want to point out that without the 1.2 multiplier from having more health than the enemy using LDR the crit damage before Jax ults would be 1.61 AD after ult would be .8 AD, this changes the significance of the number crunch for when the enemy uses mortal reminder or scraps %APen items altogether.

Post 8.11: Crit damage before Jax ults = [.85(2)(.513) + .3] AD = 1.17 (vs 147 armor) Crit damage after Jax ults = [.85(2)(.354) + .3] AD = .9 (vs 280.5 armor)

I calculated the Damage After Reduction beforehand and just put the numbers in. Overall in both cases the ADC does less damage post patch

Now there are 2 things that I found interesting. first, how much damage the ADC lost against the less tanky bruiser. Second, The difference in armor between both patches; prepatch the 137 bonus armor from Jax's ult would've halved the adc's crit damage, post patch it only reduces the damage of the adc by 23%.

Keep in mind that to some degree ADCs will have more crit chance. Previously with IE and 1 other crit item they would've have 50% crit chance now they would have 60%; if they had IE and 2 other crit items before they would've had 80% crit chance now they would hit 100% (120% but the 20% is lost). So to some degree the pain they feel in lost damage is taken care of with that.

One last thing that I wan't to point out, is that although the tank typically doesn't need to build as much armor to be effective against an adc (unless the adc skips the combo IE/LDR in which case armor would be even stronger), armor is still going to perform the same against champions that don't use these 2 items. Also a tank is going to be less effective against an ADC at high armor values.

EDIT: I forgot that Randuin's was part of the build that was posted. It reduces crit damage by 20%. That calculation is easy enough that i'm not gonna bother. Just multiply the result ADC crit damage by .8 and you get their new crit damage.