### Welcome to the Forum Archive!

Years of conversation fill a ton of digital pages, and we've kept all of it accessible to browse or copy over. Whether you're looking for reveal articles for older champions, or the first time that Rammus rolled into an "OK" thread, or anything in between, you can find it here. When you're finished, check out the boards to join in the latest League of Legends discussions.

### Armor Pen vs Crit Dmg: A Quantitative Analysis

Luminar

Member

Full Physical Tank: 300 = (100/400) = 25% Damage Before Armor Pen
w/armor pen (100/400-30) = 27.027% Damage
08.10% Increase in Damage (27.027/25)

I will show your errors for the Full Physical tank. First you must use 29.37 armor pen not 30. And you get a final damage of 26.98%. Or you get a 7.92% increase in damage. Now for the crit part.

First, your crit damage increase does not increase off your base damage but your crit damage, which is 200% of your base damage. So with 33.45% crit damage increase you will deal 266.9% of your base damage because (.3345 * 2.00) = .669. In these cases I mean base damage as in the damage you would deal normally with no crit. Although I may be wrong but, of what I was told from other forums, the crit damage increase does account for the double damage of the normal crit. Nevermind I just tested this in practice game and the crit damage bonus does apply to the 200% crit damage not just the 100% base damage.

Now crit is still affected by armor so this 266.9% is cut down to 25% from the armor. Ending with a final damage of (2.669*.25)= 66.725% damage on every crit. Now for the weighted average of these damages (25% without crit, and 66.725% with crit) to equal the 26.98% you can deal with Armor Penetration you must crit (66.725x + 25(1-x) = 26.98).
Where x in this case is 4.745%. You would only have to crit 5% of the time or 1 in every 20 hits in order to do the same damage,
not 24%.

This holds true whether you apply armor first or crit damage increase. Now this still does not count in any in game items... But overall this shows how critical hits even in a somewhat small amount does intense amounts of more damage.

MeagerEvil

Junior Member

Well Luminar, it appears you have me over a barrel.

I used 30 armor pen in my equation for 2 reasons. One, i was writing this up real quick and it was easier. And two because the totals to the right of the rune book read it as 30 and I find it likely that the developer could have rounded up and placed the value into an integer variable, as floating point math requires more clock cycles and the use of the math co-processor.

You are quite right about the threshold being entirely wrong, i kinda made a rough estimate on the fly. If you want to, you can revise the math and I will edit it in.

DreamyDays

Senior Member

Quote:
Same as above actually, he uses a 2.33 crit damage multiplier, where (I assume) it should be 2 * 1.33 or 2.66 as the total damage is modified by 33% not just added to the crit multiplier percentage. I have searched and found nothing absolute from riot, but it is how I have interpreted the runes, It is extremely hard to verify this math in game. If I find out anything new I will update it.

My assumption was that that all crit damage modifiers are added linearly, not multiplied.
Ex) 200%(base) + 33%(runes) + 10%(mastery) = 243%

An easy way to verify this(or deny this) will be the following:

1) Start a Bot Practice Game with Crit Dmg mastery and Crit Dmg book.
2) Get Last Whisper + as much Armor Penetration as you can. NO IE!
3) Test your damage out on a jungle creep.
4) Repeat, this time with IE.

With Last Whisper and ArPen items, you would deal true damage to weak creeps.
Therefore, you will be able to check how much damage your crits does easily.

1) All modifies are linearly added(IE is treated as +50% crit damage)
Step 3 will give 243% damage, and step 4 will give 293%.

2) All Crit Damage modifiers are added, then multiplied to the coefficient. (200% or 250%)
Step 3 will give 286% damage, and step 4 will give 358%.

3) All Crit Damage modifiers are multiplied. ex) (rune) * (mastery) * (skill) * (IE)
Step 3 will give 293% damage, and step 4 will give 365%

2) and 3) might seem similar. They can be differentiated with Tryndmere.
With 8 stack of Bloodlust lvl 5, you get 36% Crit Dmg.
2) 358%, 446%
3) 398%, 497%

I'm currently on a campus computer, so I cannot check now.
Not to mention that I don't have any crit dmg runes.....
If someone would try this out, I'd appreciate it.

Yeah.... even without crit dmg book, you can use Trynd to check...
But then you can't confirm the interaction of crit dmg runes with other crit related things.

MeagerEvil

Junior Member

Unfortunately there is no guarentee that Trynd's crit damage is applied the same way as the runes, not to mention any number of possible false positives, bushwak can put someone into negative armor for example. The only was to test it would be the practice game, but with no items, just the rune book. I would, but I have all Armor Pen runes...

Ferrari Murakami

Member

err..so critical damage runes are inferior to armor penetration runes? If thats true, I've wasted a lot of IP in trying to buy Tier 3 Crit. Damage runes for my Shaco.

Vlox

Member

Spreadsheet I made on crit chance vs AP runes (assuming only quints and reds are used):

Let me know if you see any mistakes. Basically it says that if you keep the enemy between 20 and 60 armor AP is better... otherwise go crit.

Comma

Member

Someone just right a bloody DPS calculator and be done with it instead of having thousands of people who are inept at Math and English trying to justify their Tunnel Vision.

Vlox

Member

Quote:
Comma:
Someone just right a bloody DPS calculator and be done with it instead of having thousands of people who are inept at Math and English trying to justify their Tunnel Vision.

Go for it... it would take a long time. Personally I just make spreadsheets to answer questions as I need the information.

Senior Member

Stop bumping this thread, the math is totally wrong and the poster is incorrect.