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Lvx's theory crafting compendium (game...

Creator: Lvx August 4, 2010 3:04pm
Lvx
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A. What the heck is this all about - and who the **** are you?
Well, I got into touch with mobafire, by doing a google search for some builds. I found some, and in some cases I thought "Okay, you could do better than this" or "Sounds nice... but they dont prove their theory, why that gear would be most suitable".
So I started to get informed about game mechanics, did some calculations on the topics I have been interested in, and started to post my first builds.

Recently, DEWO asked me to post my ideas, technical information, graphics and so on in the forum, instead of posting it in the build DB only.
As he is probably right, that a real compendium should be found at one single place, instead of making you work through different pages of builds (espc. as they also contain information that is not mere theory crafting) I decided to start this thread. But in order to keep this running, there is some rules that I kindly ask you to observe:
#1 - No responses to this thread. If you want to leave a comment or post a feedback, please the first one of you open a thread of its own (I will link it here), and use it for all your feedback, in order to keep this one well-arranged.
#2 - If you have confirmed information (i.e. patch notes) that some facts have changed, please inform me about that, so I can fix the information provided here.
#3 - You are free to use my ideas for any purposes, especially for maximizing your gaming results and K:D for sure ;) - anyway, if you use it for your builds, it would be nice to give it a credit by placing a link to this page. Thanks.


At the proper times, I will place links to my builds in the DB, if it will ease up the understanding of the provided theories - as you will find them over my profile anyways, I will mainly quote from them afterall.


B. Table of contents
I. Usage of runes: DOs and DONTs
II. The game mechanics behind ArP / MagPen and Armor / MR
III. The game mechanics behind AP: Effect of AP-scaling and AP-influencing factors
IV. The game mechanics behind critical strikes
V. The game mechanics behind cooldown reduction, and proper use of CDR

I have to ask you for your kind understanding, that I will put the abovementioned chapters together, and post them here, one after another in an order at my discretion - same about adding new chapters to this TOC.
So feel free to check back at any time, but please give me some time to put the content in a proper layout before publishing it.
Lvx
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List of abbreviations
ArP: armor penetration
MagPen: magic penetration
AR: armor
MR: magic resistance


B. I. Usage of runes: DOs and DONTs
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Lvx
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B. II. The game mechanics behind ArP / MagPen and Armor / MR
1.) General facts
First of all, I can provide you with some happy news: MagPen / ArP and MR / AR work 100% alike. So I will only write about ArP and AR, but the same mechanics, the same calculations, work for the magic effects perfectly the same way.

While this eases up things, another fact - that we have always to be aware of - wont: There is flat penetration and penetration by %.
flat penetration - almost all items, all runes.
penetration by % - atm one item each (last whisper +40% ArP, void staff +40% MagPen)
The reason this is so important is, because flat penetration is always applied before penetration by percentage!

But, however, before you will understand the way penetration works, you have to understand the way that AR itself works.
Keep in mind, that - even if the game will never show a value below zero! - AR (MR as well) can go into negative values, and will affect the calculation of your dmg taken. This information is crucial.


2.) The calculation of AR
Okay, so how does that fancy AR, that saved our ***es that often, work?
The formula for dmg reduction is:
r(modifier) = AR / (100 + AR)
(or in percent: r(%) = AR / (100 + AR) * 100)


For example with 150 AR:
r = 150 / (100 + 150) = 0,6.
Your dmg will be reduced by 60%.
The first ones of you will have figured it out already: High noon is 100 AR - 50% dmg reduction. And, to this point very obvious: more AR means more dmg reduction.
See this graphic:



3.) The calculation of ArP
But actually we want to talk about ArP and not AR. So, what about the penetration thing? As I told you before, we have to differ flat penetration and penetration by percentage.
This leads us the the following formula for ArP:
AR (after ArP) = (AR - ArP(flat)) * (100 - ArP(%)) / 100

Lets get this a bit less abstract. We will have three examples: 100 AR after 40 ArP flat, after 20 ArP flat and 40% ArP, and after 40% ArP only.
1st
AR (after ArP) = (100 - 40) * (100 - 0) / 100 = 100 - 40 = 60 AR
2nd
AR (after ArP) = (100 - 20) * (100 - 40) / 100 = 80 * 0,6 = 48 AR
3r
AR (after ArP) = (100 - 0) * (100 - 40) / 100 = 100 * 0,6 = 60 AR

What we can see from that three simple examples is, that the effect of ArP(%) is higher, the lower the value of your ArP(flat) is - see this from 2nd and 3rd example.
The only result, I want you to remember right now is, that the efficency of ArP(%) is fluctuant! We will see below, till what point ArP(%) has a reason to live, and after which values we will prefer to let it go.

3a. Wise use of ArP(%)
As you might have figuered out already: ArP(%) will be more useful, the higher your enemies AR is (cause the higher his AR is, the more AR will be left after flat penetration). To give you some more examples.
An enemies 30 AR, will be reduced by yomuus ghostblade by 20 - 10 MR will be in effect.
An enemies 30 AR, will be reduced by last whisper by 40% - 18 MR will be in effect.

An enemies 75 AR, will be reduced by yomuus ghostblade by 20 - 55 MR will be in effect.
An enemies 75 AR, will be reduced by last whisper by 40% - 45 MR will be in effect.

(In case of MR, yo will find that there is boots with MagPen - but none with ArP. So as almost everyone will play with some kind of boots, as a caster you will go for sorcerers shoes - picks will differ for physical DDs though - see my "Build on MP / MagPen - why to play hybrids" fpr more information about the caster specifically)


An enemies 100 AR, will be reduced by yomuus ghostblade + starks fervor by 40 - 60 AR will be in effect.
An enemies 100 AR, will be reduced by yomuus ghostblade + last whisper by 20 | 40% - 80 * 0,6 = 48 AR will be in effect.

If you checked the build mentioned above, you might have seen, that we managed to even out the benefits of a void staff quite easy (as MR is lower on most opponents then AR, and there is way more and potent MagPen items, than ArP items).
However: While we can easily be more efficent with flat MagPen only, in terms of ArP we will always rely on ArP(%) as well. According to the items available at the moment, there is almost no way around last whisper (the one way there is, is the black cleaver. See below.)!


4.) Conclusio
While the calculation is 100% the same, there is different results for physical and magical DDs. So please keep in mind: Identical formulas never mean, that you are supposed to copy-paste your builds - due to different items available and different enemies stats you will have to cope with, you will have to make heavily different decisions!

4a.) As a caster...
As you might have seen in the above mentioned build, it is quite simple for casters: Trash void staff, and go for a hybrid build unless your enemies have 100+ MR. You will most likely have to face enemies with 50-80 MR. In worst case 100. Never seen anyone above 150 MR yet.
Enemies MR: 20
Enemies MR: 50
Enemies MR: 75
Enemies MR: 100
Enemies MR: 150
You can see from these graphics, what item builds - more important: what ways to achieve your MagPen - are suggested. You will figure out, that its almost every case MagPen(flat) only. However, the graphics will speak for themselves - if you need explantions about the symbols / colorbars, you will find them here.

4b.) As a phys DD
However, things will go another way for you as a phsy DD. First of all: You will need boots, so we have only five item slots left.
Second, we will most likely focus our runes on crit chance (you will find more about that in the crit-mechanics section later on), dodge, maybe HP... but most likely we will not have too much rune slots for ArP. But as we have seen: The smaller our amout of ArP(flat) is, the more efficent is last whisper.

Only item we can think about as being superior to last whisper is the black cleaver:
If we manage to hit 5x, it will be a 60 ArP(flat). That is awesome.
So we might come to a point, where we have to decide, if our 6th item is to be the black cleaver or last whisper - best idea would be to buy both!, but I see ppl going straigt for AD items that often, that I want to provide you with a comparsion of TBC and LW anyways.

As you see, with an estimated dmg of 200 (with the other 5 items) and ArP(flat) of 20 (by runes, or a ghostblade i.e.) the black cleaver would be more efficent as long as your opponent has around 100 AR. Afterwards, you will score better with last whisper.
Keep in mind:
- The higher your dmg is, the earlier last whisper will be a better choice.
- The higher your opponents AR is, the earlier last whisper will be a better choice.
- The more problems you have to strike five times in a row with black cleaver, the earlier last whisper will be a better choice.

The best choice, however, is to combine AS, AD, crit chance and ArP at values as high as possible. Leaving your boots to your discretion, this means for example:
1st item: The black cleaver (75 AD, 60 ArP)
2nd item: Last whisper (10 AD, 40 AS, 40% ArP)
3rd item: Infinity edge (80 AD, 20 crits, 2.5 crit modifier)
4ht item: Sword of the divine (25 AD in average, 55 AS, - 30 ArP, no dodging for 8s)
5th item: Phantom dancers (45 AS, 30 crits)
6th item: boots
-> 2,4 x ~0,75 = ~ 1,8 attacks/s, with:
(basedmg + 190) + [ 0,5 (50% crit chance) * 2,5 (crit modifier) * (basedmg + 190)].
Featuring your 90 | 40% ArP.

For example with Tryndamere:
[(117 + 190) + ( 0,5 (50% crit chance) * 2,5 (crit modifier) * (117 + 190))] * 1,8 = 1.243 dmg/s
This value, of course, is without any additional boni by runes, by masteries, by aura effects of your team mates, etc. It is the plain, lowest value dmg you would deal to somebody with 91 AR.
150 AR would still mean 914 dmg.


So I hope you see, that you have to chose your equip based on your opponents. As a thumb rule you might remember:
As caster you will go for flat MagPen, with MagPen runes as well - MagPen(%) only at 100+ MR.
As physical DD you will go for ArP by percentage and as much AD+AS+ArP(flat)+crits as you can get on the other 4-5 items.
Mowen
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Since this information is fairly outdated, I would suggest going here for more up to date information. This is copied from my FAQ to quickly explain what the different stats do, then give a link to the more in depth analysis.
- - -

A. In a nutshell, armor protects you against physical damage. Magic resist protects you against magic damage. Armor penetration reduces enemy's armor, and magic penetration reduces enemy's magic resist.

For more detail about these mechanics, go here:

Magic Penetration

Magic Resistance

Armor Penetration

Armor

More stats - (scroll to effects chapter)
Thanks to GrandMasterD for my sig!

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