__Keywords:__ Armor Penetration, Armor Pen, Critical, Critical Chance, Critical Strike, Critical Damage, Calculations

__Introduction__

It's rather obvious that they all have it's uses at difference scenario, but what are those scenarios? and which is better? It's really hard to get a full understanding without going through bunch of variable and understanding DPS.... So most people would probably believe that these things come to you in experiences after hundreds if not thousands of games played... However, I'm more of a numbers & theory type of person. I'll bring it down to you with some simple and understandable results.

PS: I'm no guide writer and this is not "fully" complete in terms of mathematically point of view, but IMO it's good enough for me. And I'd like to spend rest of the time on playing and having fun. Anyone is welcome to continue this work if they want.

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__Theory__ - Before we start, there's a few game mechanics we need to know...

**Effective Hit Point** - Back in Dota, we learned something known as EHP. It's the real hit point after multiplying the amount of armor you have. For every point of armor, your effective health is increase by exactly 1% of your max hit point. THANK YOU Riot Games, no more of those WC3 1 point armor = 6%*HP bs...
**Damage** - Duh
**Critical Chance** - Duh... Chance to deal a critical strike (default at 2.0x)
**Critical Damage** - Oh yea thanks Riot Games again... critical strike modifier... maximum around 3.2x'ish (runes+mastery+Infinity Edge) atm?
**Armor Penetration** - for every 1 point of armor penetration, the target's armor is reduced by 1 point before your damage applies. Applied before percentage reduce (like Last Whisper)

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__Equations__- Non-Critical Damage = Attack Damage displayed on your screen
- Critical Damage (Max Hit) = Attack Damage * 1+critical chance/100%
- Remainders = EHP minus damage done

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__Conditions__- Numbers are Arbitrary... meaningless? They only serve as an approximation!
- Two Minor Categories, Non-Crit vs. Critical
- Two Major Categories, Crit Damage vs. Armor Pen
- Full Primary Tier-3 Runes of Critical Damage on Purple & Red sums to
**33% critical damage**.
- Full Primary Tier-3 RUnes of Armor Penetration on Purple & Red & Combat Mastery sums to
**35 Armor Penetration**

- Attack Damage varied: 150, 200, 250
- Critical Chance varied: 5%, 25%, 50%
- Defender's Hit Point varied: 250, 300
- Defender's Armor varied: 50, 100, 150, 200

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__Calculations__
This had to deal with at least 4 different variables at any given time to yield meaningful results IMO... although I was too lazy to do a statisical analysis of variance and extra degree of freedom, I did get some interesting results...

**TAKE A GLANCE AT THE CHART**
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__Observations__- It turns out that 1% critical chance = 1% damage, as expected (we knew that from WOW... good thing there's no hit rating in this game).
- From Remaining Hit Points, it can be observed that Armor Penetration is always better at non-critical scenario. However, It's only better than when the target have mid-to-low armor values.
- Critical Damage is only more effective than armor penetration build when fighting enemy with higher armor value (150+).
- This makes sense since critical damage is same regardless of target's armor, but 1 point of armor penetration is 1% when the target has 100 armor, but it's only 0.5% when the target has 200 armor. In that case, you really need last whisper or bloodrazor.

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__Conclusions__**Critical Chance **- This thing is only good if you believe on luck! But statistically, it' yields 1% damage all the time. Where as critical damage would yield less or equal to 1% damage. And Armor Penetration would only yield more than 1% if the target gets negative armor value.
**Critical Damage** - good at helping you record your largest critical; giving you more burst damage if you know you can crit (like shaco or have over 50% crit chance).
**Armor Penetration** - Most effective in non-critical scenario.

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__Last Words__
It really depends on the player's play style. I'd say all three are good and you should be creative by making your own builds... but I would be lying... because, personally, I like Critical Damage the best because I love seeing big numbers. However, seems that Armor Penetration is most effective.

If Anyone would like to continue on this work, what can be done is by using MATLAB or softwares alike and mapping out real values from 1-to-10000 for all variables, and find out that optimal value within the multi-dimension matrix.