Views: 2785 Testing LoLMath Theories (Sup3r sh0cking conclusion)
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Alright, this will probably be confusing as hell for most people but honestly if you don't like the numbers, just trust me and go read the *explanation* and *conclusion* parts :P. I was just trying some stuff that could MAYBE finally help me correctly compare Armor Pen vs AD and WHY they work the way they do and what is more effective in which situation... and it turns out I found some cool stuff. However, there is still mystery for me.
Case 1:
You: 200 AD, 0 Armor Pen
Target: 1000 HP, 100 Armor
Damage dealt: 100
Efective HP: 2000
Survival time: 10 seconds
Case 2:
You: 300 AD, 0 Armor Pen
Target: 1000 HP, 100 Armor
Damage dealt: 150
Effective HP: 2000
Survival time: 6.67 seconds (3.33 less, 33.33% less)
Case 3:
You: 200 AD, 66.66 Armor Pen
Target: 1000 HP, 100 Armor
Damage dealt: 150
Effective HP: 1333 (-666 EHP, 33% less)
Survival time: 6.67 seconds (-3.33 seconds, 33% less)
Explanation of Test 1: Here I just choose some (not so) random round numbers for my AD, my target's HP and armor to make it nice looking and as simple as possible. The first case is just the ''comparison case''. It has nothing special. The second case has 100 more AD than the comparison case. That made me kill the enemy 3.33 seconds faster which translated into 33.33% less total time. In the third case I gave a number of Armor pen that made me kill the enemy just as fast as when I got the +100 AD. I didn't magically fall on it, I found it with maths:
how I found how much Armor Pen I needed to increase my damage as much as +100 AD
I wanted to find the exact number of Armor Pen that would increase my damage as much as +100 AD so that now I can change the HP and Armor values and see if +100 AD and +66.66 Armor Pen will continue being just as effective against the enemy in question.
You: 200 AD, 0 Armor Pen
Target: 2000 HP, 100 Armor
Damage dealt: 100
Effective HP: 4000
Survival time: 20 seconds
You: 300 AD, 0 Armor Pen
Target: 2000 HP, 100 Armor
Damage dealt: 150
Effective HP: 4000
Survival time: 13.33 seconds (-6.66 seconds, 33% less)
You: 200 AD, 66.66 Armor Pen
Target: 2000 HP, 100 Armor
Damage dealt: 150
Effective HP: 2666.67 (-1333 EHP, 33% less)
Survival time: 13.33 seconds (-6.66 seconds, 33% less)
Explanation of Test 2: What's going on here? The enemy got a Warmog's (+1000 HP) and my +100 AD still increased my damage just as much as my +66.66 Armor Pen.
There is a special thing thing to note right here. Both my +100 AD and my +66.66 Armor Pen still made me kill the enemy 33% faster. In this case, since the enemy was longer to kill overall, 33% of that time gave out a bigger number (-6.66 seconds instead of -3.33 seconds). Remember, the enemy was still longer to kill overall, (survives 13.33 seconds with 2000HP instead of 6.67 seconds with 1000 HP) so don't go crazy thinking that building HP won't help you survive at all, that's just stupid.
Why is that? Why does my AD and Armor Pen still make me kill the enemy exactly 33% faster and not less?
Armor Pen: Your Armor Pen scales with the enemy's HP(!). If the enemy has more HP, each point of Armor you take away from him (AKA each point of Armor Pen you get) will make his Effective HP fall down by MORE. Each time you take away one of his points of Armor, ALL of his HP bar suffers from it. So if he has a bigger HP bar, he suffers more from your 1 Armor Pen :D.
AD: Honestly this one is the hardest to explain. Even I have trouble explaining it to myself with words. It kinda feels right though. What I think it is is that the enemy simply has more EHP so you get to hit him more times before he dies, therefore you get to use your bonus AD more times so it's ''more'' effective (in fact it's just as effective, it's just that 33% of a bigger number gives out a bigger number).
Conclusion: If the enemy gets HP, building AD or Armor Pen against it isn't specifically more effective than the other.
You: 200 AD, 0 Armor Pen
Target: 1000 HP, 200 Armor
Damage dealt: 66.67
Effective HP: 3000
Survival time: 15 seconds
You: 300 AD, 0 Armor pen
Target: 1000 HP, 200 Armor
Damage dealt: 100
Effective HP: 3000
Survival time: 10 seconds (5 seconds, 33% less)
You: 200 AD, 66.66 Armor Pen
Target: 1000 HP, 200 Armor
Damage dealt: 85.72
Effective HP: 2333 (-666 EHP, 22.22% less)
Survival time: 11.67 seconds (3.33 seconds, 22.22% less)
Explanation of Test 3:
I'm gonna be honest with you guys, when I came to this part I kinda started staring at the screen for 10 mins being completely clueless about what I had just created. After thinking that everything I knew was wrong for a good 10 mins I realized what happened.
If you look at the numbers, you'll see that 66.66 Armor Pen is less effective than +100 AD against an enemy with more Armor this time :O. That makes Armor Pen look like it has diminishing returns (and that buying Armor would have increasing returns, wtf?) but it's just an illusion/bad interpretation of numbers (this happens so much all the time).
It's not that Armor Pen was less effective against the higher armor target, it's that AD was better than Armor Pen against a higher armor target. I know it's almost the same thing but the difference is important.
I also know that it certainly feels backward and very strange but yes, building AD is a better idea then building Armor Pen against someone wits lots of Armor. That's just the way it is.
You can notice than in Test 1 and Test 3, 66.66 Armor Pen allowed you to kill the enemy 3.3 seconds faster in both cases. This is why Armor Pen doesn't have diminishing returns. It doesn't give you more or less or more and it doesn't depend on the enemy's armor. On the other hand, AD somehow (once again, even I have trouble explaining it to myself) scales with the enemy's EHP and gives proportionally just as much increased damage (however, 33% of a bigger number = bigger number so it's kinda ''more'' effective)
*Conclusion*: Armor Pen doesn't scale with the enemy's Armor while AD does.
Tests 4, 5 and 6)
To conclude this post, I'll just state what I've found out by going on this magical adventude and what you should take from it.
When an enemy gets HP, the effectiveness of your AD and Armor Pen are both equally increased but the enemy still becomes overall harder to kill. Therefore AD isn't specifically better than Armor Pen against an enemy with high HP.
When an enemy gets Armor, the effective of your AD is increased while the effectiveness of your Armor Pen remains the same (does not reduce, only stays the same). Therefore it is generally a better idea to build AD than to build Flat Armor Pen against an enemy investing in tons of Armor (
Last Whisper and Black Cleaver have % Armor Pen so these are different cases).
However, to make sure if AD would truly be better than Armor Pen, you would need to consider in the Gold efficiency of the items wanted, the base damages of your champion and many other factors. I could do that but this would take very very long and I don't want this blog to be 10 hours long so maybe I'll save that for a future post :P.
Feel free to comment/discuss on what you think. Do you think there is a flaw in my calculations? Is there something else that bugs you because you want to know it? Basically any question is welcomed.
Thanks for reading, I hope you enjoyed ^^
TL;DR
*****, Diamond 4 is elo hell and Vapora Dark is my girlfriend.
TEST 1:
Case 1:
You: 200 AD, 0 Armor Pen
Target: 1000 HP, 100 Armor
Damage dealt: 100
Efective HP: 2000
Survival time: 10 seconds
Case 2:
You: 300 AD, 0 Armor Pen
Target: 1000 HP, 100 Armor
Damage dealt: 150
Effective HP: 2000
Survival time: 6.67 seconds (3.33 less, 33.33% less)
Case 3:
You: 200 AD, 66.66 Armor Pen
Target: 1000 HP, 100 Armor
Damage dealt: 150
Effective HP: 1333 (-666 EHP, 33% less)
Survival time: 6.67 seconds (-3.33 seconds, 33% less)
Explanation of Test 1: Here I just choose some (not so) random round numbers for my AD, my target's HP and armor to make it nice looking and as simple as possible. The first case is just the ''comparison case''. It has nothing special. The second case has 100 more AD than the comparison case. That made me kill the enemy 3.33 seconds faster which translated into 33.33% less total time. In the third case I gave a number of Armor pen that made me kill the enemy just as fast as when I got the +100 AD. I didn't magically fall on it, I found it with maths:
how I found how much Armor Pen I needed to increase my damage as much as +100 ADI wanted to find the exact number of Armor Pen that would increase my damage as much as +100 AD so that now I can change the HP and Armor values and see if +100 AD and +66.66 Armor Pen will continue being just as effective against the enemy in question.
TEST 2 (MORE HP):
You: 200 AD, 0 Armor Pen
Target: 2000 HP, 100 Armor
Damage dealt: 100
Effective HP: 4000
Survival time: 20 seconds
You: 300 AD, 0 Armor Pen
Target: 2000 HP, 100 Armor
Damage dealt: 150
Effective HP: 4000
Survival time: 13.33 seconds (-6.66 seconds, 33% less)
You: 200 AD, 66.66 Armor Pen
Target: 2000 HP, 100 Armor
Damage dealt: 150
Effective HP: 2666.67 (-1333 EHP, 33% less)
Survival time: 13.33 seconds (-6.66 seconds, 33% less)
Explanation of Test 2: What's going on here? The enemy got a Warmog's (+1000 HP) and my +100 AD still increased my damage just as much as my +66.66 Armor Pen.
There is a special thing thing to note right here. Both my +100 AD and my +66.66 Armor Pen still made me kill the enemy 33% faster. In this case, since the enemy was longer to kill overall, 33% of that time gave out a bigger number (-6.66 seconds instead of -3.33 seconds). Remember, the enemy was still longer to kill overall, (survives 13.33 seconds with 2000HP instead of 6.67 seconds with 1000 HP) so don't go crazy thinking that building HP won't help you survive at all, that's just stupid.
Why is that? Why does my AD and Armor Pen still make me kill the enemy exactly 33% faster and not less?
Armor Pen: Your Armor Pen scales with the enemy's HP(!). If the enemy has more HP, each point of Armor you take away from him (AKA each point of Armor Pen you get) will make his Effective HP fall down by MORE. Each time you take away one of his points of Armor, ALL of his HP bar suffers from it. So if he has a bigger HP bar, he suffers more from your 1 Armor Pen :D.
AD: Honestly this one is the hardest to explain. Even I have trouble explaining it to myself with words. It kinda feels right though. What I think it is is that the enemy simply has more EHP so you get to hit him more times before he dies, therefore you get to use your bonus AD more times so it's ''more'' effective (in fact it's just as effective, it's just that 33% of a bigger number gives out a bigger number).
Conclusion: If the enemy gets HP, building AD or Armor Pen against it isn't specifically more effective than the other.
TEST 3 (MORE ARMOR):
You: 200 AD, 0 Armor Pen
Target: 1000 HP, 200 Armor
Damage dealt: 66.67
Effective HP: 3000
Survival time: 15 seconds
You: 300 AD, 0 Armor pen
Target: 1000 HP, 200 Armor
Damage dealt: 100
Effective HP: 3000
Survival time: 10 seconds (5 seconds, 33% less)
You: 200 AD, 66.66 Armor Pen
Target: 1000 HP, 200 Armor
Damage dealt: 85.72
Effective HP: 2333 (-666 EHP, 22.22% less)
Survival time: 11.67 seconds (3.33 seconds, 22.22% less)
Explanation of Test 3:
I'm gonna be honest with you guys, when I came to this part I kinda started staring at the screen for 10 mins being completely clueless about what I had just created. After thinking that everything I knew was wrong for a good 10 mins I realized what happened.
If you look at the numbers, you'll see that 66.66 Armor Pen is less effective than +100 AD against an enemy with more Armor this time :O. That makes Armor Pen look like it has diminishing returns (and that buying Armor would have increasing returns, wtf?) but it's just an illusion/bad interpretation of numbers (this happens so much all the time).
It's not that Armor Pen was less effective against the higher armor target, it's that AD was better than Armor Pen against a higher armor target. I know it's almost the same thing but the difference is important.
I also know that it certainly feels backward and very strange but yes, building AD is a better idea then building Armor Pen against someone wits lots of Armor. That's just the way it is.
You can notice than in Test 1 and Test 3, 66.66 Armor Pen allowed you to kill the enemy 3.3 seconds faster in both cases. This is why Armor Pen doesn't have diminishing returns. It doesn't give you more or less or more and it doesn't depend on the enemy's armor. On the other hand, AD somehow (once again, even I have trouble explaining it to myself) scales with the enemy's EHP and gives proportionally just as much increased damage (however, 33% of a bigger number = bigger number so it's kinda ''more'' effective)
*Conclusion*: Armor Pen doesn't scale with the enemy's Armor while AD does.
Tests 4, 5 and 6)ENDING
To conclude this post, I'll just state what I've found out by going on this magical adventude and what you should take from it.
When an enemy gets HP, the effectiveness of your AD and Armor Pen are both equally increased but the enemy still becomes overall harder to kill. Therefore AD isn't specifically better than Armor Pen against an enemy with high HP.
When an enemy gets Armor, the effective of your AD is increased while the effectiveness of your Armor Pen remains the same (does not reduce, only stays the same). Therefore it is generally a better idea to build AD than to build Flat Armor Pen against an enemy investing in tons of Armor (
Last Whisper and Black Cleaver have % Armor Pen so these are different cases).However, to make sure if AD would truly be better than Armor Pen, you would need to consider in the Gold efficiency of the items wanted, the base damages of your champion and many other factors. I could do that but this would take very very long and I don't want this blog to be 10 hours long so maybe I'll save that for a future post :P.
Feel free to comment/discuss on what you think. Do you think there is a flaw in my calculations? Is there something else that bugs you because you want to know it? Basically any question is welcomed.
Thanks for reading, I hope you enjoyed ^^
TL;DR
*****, Diamond 4 is elo hell and Vapora Dark is my girlfriend.
I ''think'' BT overall gives more burst
y u no calculate it
unless you want me to do it lal
Never bothered to do that with BotRK. You can do it if you want, I need to renew my licence on Mathematica, waiting for a key from the uni... >_>
You can, if you want, figure out the values for health and armour where BotRK = BT.
y u no calculate it
unless you want me to do it lal
Woah :O. Interesting, I never see
Yeah been doing that since the beginning, I like BotRK more as a situational item rather than must have rush thing. I think BT overall gives more burst and it definitely improves your waveclear.
Did quite a lot of math myself on this subject so I knew, nevertheless this is a good read for new players who wanna become good at league. I always apply this in mid-lane as Zed -
Woah :O. Interesting, I never see
Or maybe I'm just too drunk.
Hm, I'm glad you put the world relatively in there because it really looks like you've got the typical wrong idea that Armor pen is less effective against high armor targets than against low armor targets :|.
But did you know that your Armor pen scales with the enemy's HP? I'm sure you didn't :3
Did quite a lot of math myself on this subject so I knew, nevertheless this is a good read for new players who wanna become good at league. I always apply this in mid-lane as Zed -
Always has been common sense that getting AD is more effective against Armour stacking than Arp because the flat arp becomes relatively less effective. No big mystery there.
Hm, I'm glad you put the world relatively in there because it really looks like you've got the typical wrong idea that Armor pen is less effective against high armor targets than against low armor targets :|.
But did you know that your Armor pen scales with the enemy's HP? I'm sure you didn't :3