Hey what's up MOBAFire community! In this post I won't really be answering to someone's question. What a selfish guy I am :P. I'll try to clarify some misconceptions and weird stuff.

*Disclaimer*: You may already know some of the info below. This is a long blog, if you don't want to read it all, skip to the conclusions :P.

Answer: Wrong. Only the damage multiplier number has diminishing returns. But that number alone has no meaning at all. What's the point of reducing damage if we don't even think of what effect damage has on you? When you take damage it reduces your Health. You HAVE TO take in consideration HP to see how efficient Resistances are. Each point of Resistance makes all of your Health points more resistant. When you put HP and resistances together to see how tanky you are, you can easily see that Resistances do not have any diminishing returns at all.

The formula is:

Effective HP = HP + 1% per point of Armor
Survival Time = Effective HP / DPS

Example: You have 600 Damage Per Second and you are attacking a Teemo with 2000 HP and 80 Armor.

He has 2000 + 80% = 3600 EHP
He will stay alive for 3600 / 600 = 6 seconds

Now Teemo is angry, sold all his AP items and went full Armor. He has 2000 HP and 280 Armor.

He has 2000 + 280% = 7600 EHP
He will stay alive for 7600 / 600 = 12.67 seconds

By buying 200 Armor, Teemo didn't escape his fate but did survive an extra 12.67 - 6 = 6.67 seconds. Not bad.


Let's see if buying 200 Armor is always as effective. Now you are done with Teemo and you want to kill this stupid Malphite running after your carry. He has 2000 HP (lol) and 480 Armor.

He has 2000 + 480% = 11600 EHP
He will stay alive for 11600 / 600 = 19.33 seconds

By having 200 more armor than Teemo, Malphite was able to stay alive 19.33 - 12.67 = 6.67 extra seconds.


WAIT A SECOND. 6.67 and 6.67 are the same numbers! Each point of Armor will equally make you tougher and tougher. There is no diminishing returns on it.






It's basically wrong for the same reason as Misconception #1 but the other way around. Let's see why people have created this misconception:

Your ability does 1000 damage and the enemy has 50 Magic resist so your ability in fact does 1000 * 100/(100+50) = 666.67 damage

If you get Abyssal Mask (20 magic reduction), the enemy's MR goes down to 30 and you ability will do 1000 * 100/130 = 769.23

20 Magic reduction increased your damage by 769.23 - 666.67 = 102.564
or by 15.384% if you like


Let's see what happens against an enemy with 200 MR
1000 damage * 100/300 = 333.33 damage

With Abyssal Mask:
1000 damage * 100/280 = 357.143

In this case, 20 Magic reduction increased the damage of your ability by only 357.143 - 333.33 = 23.81
or 7.143%

It really looks like Magic Pen is more effective against low MR targets doesn't it ?!


Well, the thing is Magic/Armor pen doesn't actually increase your spell's damage, it decreases the enemy's Health points ability to reduce your damage. So each point of Armor/Magic resist that you subtract from the enemy will effectively reduce the resistance of his ENTIRE lifebar. And each point will reduce it by the same exact amount, no matter how much Magic Resist/Armor he already had.

Let's see it this way first. With the same example:

Your ability does 1000 damage and the enemy has 50 Magic resist so your ability in fact does 1000 * 100/(100+50) = 666.67 damage
The enemy has 2000 HP so you will have to cast the spell 2000/666.67 = 3 times to kill the enemy

If you get Abyssal Mask (20 magic reduction), the enemy's MR goes down to 30 and you ability will do 1000 * 100/130 = 769.23
The enemy has 2000 HP so you will have to cast the spell 2000/769.23 = 2.6 times to kill the enemy

20 Magic Penetration made you kill the enemy 3 - 2.6 = 0.4 casts faster


Let's see what happens against an enemy with 200 MR
1000 damage * 100/300 = 333.33 damage
2000 HP/333.33 damage = 6 ability casts to kill the enemy

With Abyssal Mask:
1000 damage * 100/280 = 357.143
2000 HP/357.143 = 5.6 ability casts to kill the enemy

Getting 20 Magic Penetration made you kill the enemy 6 - 5.6 = 0.4 casts faster.

0.4 and 0.4 are indeed the same number! In both cases, 20 Magic Pen helped you to kill the enemy 0.4 ability casts faster even though they had different amounts of Magic Resist.


So I guess what you can take out of this is that:






''Wtf are you talking about DarkPercy? Are you high lol?!''

Firstly, I don't smoke. Secondly, you may call me Percy. Thirdly, have a seat and listen to me my friend.

When you buy a stat, it will give you something in return. For example, if you buy Attack Speed, it will make you deal more damage per second with autoattacks.

For most stats (every stat except cooldown reduction), each point of a stat will always give you the same amount of whatever. For example, like we proved just above, each point of Armor will always give you the same amount of extra EHP if your HP doesn't change..

However, most stats (and by most I mean like literally every stat in the game) will be multiplicative with at least one other stat, making those stats increase the effectiveness of each other!

Example: The extra EHP you gain from armor is = Armor*0.01*HP. See? HP is in the formula and is multiplied by Armor. If you get more HP, each extra point of armor will grant you more EHP. And if you get Armor, each extra point of HP will grant you more EHP.


Another example could be: raw DPS = AS*AD
Attack Damage and Attack Speed increase each other's effectiveness. Getting too much of only one of those stats is incredibly not effective, but getting a good balance between those is super good.

Some stats will increase each other's effectiveness and at some point one stat becomes more effective than the other. At what point exactly? I could go in detail with this but that would take long and I don't feel like it fits this post. If you guys would like me to make another post to go further about this, I could :D.

I guess the misconception is: ''If you keep stacking Armor, buying Health will become more effective than buying Armor at some point because Armor has diminishing returns!''

You should actually say: ''If you keep stacking Armor, buying Health will become more effective than buying Armor at some point because when you buy Armor, it increases Health's effectiveness and eventually, Health's cost effectiveness will become higher than Armor's cost effectiveness''

That means that if you want to be as Tanky as possible, you need to find a perfect balance between Magic Resist, Armor and Health :D

And sometimes there are more than two stats that scale with each other. If we talk about DPS and AD carries, they have many many stats that scale with each other (AD, AS, Crit Chance, Crit damage, Lifesteal). Since these stats make each other exponentially better, it is why champions that buy a lot of these stats are so powerful late game and usually pretty weak early game.

Sometimes stats will scale with each other indirectly as well. For example, buying Armor will make the Health you gain back from Lifesteal more efficient. So indirectly, the Crit Chance you bought made your Armor stronger. Weird huh?

Another example would be getting AP increased Magic Resist's effectiveness. For example if you're playing Fiddlesticks, AP will make your Bountiful Harvest give you more Health back and thus the Magic resist you bought will be more useful!

This is one of the subtle ways in which offensive and defensive stats scale with each other and they're the reason why having a good balance between defense and offense (just like having a good balance between Armor and HP), will give you the best ending result. And by defense I don't necessarily mean stats. ''Defense'' can be seen as having a team around you to protect you or having a slow to peel enemies off you or simply NOT dying. You still need to know if you have enough defense from your team or if you need to buy a Guardian Angel to make the balance between Damage and Defense correct.

If this isn't too clear for you; I'll give you an example.

Let's say you have a team of 5 Malphites that all have 6 Warmog's Armors. They are all dealing 30 damage per second but they are able to stay alive for 30 seconds. Over the entire fight, each of them did 30*30 = 900 Percy Units. That's terrible. I call it Percy units because no one ever talks about what I'm talking atm so I decided I'd give the units my name :3.

If your team consists of 5 Ashes with a full ADC build (6 damage items), they all deal 1000 damage per second, but since they have no defense at all, they all get CCed and die in 1 second so they did 1*1000 = 1000 Percies each. Which is also terrible.

Finally, let's assume you have a well-balanced team with a bunch of carries and a bunch of tanks/supports that can peel enemies off them. The team will deal on average 400 damage per second but will survive the entire 10 seconds fight and will deal overall 400*10 = 4000 Percies each. Clearly our winner here.

I guess what I'm trying to say is that if Awesomeness = Offense * Defense, get a good balance between those two multiplicative numbers. Having one of those two numbers really big is completely useless if the other is too small.

If you take a step back and look from even more far away, you could even think of the formula

Offense * Defense = Chances to win

for the entire team as a mathematical proof that having a team of 5 carries or having a team of 5 tanks isn't going to work at all if you compare it to a well balanced Defense-Offense Team.


Some stats scale with non-existant stats: For example, AD will scale with your ability to go through units that you gained from Phantom Dancer if that made you able to kill/chase someone by not get minion blocked. (It allows you to attack more)

Non-stats factors ^ are the biggest reason why people will often misinterpret Math's numbers or will simply over/under rate something. Keep them in mind.

Always try to find the best balance between stats that scale with each other.



Cooldown reduction is a very strange stat that can scale with itself. Unlike every other stat, CDR has increasing returns (and doesn't even depend on another stat).

For example, if your spell has a 5 seconds cooldown and does 400 damage, it will deal 400/5 = 80 damage per second.

If you get 10% cooldown reduction, your spell now has a 4.5 seconds cooldown and it deals 400/4.5 = 88.89 DPS
10% CDR increased your DPS by 8.89.
Or by (1 - 88.89/80)*100 = 11.11%

If you get another 10%, you're now at 20% and your spell has a 4 seconds coodown. It deals 400/4 = 100 DPS.
10% extra CDR increased your DPS by 100-88.89 = 11.11
Or by (1 - 100/88.89)*100 = 12.5%

At 30% CDR, your spell has 3.5 seconds CD and deals 400/3.5 = 114.286 DPS
10% extra CDR increased your DPS by 114.286-100 = 14.286.
Or (1 - 114.286/100)*100 = 14.286%

And at 40% CDR: 400/3 = 133.33 DPS
133.33 - 114.286 = 19.047 extra DPS
The last extra 10% CDR increased your damage by (1 - 133.33/114.286)*100 = 16.66%


You may be thinking, what the hell ?!. Well yup, the first % of CDR isn't as good as the % of CDR that made you go from 39% to 40%. What does that mean? If you're getting CDR, you should really try to hit exactly 40% and not 38% or 39% since the last % are the best ones. Cooldown reduction is good.


Another misconception is that champions with ''long cooldowns'' should be buying CDR more than champions with low cooldowns in order to do good damage. This is absolutely wrong. Getting CDR will increase the DPS you do with your spells by the exact same increasing amount no matter what the cooldown on your spell is.

To prove it, I'll compare the damage increase from CDR for a 1000 damage 50 second cooldown spell with the damage increase shown above.

1000 damage and 50 CD means you are going 1000/50 = 20 damage per second

If you get 10% CDR, the spell now has 45 seconds cooldown and does 1000/45 = 22.22 DPS.
Damage increase = (1 - 22.22/20)*100 = 11.11%

Let's get another 10% CDR. 1000/40 = 25 DPS
(1 - 25/22.22)*100 = 12.5%

Another 10%. 1000/35 = 28.5714 DPS
(1 - 28.5714/25)*100 = 14.286%

ETC.

There we go. It doesn't matter if your spell's cooldown is small or big, Cooldown reduction will increase its damage by the exact same amount.

Champions that really really want to get CDR are the ones that have spells that do different things than damage that are essential to the kit. For example, a dash ability on a tanky bruiser (like Xin Zhao's Audacious Charge), a powerful CC ability on a support ( Lulu's Whimsy) or an ability that has exponential scaling with CDR ( Ezreal's Mystic Shot, Xin Zhao's Three Talon Strike, Zilean's Rewind, etc.)

Well. That's it guys. I hope you enjoyed this. Tell me what you'd like to see next :3