Trying to clear up a misunderstanding about diminishing return for Armor/MR and CDR/Haste

Many people on this sub claim that Armor/MR and Ability Haste have diminishing returns. I can see where that misunderstanding comes from and thought I make a post and try to clear that up.

Armor/MR and damage taken values

The formula for damage taken is 100/(100+Armor).

Here is a graph that shows how the value changes from 0 armor to 500 armor.

This is where most people take the diminishing return from. With 100 armor you take 50% damage so a 50% reduction. With 200 armor you take 33% damage so a 66% reduction. That's only 16% more damage reduction than before.

The misunderstanding is that armor doesn't exist in a vacuum and is simply an amplifier to your health similar to crit% and crit dmg to AD. Armor without Hp makes no sense in the game. Health is the most important stat for gameplay functions in the game.

Remove Armor and MR? The game still works.

Remove all damage values from the game? It's a standstill but the game works.

Remove all Hp values from the game? The game doesn't work anymore.

That's why we have to look at how much more damage you can absorb with your armor.

You have 1000 HP with x armor. How many hits does it take an enemy with 100 ad to kill you

Here is a graph

As you can see now it has become a linear graph. Why is that so? (Nitpickers please ignore the hp/AD unit mess)

At 0 armor you take 100% of the damage. 1000 hp/100 AD means you die in 10 hits.

At 100 armor you take 50% of the damage. 1000 hp/100*0.5 AD means you die in 20 hits.

At 200 armor you take 33% of the damage. 100 hp/100*0.33 AD means you die in 30 hits.

Every 100 armor buys you and additional health bar. This modified hp value is called effective HP. Every 100 armor increases your eHP against physical damage by 100% of your Hp.

This symbiosis between Hp and Armor/MR means that the other stat becomes more valuable if you have a lot of one of them.

If you have 500 Armor and 2000 Hp, your effective Hp against physical damage is 12000 eHp.

Buying 100 Armor takes you to 14000 eHp. Buying 1000 Hp instead takes you to 18000 eHp.

If you have 100 Armor and 5000 Hp, your effective Hp against physical damage is 10000 eHp.

Buying 100 Armor takes you to 15000 eHp. Buying 1000 Hp instead takes you to 12000 eHp.

Every point of Hp you add makes you Armor more valuable and every point of Armor you have makes your Hp more valuable.

These things get muddier when you take %damage, Hp scaling, Armor Pen, True Damage, Flat Damage reduction, Shields, Heals etc into account, but generally speaking you get the most value out of a balanced build, rather than leaning fully into 1 direction.

The way old CDR used to work

For those that don't remember there was a stat called Cooldown Reduction and it was the predecessor to Ability Haste. It worked like people think linear scaling should look like and had to be capped at 40%, because it scaled exponentially.

That's why it is great to show why Armor and MR have to scale the way they do.

The formula for CDR was BaseCD*(1-(CDR/100))

Here is a graph of the cooldown for a 10s CD ability

Look perfectly linear, great isn't it? Well the problem is that we have to go 1 step deeper to really understand what is going on.

How often can you cast that abliity in 100 seconds

Hmm that doesn't look linear at all. Where does this exponential curve come from? Let's take a look at some specific values.

At 0 CDR you reduce your CDs by 0%. 100s/10s means you can cast it 10 times. 0% more casts in the same timeframe

At 25 CDR you reduce your CDs by 25%. 100s/7.5s means you can cast it 13.3 times. 33% more casts in the same timeframe.

At 50 CDR you reduce your CDs by 50%. 100s/5s means you can cast it 20 times. 100% more casts in the same timeframe.

At 75 CDR you reduce your CDs by 75%. 100s/2.5s means you can cast it 40 times. 300% more casts in the same timeframe.

At 100 CDR you reduce your CDs by 100%. You have no CDs and can cast an infinite amount of time.

CDR as a stat had more value the more you had of it. Going from 0% to 10% was way less valuable than going from 30% to 40%. It was capped at 40%, because of that and Riot reworked it into Ability Haste which works like Armor and MR.

If Armor/MR worked the way some people think linear scaling should look like you would have 50% damage reduction at 100 Armor and 100% damage reduction at 200 Armor. You would become immortal at 200 armor.

Ability Haste

To wrap it up quickly Riot changed to CDR to Ability Haste and it works exactly the same as Armor and MR do.

The formula is: CDR (this is what you could buy before) = 100/(100+Haste).

Here is a graph for a 10 second CD ability

As you can see it's the same as Armor and MR. 100 Haste reduce your CDs by 50%, 200 Haste reduce your CDs by 66% etc..

Ability casts in 100 seconds

At 100 Haste you double your casts, At 200 Haste you triple your casts.

Summary

Ability Haste and Armor/MR scale linearly. CDR used to be OP. Hope some people learned something