Physical / Magic Damage taken
The calculation for Armor/MR in TFT works the same way as in League of Legends:
Armor/(100+Armor) = Reduced physical damage
Here are a two examples:
Kayle has 15 Armor.
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15/(100+15) = 0.13
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Kayle takes 13% less physical damage
Renekton has 45 Armor.
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45/(100+45) = 0.31
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Renekton takes 31% less physical damage
This means that you can come close to receiving no damage, but you will never create an unkillable unit simply with high Armor or MR stats. You want to combine high defensive stats with an ability that reduces damage taken like Redeemed Leona in Set 5.0, which caused her to become an Exodia Tank.
Negative Values
Until recently it was possible with certain abilities to reduce the enemy values below zero. Samira was the main reason behind the overhaul to this system. A unit with negative Armor/MR received more damage, which was a very powerful way to get rid of the enemy frontline.
Since Samira was too efficient at removing enemy Armor, the current system only allows Armor to get reduced to 0, which is effectively true damage and nothing to sneeze at.
Patch Notes 13.16

Flat Reduction vs Percentage
A Question that came up a lot in the Samira meta was the interaction between items like Last Whisper or Evenshroud and her ability. How effective is the combination of both?
The answer to this is very simple, Flat Armor Reduction will always be calculated first. A Percentage effect from an item like Last Whisper will constantly readjust its value based on the remaining Armor and therefore become increasingly inefficient.
Here are some examples to showcase this problem:
The enemy Illaoi starts the fight with 60 Armor. Now Evenshroud will reduce her Armor by 30%, leaving her with 42 Armor. Samira*2 with Blue Buff will take away around 19 Armor with every ability cast. After hitting her once, Illaoi is left with 29 Armor.
This is because Samira reduces the 60 base Armor by 19, leaving the enemy Illaoi with 41 Armor. Evenshroud will now take away 30% of 41 Armor, which results in 29 Armor remaining.
After another Samira Cast Illaoi would have 22 base Armor, so the Sunder Effect from Last Whisper or Evenshroud would reduce the new value to 15.
This doesn’t mean the interaction between these Flat and Percentage is completely useless, but the amount of Armor that is getting reduced by the Sunder effect will become smaller with every Samira Cast.
Reducing Armor and Magic Resistance
Currently in Set 9.5 there are several ways of reducing the Armor or Magic Resistance of enemy units:
Flat Armor Pen
- Samira 10/15/20 with every cast
- Nasus 4/4/20 stealing flat stats
Sunder (Armor Percentage)
- Vi
- Zaun Ryze
- Freljord
- Baron First Cast Rotation
- Apex Turret Shrink Module
- Last Whisper
- Evenshroud
- Black Cleaver
Shred (MR Percentage)
- Kayle Level 6
- Zaun Ryze
- Freljord
- Baron First Cast Rotation
- Apex Turret Shrink Module
- Black Cleaver