Damage reduction

**Damage reduction** is a hidden player statistic that decreases damage taken. All boosts (except Warmth Potion) affect damage taken *after* defense.

## Notes

* The Solar Blaze, Beetle Endurance, Warmth, and Paladin's Shield buffs calculate damage multiplicative with each other, while the other effects calculate additive. So firstly the raw damage is decreased by the banner's effect (25% / 50% reduction) and Warmth Potion (30% reduction from cold sources), then the remaining damage is reduced by defense (50% / 75% / 100%), the remaining damage is then reduced by all additive damage reduction, then by Beetle and Solar Flare armor's buff, and finally by Paladin's Shield. (Also, each step will round down the damage value, but the value cannot be less than 1.)
	+ For example, if in a Master world, a cold-themed enemy somehow dealt 2000 damage to a player, the player wears a full set of Solar Flare armor (with its buff), a Worm Scarf, a Frozen Turtle Shell (with its buff on), with buff of Endurance, Warmth, a banner of that enemy, a teammate with Paladin's Shield and 140 defense.
		1. The banner reduces the damage by half to 1000.
		2. The Warmth buff reduces it by 30% to 700.
		3. The defense reduces it by 140 to 560.
		4. The Worm Scarf (17%), Endurance (10%), Solar Flare armor (12%) and Frozen Turtle Shell (25%) reduce damage additively, so they reduce it by 64% to 201.6, rounded down to 201.
		5. Solar Flare armor's buff reduces it by 20% to 160.8, rounded down to 160.
		6. A teammate's Paladin's Shield reduces it by 25%, so the player will take 120 damage.
		7. The teammate will take 40 damage, and it will be further reduced by that player's status (banner and Warmth will not take effect, though).

## Maximum damage reduction

The highest damage reduction possible is 73.6% (or 81.52% against cold-themed enemies), using the following setup:

### PC version, Console version, Mobile version, Old Chinese version, tModLoader version, and tModLoader 1.3-Legacy version

* Armor (multiplicative)
	+ Beetle armor with shell – 45% reduction
	+ Warmth Potion – 30% reduction against cold-themed enemies
* Accessories and potions (additive)
	+ Frozen Turtle Shell – 25% reduction
	+ Worm Scarf – 17% reduction
	+ Endurance Potion – 10% reduction
	+ If Paladin's Shield buff is on, it can reduce additional 25% damage after defense.

Therefore, the maximum damage reduction is:

(
1
−
0.45
)
∗
(
1
−
(
0.25
0.17
0.1
)
# 0.264
26.4
%

 damage taken

=
73.6
%

{\displaystyle (1-0.45)\*(1-(0.25+0.17+0.1))=0.264=26.4\%{\text{ damage taken}}=73.6\%}

The maximum damage reduction against cold-themed enemies is:

(
1
−
0.45
)
∗
(
1
−
0.3
)
∗
(
1
−
(
0.25
0.17
0.1
)
# 0.1848
18.48
%

 damage taken

=
81.52
%

{\displaystyle (1-0.45)\*(1-0.3)\*(1-(0.25+0.17+0.1))=0.1848=18.48\%{\text{ damage taken}}=81.52\%}

 (note that the Warmth Potion is calculated *before* defense).

### Old-gen console version and Windows Phone version

* Armor (multiplicative)
	+ Beetle armor with shell – 45% reduction
* Accessories and potions (additive)
	+ Endurance Potion – 10% reduction
	+ Warmth Potion – 30% reduction against cold-themed enemies
	+ This does not include the Paladin's Shield buff, since its damage reduction occurs before defense, and all others occur after defense.

Therefore, the maximum damage reduction is:

(
1
−
0.45
)
∗
(
1
−
0.1
# 0.495
49.5
%

 damage taken

=
50.5
%

{\displaystyle (1-0.45)\*(1-0.1)=0.495=49.5\%{\text{ damage taken}}=50.5\%}

The maximum damage reduction against cold-themed enemies is:

(
1
−
0.45
)
∗
(
1
−
(
0.1
0.3
)
# 0.33
33
%

 damage taken

=
66
%

{\displaystyle (1-0.45)\*(1-(0.1+0.3))=0.33=33\%{\text{ damage taken}}=66\%}

### Nintendo 3DSversion

* Armor (multiplicative)
	+ Beetle armor with shell – 45% reduction
* Accessories and Potions (additive)
	+ Endurance Potion – 10% reduction
	+ This does not include the Paladin's Shield buff, since its damage reduction occurs before defense, and all others occur after defense.

Therefore, the maximum damage reduction is:

(
1
−
0.45
)
∗
(
1
−
0.1
# 0.495
49.5
%

 damage taken

=
50.5
%

{\displaystyle (1-0.45)\*(1-0.1)=0.495=49.5\%{\text{ damage taken}}=50.5\%}