Damage Resistance, also referred as Res, is a special defense value that applies to damage done to a ship's armor, sails and structure. It lowers incoming damage by a percentage and not by a definite number like Damage Reduction. In some circumstances it can reduce the incoming Damage to only one (1) damage per shot! (which is the lowest number, zero (0) isn't possible).

Damage Resistance (Res) gets applied AFTER Damage Reduction (DR). Thus, in theory Res gets less effective if you have a high number of DR.

Example 1:

You have 10 Damage Reduction (DR) and 10% Damage Resistance (Res). Enemy has 10 cannons, which deal 20 damage each.

Normally you would get 10 x 20 = 200 damage. However, 10 DR lowers this value to 10 x (20-DR) = 10 x (20 - 10) = 10 x 10 = 100.

Now the 10% Damage Resistance gets applied. 100 x 0,9 (1 - 0,01x %) = 90. I

So in this example 10 DR reduces incoming damage by 50%, while 10% Res only reduce incoming damage by 5% (10/200).

Formular 1:

[Damage = [Damage of Cannons - Target DR] x [Amount of Cannons]] / Res

Damage Resistance (Res) can be any numbers from -50% to +50%. Meaning, enemy damage gets either increased (-50%) or decreased (+50%). This may sound controversary, but it's simple. If your **Resistance is lower, the chance you get hit is higher, in PotBS case, the Damage will be higher. **
In example 1 we saw that 10 DR was way more effective than 10% Res. This is true in most cases. Portalus Games thinks that 1 DR is equal to about 4% Res. This is because they reworked Focused Fire (skill) a while ago, from -6DR to -25% Armor Damage Resistance.

Example 2:

If you have +25% Damage Resistance (green in stats) you take 25%

lessDamage.

If you have -25% Damage Resistance (red in stats) you take 25%

moreDamage.

So what's better you may ask? Damage Reduction (DR) or Damage Resistance (Res)? Well ... that's extremly hard to tell since it matters from alot of factors! General speaking: Damage Reduction is good against small amount of damages (so light cannons) and Damage Resistance is better against big amount of damages (so heavy cannons). For more information: Damage Reduction, Damage, Hull

This information is provided by the update that PotBS Wikia is undergoing, by Captain Vuur.