Combat mechanics

Elemental Mastery & Affinity

Your Elemental Mastery and your five Affinities are never used raw. The game divides each by a hidden value that grows every level. That is why the same gear feels strong at the end of a rank and weak at the start of the next, and why a point of the right Affinity is worth far more than a point of Mastery.

The formula

Elemental damage is multiplied by a ratio: your offence over their defence.

                  1 + (your X Affinity / their Base Elemental Add) + (your Elemental Mastery / their Base Elemental Mastery)
Elemental mult. = -------------------------------------------------------------------------------------------------------
                  1 + (their X Aegis   / your Base Elemental Add)  + (their Elemental RES    / your Base Elemental Mastery)

Here X is the hit's element. Two layers add up: the Affinity of that one element and the general Elemental Mastery. A Physical hit (no element) is scored the same way with Physical Mastery against Physical RES. See Physical hits below. The game keeps a separate hidden divisor for the Affinity side, but it always holds the same number as Base Elemental Add, so this page calls both "Base Elemental Add".

What the number on your Character screen means

Each Affinity is shown on the Character screen in points, and the formula uses those points exactly as shown: they are divided, never rescaled first. Water Affinity's own description reads: "Increases Water DMG dealt by the caster's skills. When against enemies of the same level, increases by approximately X." The game fills in X as your Water Affinity divided by your own Base Elemental Add, the hidden value in the table below. The other four say the same for their element.

The damage formula divides by the target's hidden value instead. Against a target of your own level the two are the same number, so the percentage the game shows is exact. Against a higher-level target the divisor is bigger and the bonus smaller. Against a lower-level one it is larger. Elemental Mastery is shown the same way, divided by your own Base Elemental Mastery, which is why its percentage looks so small at Champion.

At Champion I's cap (level 110) Base Elemental Add is 6,693 and Base Elemental Mastery 82,698, so:

• 1,000 Wind Affinity adds 1,000 / 6,693 = +14.9% to the offence side of a Wind hit, and nothing to a Fire hit.
• 1,000 Elemental Mastery adds 1,000 / 82,698 = +1.2% to a hit of any element.
• 200 of each of the five Affinities adds 200 / 6,693 = +3.0% to a Wind hit (only the Wind 200 counts) and the same +3.0% to a Physical hit (the average of the five).

Both land in the same 1 + … sum, so they add rather than multiply: Wind Affinity equal to its divisor and Mastery equal to its divisor together give 1 + 1 + 1 = ×3 on a Wind hit before the target's Wind Aegis and Elemental RES divide it. Affinities never roll on equipment. They come from relics, Fantomon and skills.

Physical hits

A Technique or Charm with no element deals a Physical hit. The game runs it through the same ratio with two swaps:

                 1 + (avg of your 5 Affinities / their Base Elemental Add) + (your Physical Mastery / their Base Physical Mastery)
Physical mult. = ----------------------------------------------------------------------------------------------------------------
                 1 + (avg of their 5 Aegis     / your Base Elemental Add)  + (their Physical RES    / your Base Physical Mastery)

Physical Mastery and Physical RES replace Elemental Mastery and Elemental RES, so Elemental Mastery adds nothing to a Physical hit and Physical Mastery adds nothing to an elemental one. The Affinity and Aegis terms take the average of all five elements, so an Affinity counts at a fifth of its value on a Physical hit.

Base Physical Mastery is a separate hidden value, but it holds the same number as Base Elemental Mastery from No Rank to Paragon III. From Saint I up it runs 0.5% to 1.7% higher. The table below lists both, so it serves for Physical hits as well.

A worked hit at Champion II's cap (level 120): Base Physical Mastery 105,649, Base Elemental Add 7,677. The attacker has 30,000 Physical Mastery and 5,000 Wind Affinity with none in the other four, so the average is 1,000. The target is the same level, with 10,000 Physical RES and no Aegis.

• Offence: 1 + 1,000 / 7,677 + 30,000 / 105,649 = 1.414
• Defence: 1 + 10,000 / 105,649 = 1.095
• Multiplier: 1.414 / 1.095 = ×1.29

What 1,000 more points add to that hit: Physical Mastery +0.7%, Wind Affinity alone +1.8% (a fifth of it reaches the average), and 1,000 in each of the five Affinities +9.2%. At Champion, Physical Mastery is weak for the same reason Elemental Mastery is, and Affinity spread across all five elements is the stat that moves Physical hits.

What "Base Elemental Mastery" is

It is a stat, but the game hides it from the stat screen. It is a per-rank, per-level constant: the expected value for a character at that point in the game. Your actual Mastery is scored against it.

Worked at one rank

At Expert III (level 100) the base value is 10,987:

The hidden divisors by rank

The values are at each rank's level cap. Within a rank both climb a little every level. Base Elemental RES equals Base Elemental Mastery on every row, and Base Elemental Reduce equals Base Elemental Add. The last two columns are what 1,000 points add to the offence side against a target at that level: the Affinity of the hit's element, or Elemental Mastery.

The Champion wall

One transition dwarfs the rest. Promoting out of Expert III multiplies the base value by ×4.56 at the same level (10,987 → 50,061), and by the time you reach Champion I's own cap it has risen ×7.53 overall. Every other rank-up in the game falls between ×1.04 and ×1.7.

A dial the developers left in

The scoring works as (your stat / your base) × (your base / their base)^k, with k set to 1. At 1 the exponent changes nothing, but it is clearly a dial for how much the level gap matters. If elemental scaling ever shifts without a stat change, this is the likely cause.