Summoners War Mechanics

Multipliers are the values shown in swarfarm or in the skill selector in `/damage-optimizer`.

Buffed stats: ATK/DEF/SPD scaling uses the overall stat, so ATK buff, DEF buff, and SPD buff multiply the total stat by 1.5, 1.7, and 1.3 respectively before the hit scales from it.

ATK/DEF Increasing Effect: the bonus is calculated as BaseBuff% × (1 + effect/100) and truncated. Example: +11% ATK up effect gives ATK buff 50 × 1.11 = 55.5% potency, which gets truncated to exactly 55%, not 56%. Similaryly DEF buff 70 × 1.11 = 77.7%, which gets truncated to 77%, not 78%.

SPD Increasing Effect: uses the same truncation rule. Example: +24% effect gives SPD buff 30 × 1.24 = 37.2%, which gets truncated to 37%.

• CD High/Low HP +N% always active, applies to all hits.
• S1 / S2 / S3 Crit DMG +N% only applies when that specific skill is used.
• First Attack Crit DMG +N% applies to the monster's first attack against each enemy on any given turn. This means Teshar S3's AoE damage will benefit from it (the primary target will not). Similarly, Astar S1's final hit on the other units will benefit from S1 CD.
• Own 1-target CD +N% applies on the monster's turn for all hits. Even if the monster happens to trigger Co-op.

Other includes passives (Lucas, Sonia, Leah) and skill effects (Brandia S3, Argen S3).

Deborah is modeled through the effective DEF break:

Dbreak = 1 - EffectiveDefBreak

Effective DEF break is 91% (normal). Boss Deborah reaches 80.5%, which the game rounds down to exactly 80%.

Herteit S3 Absorb is treated as stat transfer:

stolen = rate × knowledge × BaseStat

Rate is 0.25 (normal) or 0.10 (boss).

Both scaling buckets use independent triangular samples:

function sampleRandomVariation () {
  const triangular = spread => 1 + (Math.random() + Math.random() - 1) * spread
  return {
    attackScaling: triangular(0.028),
    maxHpScaling: triangular(0.0235)
  }
}
          

Additional damage by X% cannot crit, does not benefit from DMG dealt on Element, and bypasses DefenseFactor. Skill-based fixed damage also cannot crit and bypasses DefenseFactor, but unlike artifact additional damage it is still multiplied by (1 + DMG%).

Example, Coco S3: 5 hits dealing Fixed damage. Each fixed hit still scales with artifact DMG% bonuses, while artifact Additional Damage by +N% stays as a separate flat add after that.

Reflect Damage buff: Acts as a separate DamageDecrease effect and reduces incoming damage by 30%. Passives that reflect damage also decrease the damage taken and fall in this bucket. Reflected damage is calculated from the Raw damage before any damage decrease but after defense factor. Examples of effects: Camilla, Dark golem, Reflect damage buff These lists are not exhaustive, and each effect not listed here, should be tested on a case by case basis.

Swift correction: the game display uses ceil() on rune speed and ignores speed lead/tower/swift interaction in that view, so SWCALC corrects the rounding error when calculating true combat speed.

const frac = (BaseSpd * 0.25) % 1
const swiftCorrection = (isSwift && frac > 0) ? (1 - frac) : 0
const speed = speed - swiftCorrection
          

Speed-up effect truncation: potency is truncated down. Example: +22% speed-up effect gives floor(30 * 1.22) = floor(36.6) = 36%, not 36.6%.

Leo rule: if Leo exists, non-Leo monsters are capped to the lowest Leo combat speed.

Turn trigger: a unit can move when attack_bar >= 100. If multiple units are ready, highest attack_bar goes first.

Same speed order: when monsters have the same speed/priority, they move in the same order they were selected in setup.

Unit has 105 base SPD, lead 33%, totem 15%, +150 speed on Swift, Speed Buff active, and Speed Up Effect of 13%.

Step 1: Base-with-lead+tower speed = 105 × (1 + 0.48) = 155.4.

Step 2: Swift correction: frac = (105 × 0.25) % 1 = 0.25, so correction = 1 - 0.25 = 0.75, and effective rune speed = 150 - 0.75 = 149.25.

Step 3: Add rune speed = 155.4 + 149.25 = 304.65.

Step 4: Round up before buff: ceil(304.65) = 305.

Step 5: Speed Buff potency = floor(30 × (1 + 0.13)) = floor(33.9) = 33%, so buff multiplier is 1.33.

Step 6: Apply buff: 305 × 1.33 = 405.65 combat speed.

Result: Final combat speed is 405.65.

Note: If the unit is not Swift, no correction is applied, so pre-round speed is 155.4 + 150 = 305.4 and ceil(305.4) = 306, exactly 1 higher.

Agrius has 104 base SPD, tower 15%, +145 speed on runes, Speed Buff active, Speed Up Effect of 24%, no lead.

Step 1: Base-with-tower speed = 104 × 1.15 = 119.6.

Step 2: Add rune speed = 119.6 + 145 = 264.6.

Step 3: Round up before buff: ceil(264.6) = 265.

Step 4: Speed Buff potency = floor(30 × (1 + 0.24)) = floor(37.2) = 37%, so buff multiplier is 1.37.

Step 5: Apply buff: 265 × 1.37 = 363.05 combat speed.

Step 6: Enemy speed is 163, so gap = 363.05 - 163 = 200.05.
Result: Agrius is more than +200 faster, so he gets full ignore defense.

Deborah is modeled through the effective DEF break:

Dbreak = 1 - EffectiveDefBreak

Effective DEF break is 91% (normal). Boss Deborah reaches 80.5%, which the game rounds down to exactly 80%.

Herteit S3 Absorb is treated as stat transfer:

stolen = rate × knowledge × BaseStat

Rate is 0.25 (normal) or 0.10 (boss).

Chilling: Chilling gets exactly +20 flat speed for each buff on himself. If 2 monsters have the same highest attack bar, the tie-break turn order only considers pre-combat speed, which excludes passives. That means Chilling will always go last in a speed tie-break scenario.

Tested with Rigna and Tablo on various speeds, speed lead, and swift/non-swift configurations.

Sonia: Sonia gets full bonus at +50 speed faster than the enemy.

Leah: Leah gets full bonus at +150 speed faster than the enemy.

Agrius: Agrius gets full ignore defense at +200 speed faster than the enemy.

Full ignore defense at +126 speed faster than the enemy.

Rigna: Rigna will auto-crit in case she is faster than the enemy by any amount (tested at 0.02 speed faster). If 2 monsters start at 0 speed in the same tick and Rigna outspeeds but does not auto-crit, the 2 monsters have exactly the same speed.

Arena/RTA (towers only): +730 ATK, +884 DEF, +129 SPD. Siege/Guild War (towers + guild flags): ~+583 ATK, ~+737 DEF, +129 SPD.

Gets 3.5x combat speed added to her attack.

Skill 3 works as 25% negative damage resistance (the recent buff said "25% > 30%", but the actual tested damage numbers did not change). It stacks additively with -DMG% taken artifacts, but neither effect applies to bomb or fixed damage.

Each attack adds a damage bonus for future attacks. Whenever an attack deals more than 5000 damage increases the damage of further attacks by damage / 5000 (rounded down) and increases the attack bar of all allies by the same amount. The damage bonus is cumulative. A multi-hit attack uses one unchanged bonus for every hit; its bonus is added only after the whole attack ends.

added bonus % = attack damage dealt ÷ 5,000

• 5,000 damage: future attacks get +1% damage, and all allies gain 1% Attack Bar.
• 12,500 damage: future attacks get +2% damage, and all allies gain 2% Attack Bar.
• Multi-hit: For example Julie S3 - all 6 hits use the same damage bonus, so hit 6 gets no more damage than the first hit.

Needs testing.

Needs testing.

Needs testing.