Battle formulas

At a glance

Melee kernel

FUN_801EC3E4 in the battle overlay (PROT 0898) - every direction-command and Art hit

Magic kernel

FUN_801DD0AC - Seru magic, monster specials, boss casts (INT-driven, separate finisher)

Applicator

FUN_800402F4 in SCUS_942.54 - the selector dispatch every HP / status / buff change funnels through

RNG

Standard PsyQ rand(): seed × 1103515245 + 12345, top 15 bits

Engine mirror

crates/engine-vm/src/battle_formulas.rs - pure functions, retail RNG draw order

Confidence

Confirmed against the disassembly, hit by hit (how we know)

• Your attack is base ATK (the unequipped number) plus half the gear the command uses, folded at swing time - never at battle load.
• An Art multiplies by 1.3 (1.4 with War Soul) and takes the element factor twice.
• Damage = Offense − Defense, capped at 9999 - with an underdog rewrite instead of a floor-at-1 when the defense would win outright.

Physical damage - Offense Value and Defense Value

One routine, two rolls, subtracted. Integer arithmetic throughout; Rnd(1..1.125) is shorthand for x + rand() % (x/8 + 1).

Base Offense = Base ATK + Equipment ATK / 2

Offense = [ Base Offense * Rnd(1..1.125) * Power / 16
          + Current HP / 256
          + Base Offense * Juggle / 64
          + Base Offense * Angle / 65536 ]
          * Arts Modifier * Element * (Element again for an Art)

Defense = Base DEF * Rnd(1..1.125) + Base DEF * Distance / 1024

Damage  = Offense - Defense                 (cap 9999; underdog rewrite below)

Base Offense: base ATK plus half of one slot

Base ATK is the character's ATK with nothing equipped - the battle loader copies it into the actor with no equipment folded in (it folds UDF / LDF / SPD, and skips ATK). The menu's ATK figure is base plus all gear, so the two never match. The equipment half is added at swing time, per command:

The arms are keyed by slot, not item type: Vahn and Gala carry the weapon in slot 2 and the Ra-Seru in slot 3; Noa carries Terra in slot 2 and her claws in slot 3, so hers are swapped. The Art arm sums body and head too - those normally carry no ATK, so in practice it is weapon + Ra-Seru + footwear.

Term by term

Worked example - Vahn vs Evil Fly

ZetaPhoenix's playtest: Vahn at base ATK 188, weapon ATK 98, footwear ATK 86, Ra-Seru ATK 100, HP 2747; an Evil Fly with UDF 42 / LDF 49, neutral element. The combo is Left arm, Right arm, then Hyper Elbow (a 20-power, LDF-targeting Art); the random draws are the observed ones.

Total 274 + 283 + 536 = 1086, matching the in-game figure. The second hit's juggle 2 is why it out-damages the first from a near-identical base, and the Art takes all three gear ATKs at half and then the ×1.3 - which is where most of an Art's advantage comes from.

The underdog floor

When Offense does not clear the defense, the routine does not floor the hit at 1 - it rebuilds the attack on top of the defense: Defense + (3/4 × Offense + rand() % (Offense/4 + 1)) × Power / 64 plus the juggle terms, re-applies a reduced Art multiplier (×11/10, or ×12/10 with War Soul) and the element pass, and finally a chip floor guarantees a few points (rand()%3 + 3 plain, rand()%4 + 5 for an Art). The "minimum damage" against a heavily-armoured enemy is therefore a fraction of your own roll, not a constant. A petrified defender takes nothing; the whole hit caps at 9999.

The juggle window - what makes a monster "juggleable"

Every hit adds BaseOffense × juggle / 64. The counter climbs by one for each hit that lands while the defender is still reeling from the last, and snaps back to 1 if you miss the window. The bonus is modest - the fourth hit of a juggle carries an extra ~6% - but it is the term that rewards a tight string. Three facts define it:

• The window is a property of the reaction clip, not the monster's stats: it is open while the defender's current clip is before its first authored event frame. Two bytes of the light-flinch animation entry - a beat and a rate - set its length: window = 4 × beat / rate ticks at 60 Hz in normal play.
• It restarts on every hit that lands inside it, so what matters is the gap between consecutive hits, never the length of the string.
• An Art's slow-motion halves or quarters everyone's play speed, which doubles or quadruples every window while it runs - part of why Arts chain so well.

Party members have the same mechanic - the kernel reads the defender's reeling byte whichever side it is on. legaia-patcher monster-stats prints the juggle column for every monster.

The smaller formulas

Actor stats and the monster record

The per-actor stat block runs +0x14C..+0x16A, each stat a pair of halfwords (working value, base). The loader copies each monster-record halfword into it; the names come from the formulas that consume each slot:

The single "Defense Up" buff raising UDF and LDF together confirms they are two facets of one defense. The parser exposes all six via legaia_asset::monster_archive::MonsterRecord; the enemy table renders them per enemy, along with each monster's castable spell list and AGL costs (decoded from the record's spell-offset array - entry head byte is the spell id, +0x74 the AGL cost the AI checks and spends).

Seru-magic side-effects

A levelled Seru spell does more than damage: the stager FUN_801F3D3C, called once per cast from inside the spell's own summon module, stages a secondary effect keyed on the summoned creature's element (the slot-7 record's +0x1D, the byte the affinity scale reads) and scaled by the caster's magic level for the spell (record +0x161). It writes a percent to 0x801F6960 and a banner string to 0x800775B4; the damage finisher FUN_801DDB30 then shaves stat × pct / 100 off the target on every hit. The table is 0x801F6870 (PROT 0898 file 0x28058), parsed by legaia_asset::seru_side_effect.

The gates, in order: level below 3 stages nothing. With the scripted-fight flag ctx[+0x287] set (a formation row's non-zero header byte - every boss), four casts in five are suppressed unless the spell is light or affinity[summon][first enemy] ≥ 101 (thunder against the four base elements, or the opposite pair). Then, for earth / fire / wind / thunder / dark in a scripted fight and for water always, the target's base stat halfword is compared with the raw record and the effect is dropped when they differ. Because the scripted boost profile has already raised ATK, UDF/LDF and INT, those three debuffs can never land on a boss; SPD and AGL land once per battle - literally once: the first cast that passes moves the value the compare reads, and every later cast of that element prints "No effect." for the rest of the fight; MP-down compares a value the hit never moves and lands every time. A random encounter runs neither the roll nor the compare (water aside), so everything lands and stacks. There is no per-monster immunity field - the record's +0x24..+0x43 is zero across the roster. The enemy table renders the verdict per enemy; the "No effect." banner is the return-from-fade pass FUN_801F3C34 announcing a suppressed or already-landed effect.

Engine: engine-vm::seru_side_effect::{stage_side_effect, apply_hit} both run in the live loop - the stager once per player Seru cast at the engine's single cast fold, the finisher switch per damaged target inside it. Three pieces of live state carry them: the base stat halfwords (written equal to the working halves at battle entry, the way the record copy does, and untouched afterwards except by a debuff), the scripted-fight flag derived from the formation's header byte, and the enemy stat seed picking its boost profile from that same flag - so a random encounter really does install the ×7/4 defence profile. A host with no disc installs no table and the stager returns before its one rand() draw.

Victory spoils

EXP / gold / drop are inline in each monster record; the spoils routine walks the dead enemies and applies the scaling in the table above:

The drop is one item per battle, not one per enemy. Every enemy costs one rand() % 100 against its chance (plus 30 when a living member carries Items Up), and the last enemy whose roll wins supplies the item - a captured one cannot. Then, unless some enemy has a 100% chance or the bonus applies, a further rand() & 3 must come up zero or the drop is lost: a lone 10% enemy drops 2.5% of the time. The item is not granted when 99 are already held.

Runtime-confirmed by write-watchpoint (Gimard credits exactly +15 gold) and cross-checked against the curated game-data tables (Gimard drops Healing Leaf at 10%). The engine wires the scaling into World::apply_battle_loot / apply_battle_xp, so the credited reward is the scaled amount, not the raw record sum.

The special-battle word _DAT_8007BAC0 is not the scripted-fight flag - a boss row leaves it alone. It is non-zero in an arena leg and in the two Ra-Seru-forbidden fights (the Rim Elm ambush, first monster 0xAF), and any bit of it zeroes the gold and each member's EXP, skips the drop walk and the steal, makes the Seru absorb answer "known", skips spell XP and drops a monster flee the roll granted. The same word opens no result window at the end, ends the battle as a party wipe once the leader has all three limbs rotted, and in an arena leg hands a Run round's first turn to the leader and records the leg as run; its 0x100 bit forces the party's flee. The engine reads all of these through World::special_battle_word.

Engine port

crates/engine-vm/src/battle_formulas.rs ports every formula above as pure functions, drawing rand() in retail call order so the RNG stream matches. Live in the battle loop:

• Melee: physical_predamage + the per-command equipment fold; accuracy rolls; MP-saver accessories.
• Magic: the faithful summon kernel for player Seru-magic and arts_physical_predamage for monster specials, seeded by the move-power table.
• Element affinity in both directions - and by slot, not spell: a player Seru cast attacks as the summoned creature, scaling by matrix[creature element][target element]; a monster's element reads record-direct.
• Finisher: damage_finish - elemental-guard halving, guard halve, the rand()%9+8 floor, the 9999 cap, spirit-gauge accrual.
• Spoils and escape: the reward scaling and the Run roll.

Every disc-seeded path is gated so an uninstalled table reproduces the placeholder baseline bit-identically - disc-free battles stay deterministic.

How we know

Each claim of the community analysis is checked against the disassembly; every term is confirmed, with one correction (the random source is 15-bit, immaterial after the modulo) and two open magnitudes (the negative-angle behaviour; the walk-in distance is runtime state, not a constant). The full claim-by-claim table, register-level stage list and address appendix - plus the summon kernel, spell-XP accrual and poison ticker in full - are in docs/subsystems/battle-formulas.md.

Credits and sources

• ZetaPhoenix - the Offense Value / Defense Value shape, the per-command equipment halving, the Rnd(1..1.125) reading, the juggle / angle / distance terms, the juggleability question (his guess - the state of the damage animation - was right) and the worked example, all measured against the running game and checked here against the disassembly. His Legaia Arts Data spreadsheet is what the legaia-art trigger tables are validated against.
• Meth962 - the original forum analyses the above corrects: thread 800 and thread 941 (Wayback Machine); his 100% walkthrough grounds the curated enemy tables.

See also