← Digimon World 2003 Data

Digimon World 2003 — battle formulas

How the original European version (SLES-03936) computes damage, healing, buffs and fields, read from its decompiled C code (dw3_decomp). Each section names the function and file it comes from, so you can check it yourself.

Integer division rounds down everywhere, as on the PlayStation. Many values are stored in 128ths or 64ths: a value of 64 in 128ths is 50%.

What each stat does

Where the battle code reads each stat:

Defense, Spirit and Wisdom are three different defenses: Defense against physical damage, Spirit against magic damage, Wisdom against being hit by magic and against status ailments.

What Wisdom does, in detail:

Physical damage

FIGHTSTG_computeDamage, FIGHTSTG_adjustDamage — src/fightstg/damage.c

base = Power × Attack(user) / Defense(target)

Example: level-5 Kotemon vs the first Kunemon

Kotemon's basic attack (technique 1: power 60, accuracy 110, no element) against the Kunemon of the first areas (level 1, 120 HP, strength 16/16, from src/fieldstg/data/fieldstg.c). Kotemon has no equipment.

Kotemon's Attack at level 5. A new game starts it at 48 Strength (DIGIMON_DATA, initNewGameData in src/main/game/party.c). Each level adds STFGTREP_statGains[tier][growth + random(0–4)] (STFGTREP_raiseStats, src/stfgtrep/growth.c): with Kotemon's Strength growth 4, +8 to +14 for levels 2–4 and +6 to +11 for level 5. So at level 5 its Attack is 78 to 101, 91 on average.

Kunemon's Defense. 42 in the enemy table, × strength 16 / 16 = 42.

damage = Power × Attack(user) / Defense(target)
       = 60 × 91 / 42 = 130

None of the other steps apply: no field, no family, no charge, no element.

Hit chance: 110 + 110 × (SpeedDiff / 8 + LevelDiff) / 128 in 128ths (FIGHTSTG_rollHit). With Kotemon's Speed about 63 against 48 and 4 levels more: 110 + 110 × (1 + 4) / 128 = 114 → 89%.

Critical: 4/128 = 3.1%, for ×1.5 to ×2.5.

Kunemon has 120 HP, so a level-5 Kotemon's basic attack kills it in one hit 96% of the time when it lands.

Example: an elemental physical technique

The same level-5 Kotemon (Attack 91) and Kunemon (Defense 42), now with Kotemon's own technique Hot Head (technique 53: power 75, Fire, element strength 48, accuracy 127, 20 MP). Kunemon's Fire resistance is 90.

base   = Power × Attack(user) / Defense(target)
damage = base + base × 2 × ElementStrength / Resistance(target, element)
       = base × (1 + 2 × ElementStrength / Resistance)

base   = 75 × 91 / 42                = 162
damage = 162 × (1 + 2 × 48 / 90)     = 334

The element multiplier is 1 + 2 × ElementStrength / Resistance, so with Hot Head's 48:

A physical technique's element only ever adds damage; a high resistance just adds less. (Magic is different: a high resistance can halve it.)

Example: a Fire Field

The same Kotemon (Attack 91) and Kunemon (Defense 42, Fire and Water resistance 90) with a Fire Field set by a Digimon with 80 Spirit. The field acts before the element, on the base value (FIGHTSTG_getElementBoost, see Elemental fields):

FieldBoost = 64 + Spirit(whoever set the field) / 10          (at most 127)

technique of the field's element:  boosted  = base × (1 + FieldBoost / 128)
technique the field weakens:       weakened = base × (1 − FieldBoost / 256)
technique with no element:         unchanged
then the element step:             damage   = boosted × (1 + 2 × ElementStrength / Resistance)

FieldBoost = 64 + 80 / 10 = 72
base       = 75 × 91 / 42  = 162          (Hot Head's power; the basic attack's base is 130)

Fire attack (Hot Head):   162 × (1 + 72 / 128) = 253  →  253 × (1 + 2 × 48 / 90) = 522
Water attack (weakened):  162 × (1 − 72 / 256) = 117  →  117 × (1 + 2 × 48 / 90) = 241
Basic attack:             no element, so the field does nothing  →  130

With more Spirit the field is stronger, but the code caps FieldBoost at 127 (if (element >= 0x80) element = 0x7F in boostFieldElement). That is reached at 630 Spirit; above it, up to the maximum of 999, the field does not improve (64 + 999 / 10 would be 163):

The percentages compare with 334, the damage without a field. The basic attack stays at 130 in all three.

The game rounds each part down on its own (162 − 45 = 117, where 162 × 0.719 would give 116), so a result can differ by 1 from the one-line formula.

These are the numbers of a field that works as intended (with Harmony's Fixed Field Moves). In the original game and the PC port the Fire Field boosts Thunder and weakens Dark instead, so against Kunemon all three stay as without a field.

Example: a technique against its family

Bug Buster (technique 131: power 130, accuracy 110, 24 MP, no element, family Insect; learned by Hookmon and Armormon) against the same Kunemon, which is an Insect. Same Attack 91, to compare.

base   = Power × Attack(user) / Defense(target)
family = base × (1 + 1/2)                 when the technique's family is the target's

base   = 130 × 91 / 42  = 281
family = 281 × 1.5      = 421

The family match also adds 60/128 to the critical chance (FIGHTSTG_rollCritical), which the game's description doesn't mention: (4 + 60) / 128 = 50% instead of 3.1%.

Against its family a Buster does +50% and lands a critical every other hit: on average almost twice an elemental technique that hits a weakness. No technique has both a family and an element: the 13 family techniques have none.

Families, named from the Buster techniques' descriptions: 2 Dinosaur, 3 Evil, 4 Ghost, 5 Machine, 7 Bird, 8 Insect, 10 Aquatic, 11 Dragon.

Example: elemental accessories

The accessories Fire Power, Water Power, Ice Power, Wind Power, Bolt Power, Metal Power and Dark Power give the Digimon an element (FIGHTSTG_computeStats). Each comes in three strengths:

Only one can be worn: all 21 are one accessory group, and the equipment screen allows one of a group at a time (EQUIP_KIND_GROUP_ACCESSORY, src/stitshop/equip.c). So two Fire, or Fire and Water, is not possible.

The battle uses the accessory's element for the basic attack and the shared techniques without an element (Bug Buster, Big Shot, Hammer Rush…). It does not use it for a Digimon's own techniques (Vee Head Butt, Bear Fist, Terra Force…) or pair techniques, even when they have no element. A technique with an element uses its own and ignores the accessory. The elemental field looks at the technique's element only, so it never boosts an accessory's element.

damage = base × (1 + 2 × AccessoryStrength / Resistance(target, accessory's element))

basic attack, Fire Power S:  130 × (1 + 2 × 24 / 90) = 199
Bug Buster,  Fire Power S:   421 × (1 + 2 × 24 / 90) = 645      (421 = 281 × 1.5, the family bonus)

Same Kotemon (Attack 91) and Kunemon (Defense 42, Fire resistance 90):

The accessories are weak next to a technique's own element (Hot Head 48, Burn Slash 64), but they add to the Buster techniques, which have none: Bug Buster with Fire Power S does +53% on top of its family bonus. Against a given enemy, the accessory worth wearing is the one of the element it resists least.

Hit chance

FIGHTSTG_rollHit — src/fightstg/rolls.c

chance (in 128ths) = Accuracy + Accuracy × (SpeedDiff / 8 + LevelDiff) / 128
SpeedDiff = Speed(user) + accessories' accuracy − Speed(target)
LevelDiff = Level(user) − Level(target)

The game draws a number from 0 to 127 and the hit lands if it is below the chance, so a chance of 128 or more never misses. Each technique has its own Accuracy: a level-5 Kotemon (Speed 63, 4 levels above) against Kunemon (Speed 48) gets SpeedDiff = 15, which counts as 15 / 8 = 1, and LevelDiff = 4:

An enemy's hit chance uses the same formula minus the target's evasion, and is never below 32 (25%).

Magic damage

FIGHTSTG_computeMagicDamage — src/fightstg/damage.c

power = Power × (Spirit(user) × 50 / Spirit(target) + 50) / 100

The multiplier is 0.5 + 0.5 × Spirit(user) / Spirit(target): ×1 with equal Spirit, ×1.5 with twice the target's, ×2 (the cap) from three times; ×0.75 with half, ×0.625 with a quarter, never below ×0.5. Physical damage has no such bound: twice the Attack is twice the damage.

Wisdom does not reduce magic damage: the target's Spirit plays the part Defense plays for physical attacks. Wisdom decides whether magic lands (FIGHTSTG_rollMagicHit):

chance (in 128ths) = Accuracy + Accuracy × (WisdomDiff / 8 + LevelDiff) / 128
WisdomDiff = Wisdom(user) − Wisdom(target)

and also counts for status chances and healing.

Then: the field boost, and the target's resistance to the element:

A magic technique's element strength does not change its damage: only the element against this table does. It raises its critical chance instead (see below).

Then +50% against the target's family, the critical hit (+50% to +150%), the damage cut, at most 5 × power, and at most 9999 (European version).

Example: level-5 Renamon's Diamond Storm vs the first Kunemon

Diamond Storm (technique 59: magic, power 100, Ice, element strength 32, accuracy 127, 30 MP), Renamon's own technique from the start, against the same Kunemon (level 1, Spirit 40, Wisdom 50, Ice resistance 90).

Renamon's Spirit at level 5. It starts at 61 with Spirit growth 5. The gain table only has columns 0–8, so growth + random(0–4) can read column 9, which on the PlayStation is the first value of the next row: a tiny gain now and then. At level 5 its Spirit is 64 to 114, 99 on average.

power  = Power × (Spirit(user) × 50 / Spirit(target) + 50) / 100       (kept between Power/2 and Power × 2)
damage = power × (400 − 3 × Resistance) / 100                            (resistance under 100)

power  = 100 × (99 × 50 / 40 + 50) / 100 = 100 × (123 + 50) / 100 = 173
damage = 173 × (400 − 3 × 90) / 100      = 173 × 1.30              = 224

Hit chance: 127 + 127 × (WisdomDiff / 8 + LevelDiff) / 128. Renamon's Wisdom is about 92 against 50, so 127 + 127 × (5 + 4) / 128 = 135: it never misses.

Critical. A magic critical depends on the element (FIGHTSTG_rollMagicCritical):

value  = ElementStrength × 100 / Resistance(target, element)        (at most 64)
chance = value + 4                                                  (in 128ths)

Diamond Storm (strength 32) vs Kunemon (Ice 90):  value = 32 × 100 / 90 = 35  →  39 / 128 = 30%
Flame Ball    (strength 16) vs Kunemon (Fire 90): value = 16 × 100 / 90 = 17  →  21 / 128 = 16%

Both have power 100 and do the same 224 to Kunemon, since a magic technique's element strength doesn't change its damage; Diamond Storm, with twice the strength, lands almost twice as many criticals. A critical adds +50% to +150%.

Diamond Storm's critical chance by the target's Ice resistance:

So magic of an element the enemy is weak to gets more damage and more criticals.

A target with a status ailment takes more criticals, physical and magic alike, by the strength of the technique that inflicted it:

Diamond Storm against a Kunemon confused by Confuse Nebula: 39 + 63 = 102 → 80% criticals.

Kunemon has 120 HP: Diamond Storm always kills it. For comparison, Renamon's basic attack (Attack about 61) does 60 × 61 / 42 = 87.

How the target's resistance changes Diamond Storm (power 173):

Unlike a physical technique's element, magic can be halved by a high resistance, and more than doubled by a low one.

Critical hits

FIGHTSTG_rollCritical — src/fightstg/rolls.c

A physical hit is critical with this chance, in 128ths:

chance = 4                                  (3.1%)
       + EffectStrength                     if the technique has the Higher critical effect
       + the equipment's critical bonus     (×2 for special Digimon) if the technique has no effect at all
       + 60 if the technique is strong against the target's family (+16 for a weapon's family instead)
       + more while the target is paralyzed, asleep or confused

A critical adds damage × (32 to 95) / 64: +50% to +148%, about double on average.

A magic critical (FIGHTSTG_rollMagicCritical) has its own chance, from the technique's element strength against the target's resistance:

chance (in 128ths) = min(64, ElementStrength × 100 / Resistance(target, element)) + 4

(+60 more against the technique's family), and adds +50% to +150%.

Multi-hit

FIGHTSTG_rollMultiHit — src/fightstg/tech_effects.c; the total in src/fightstg/tech_action.c

The damage is computed once (with one critical roll) and multiplied by the hits that land:

total = damage × hits landed          (at most 9999, European version)

The first hit uses the technique's accuracy; each further hit rolls accuracy again. Blade Twister (power 120, 3 hits) is like a 360-power technique when all three land.

Healing

FIGHTSTG_computeHeal — src/fightstg/damage.c

HP = Power × 64 + Wisdom × Power / 8        (at most 9999, European version)

Buffs and debuffs

FIGHTSTG_changeBoost — src/fightstg/boosts.c; the techniques' amounts in FIGHTSTG_techBoosts and FIGHTSTG_sideBoosts — src/fightstg/tech_action.c

boost += stat × EffectStrength / 128        (− for debuffs)

The boost is a share of the stat without boosts. It stacks with each use, between −50% and +100% of the stat. It ends after random(0–2000) + 2000 + Spirit × 10 battle time units, and using it again resets the timer. The Spirit is that of the Digimon the boost is on: a debuff on a high-Spirit enemy lasts longer.

In turns: battles run on a timeline, not fixed turns. An enemy acts about every 1000 units (707 to 1414, from both sides' Speed: 1000 × Speed(other) / √(Speed(own) × Speed(other))), so a buff lasts about 2–4 turns, plus one turn per 100 Spirit.

Charge

chargeUser — src/fightstg/tech_action.c; used by FIGHTSTG_adjustDamage as the damage bonus

Soul Charge (80) and Misshukikou (127) add EffectStrength / 64 to the next physical technique's damage: +125% and +198%. The charge is spent by that technique.

Drains

Drain HP techniques heal EffectStrength / 128 of the damage dealt: Energy Leech 50%, Touch of Evil 62.5%, Energy Drain 99%. Vampire Jewel drains 6.25% of the target's max MP.

Status ailments

src/fightstg/rolls.c

chance (in 128ths) = EffectChance + Wisdom(user) / 8 − (Resistance(target) + Wisdom(target) / 2) / 8

kept between 1 and 127, rolled when the hit lands. The resistance is the target's resistance to that ailment (PSN, PAR, CNF, SLP, KO on the enemy explorer) plus one of its element resistances:

What each ailment does

Poison techniques

Each poison technique has two numbers: the chance to poison (EffectChance) and the poison's strength (EffectStrength), which sets how much it hurts (FIGHTSTG_getDamage, src/fightstg/damage.c):

HP lost each tick = (strength / 2 − (Poison res. + Water res.) / 10)% of the max HP     (at least 1, at most 50%)

A tick comes about once a turn (every 1000 time units) until the poison is cured or the battle ends; as a share of the max HP, it is as strong against bosses. Poisoning a target that is already poisoned replaces its poison (FIGHTSTG_inflictPoison overwrites the queued damage): a Poison Bites after a Deadly Poison brings it down from 44% to 21%.

Example: a poison technique vs Yanmamon

A technique with EffectChance 64, used by a Digimon with Wisdom 100, against Yanmamon (Poison 99, Water 91, Wisdom 70):

64 + 100 / 8 − (99 + 91 + 70 / 2) / 8 = 64 + 12 − 28 = 48   →   48 / 128 = 37.5%

Every 8 points of your Wisdom add 1/128 (about 0.8%).

Status weapons

A weapon with a status (worn in a weapon slot, not as an accessory) gives its chance to the basic attack and the physical techniques with no effect of their own, when the hit lands (never to magic); a technique with its own effect uses the technique's chance instead. The same formula, with the weapon's chance as EffectChance:

Battles that block them

Each battle can keep you from inflicting each ailment at all (Encounter.blocks, copied to BATTLE_SETUP.blocks), whatever the chance. Most story battles block some: of 150, 39 block poison, 48 paralysis, 58 confusion, 53 sleep and 62 knock-out; of the other 184 battles, only 2 to 10 block each. The first boss, Pharaohmon, cannot be confused, put to sleep or knocked out. The same list also blocks drains, steals, lowering the enemy's attack, defense or speed, and running away.

Elemental fields

boostFieldElement — src/fightstg/tech_action.c; FIGHTSTG_getElementBoost — src/fightstg/damage.c

boost = 64 + Spirit / 10        (at most 127)

• Techniques of the field's element: +boost / 128 → +50%, up to +99%.
• Techniques whose element the field weakens: −boost / 256 → −25%, down to −50%.
• The field lasts Spirit × 12 + 1000 battle time units: about 1 turn, plus one per 83 Spirit.

Which element each field weakens, according to the code (FIGHTSTG_opposedElements):

The game's own descriptions name other elements ("Strengthen fire, weaken ice"); the table above is what the code does.

Bug in the original game: boostFieldElement takes the field's element from the technique's icon field, which is 6 (Thunder) for all seven fields. So every field boosts Thunder (and weakens Dark), whatever its name says. The Harmony mod's Fixed Field Moves patch fixes it. The native PC port, built from the original code, keeps the bug.

Learning digivolutions

STFGTREP_learnDigimon — src/stfgtrep/growth.c; the lists in STFGTREP_evolutionLists

After a battle the game walks the partner's list of 44 forms in order and gives it the first form it doesn't have whose requirements are all met:

• up to two forms the partner must have, each at a minimum DV level (that form's own level), and
• one stat at a minimum: a battle stat, the partner's level, or a resistance.

The form takes the first free DV slot. The requirements of every form for every Rookie are in data/evolutions.csv and on the evolution chart.

Notes (to place)

Where Attack and Defense come from

FIGHTSTG_computeStats — src/fightstg/stats.c

• A partner: its own Strength or Defense, plus what its weapons and armor add, plus the digivolved form's stats (each form adds its own, as in DIGIMON_DATA), plus active buffs. A stat that ends at 0 or less counts as 1.
• An enemy: its battle table stats × the battle's strength / 16. The same Digimon gets stronger in later areas: the first Kunemon has strength 16 (×1), later ones 35, 38 and 45 (×2.2 to ×2.8).

Equipment that changes physical damage

Counterattacks

FIGHTSTG_computeCounterDamage — src/fightstg/damage.c

Counter techniques (Maul Attack, Counter Alert, Counter Strike) hit back for damage received × EffectStrength / 64 (/ 32 for special Digimon), then go through the steps above.

Enemies attacking you

Same formula, with the battle's strength already in the enemy's Attack and in its techniques' power. An enemy hits at least 25% of the time (a chance of 32/128), however fast you are, and its criticals work like yours.

Rounding and limits

Every step rounds down on its own, as on the PlayStation. There is no minimum damage: when Defense is much higher than Attack, or a damage cut absorbs it, a hit can do 0.

The steps after the base value

An enemy's technique is also multiplied by its strength / 16 (BATTLE_SETUP.enemies[].strength).

Then, in this order:

1. Field boost: if the technique's element is the field's, + base × boost / 128. If the field weakens it, − base × boost / 256 (see Elemental fields).
2. Family: +50% if the technique (or, for techniques with no family, one of the user's weapons) is strong against the target's family.
3. Damage bonus (a charge from Soul Charge or Misshukikou): + damage × bonus / 64.
4. Element vs resistance: + damage × ElementStrength × 2 / Resistance(target, element). With resistance 100 and strength 48 that is ×1.96; with resistance 300, ×1.32. A technique without an element uses the user's element from an accessory, if any (not for a Digimon's own techniques or pair techniques).
5. Triple hit accessory: each hit does × 4 / 10.
6. Critical hit: + damage × (32 to 95) / 64, i.e. +50% to +148%.
7. Damage cut of the target: subtracted, never below 0.
8. Caps: at most 5 × the base value, and at most 9999 (European version only).