(cache)Damage Calculus 101 – Attack, Defense, and Elemental Effects in TTYD

Following my article on evasion badges and misconceptions about how they stack, here’s an in-depth article explaining the Paper Mario: TTYD damage calculation process and all its subtleties. Normally I’d cover PM64’s equivalent mechanics at least in passing, but Floogal’s GameFAQs guide on Paper Mario stats and attacks is comprehensive and accurate on that matter already, so I’ll not waste words treading already-paved ground.

That said, here’s a list of stuff that will be (mostly) out of the scope of this investigation, unless I flesh out the post after the fact:

Details about the base attack power for every move with variable damage (any player moves, stackable move badges, etc.)
Details about various defensive and elemental-effect states of every enemy (e.g. Buzzies having different defenses when flipped than when upright).
In general, interactions other than simple damage calculation; e.g. flipping shelled enemies, exploding bomb enemies, etc.

For the special point of FP-damage calculation, there’s not much to be said:

Poison BINGOs erase half the party’s FP rounded up; this cannot be changed in any way.
Flower Fuzzies deal a 0 HP-damage hit and 3 FP-damage hit simultaneously if the party has at least 1 FP, or a 3 HP-damage hit alone if they have none. In either case, the FP lost is a constant 3 (or 2 if blocked), and the HP damage is dealt with like any normal HP-reducing attack.
Point Swaps do not follow damage calculation rules, simply swapping the stats in question (while abiding by the caps of the respective stats, if necessary).

All that out of the way, let’s get into some basic definitions going forward:

Technical Specifications & Mumbo-Jumbo

Attacker – The entity responsible for dealing the damage. For stage hazards, the “attacker” is the stage itself.
Attack – The move, action, stage effect, etc. responsible for dealing the damage. Has its own base attack power (“ATK”), as well as a number of “properties” determining what parts of the damage calculation process apply. Of note, each Attack has three properties determining how their ATK can be changed independent of the target’s defenses — “badge-mutability”, “status-mutability”, and “chargeability”. Most attacks have all of these properties or none; of particular note, Yoshi’s Mini-Egg is not “chargeable”, but does have the other two properties. Additionally, what are generally thought of as single moves may consist of multiple attacks with different properties; e.g. Tornado Jump / Gulp / Super Hammer’s initial hit (which is susceptible to changing ATK), and successive hit(s) (which are not).
Element – The class of attack being used, which determines which of the target’s set of defensive parameters (Defenses / Elemental Effects) to use. The different elemental types are Neutral (“non-elemental” / “null-element”), Fire, Ice, Explosion, and Electric.
Defender / Target – The entity taking the damage.
Defense – The base defensive power (“DEF”) used to reduce damage dealt; the defender has a separate Defense value for each Element.
Elemental Effect – A special effect the defender has for each Element that applies at the end of the damage calculation process. The elemental effects that can change the output damage are Elemental Weakness, Elemental Immunity, Elemental Healing, and “Iron Cleft Achilles’ Heel” (immunity to all attacks except Gulp); most of the time there is no such special effect for a given attack element and defender.

The properties of any Attack, as well as any entity’s Defense powers and Elemental Effects may change in any number of ways based on their state outside of the damage calculation process; some of the more salient ways will be brought up in the middle of the damage calculation discussion.

Now, let’s get into the meat of things!

Step 1: Sanity Checks & Elemental Transmutations

A few basic checks happen before any damage calculation occurs:

If the Attack has the “ignite” property and the Defender has the Burn status, the attack is treated as Fire-elemental for the rest of the process on that particular target, regardless of what its element would have been otherwise. Unlike the rest of the damage calculation process, I confess I am not aware of any attacks (player or enemy) that work this way, so I’d be curious to know if any readers can help out!
If the Defender is immune to all attacks (e.g. Doopliss before discovering his name, or Shadow Queen after Phase 1), 0 damage is dealt and calculation stops.
If the Attacker has any All or Nothing badges equipped, the Attack is “badge-mutable”, and the Attacker missed the Action Command for the attack, 0 damage is dealt and calculation stops.

Step 2: ATK Calculation

That out of the way, the attack power is calculated first in the following procedure:

Start with the Attack’s base ATK. This can be calculated in a number of ways; it can be constant (most enemy attacks and items), influenced by the player’s Action Commands, equipped badges, and/or partner/equipment ranks, etc. Of note, Jumpman/Hammerman’s extra power on jump/hammer attacks and Hooktail’s attacks being weakened by Attack FX R are factored in at this stage, as is the calculation for Poison Shroom / Poison BINGO’s half-damage-rounded up.
If Merlee’s ATK curse activated on this entity’s turn and the Attack is “status-mutable”, increase power by 3. Note that this does not depend on who the Attacker is, but only whether the Attack’s power can be influenced by statuses! As such, if Mario sets off a Bulky Bob-omb or Bob-Ulk with a Merlee-boosted Fire-elemental attack, their explosions’ power increases by 3 as well!
If the Attack is “badge-mutable”:
- Add 1 power per the Attacker’s equipped All or Nothing, Power Plus, and P-Up, D-Down badges.
- If the Attacker’s HP is sufficiently low, add 2 power per Power Rush and 5 power per Mega Rush equipped. The former requires 5 HP or less to activate on player characters and 1 HP on enemies, and the latter activates only at 1 HP.
- If the Defender has the “weak to Ice Power” property (which is separate from elemental Defenses/Effects), add 1 per Ice Power equipped by the Attacker.
If the Attack is “chargeable”:
- Factor in (and expend) the Attacker’s Charge status.
If the Attack is “status-mutable”:
- Factor in the Attacker’s Huge and Attack+ status, if applicable.
If the Attack is “badge-mutable”:
- Subtract 1 power per the Attacker’s equipped P-Down, D-Up, HP Drain, and FP Drain badges.
If the Attack is “status-mutable”:
- Factor in the Attacker’s Tiny and Attack- status, if applicable.

If the final attack power is negative, set it to 0.

Step 3: DEF Calculation

If the Defender has the “Elemental Healing” effect for the Attack’s element or the Attack is piercing, this whole step is skipped altogether.

Start with the Defender’s base elemental DEF for the Attack’s element. This can change based on the enemy’s state; for instance, flipping shelled enemies generally drops all defenses to 0. Of particular note, Grodus normally has 1 DEF to all elements, but gains an additional 1 DEF to null-elemental attacks per living Grodus X.
Add 1 defense power per the Defender’s equipped Defend Plus badges.
If a successful guard command was performed, add 1 defense power per equipped Damage Dodge.
If the “Defend” command was used this turn, add 1 defense.
Factor in the Defender’s Defend+ and Defend- (Soft) status.
Increase defense to 0 if currently negative.
If Merlee’s DEF curse activated this turn and the Defender is Mario, add 3 defense.
If Defender is weak to Attack FX R, decrease defense by 1 per hit previously taken with the sound effect.

The final defense power is again brought to 0 if currently negative, and subtracted from the previously-calculated attack power.

The resulting ATK – DEF value is not yet brought up to 0 if negative.

Step 4: “Non-Pierceable Defense”, etc.

Further alterations to the previously calculated ATK – DEF damage (or just ATK, for defense-piercing / healing attacks).

Add 1 damage per P-Up, D-Down worn by the Defender.
If the current damage is greater than 1:
- If the attack has repeated-hit diminishing returns (e.g. Power Bounce), reduce damage by 1 per previous hit, to a minimum of 1.
- If the attack has successive-hit diminishing returns (e.g. Fire Drive), reduce damage by 1 per previous target hit, to a minimum of 1.
If a successful guard command was performed, subtract 1.
If the Attack is Fire-elemental, reduce damage by 1 per Defender’s Ice Power badges equipped.
Subtract 1 per P-Down, D-Up worn by the Defender.
Multiply damage by the number of Double Pain badges worn by the Defender + 1.
If the Defender’s HP is sufficiently low (5 or below for player characters, 1 for enemies), divide the damage by the number of Last Stand badges equipped + 1, rounding up to the nearest integer.

At this point, if the absolute damage dealt is negative, it is brought to 0.

Step 5: Elemental Effects

The aforementioned elemental effect (if any) for the Attack’s element is applied here:

Elemental Weakness – Final damage is increased by 1.
Elemental Immunity – Damage is nullified.
Elemental Healing – Defender’s HP is increased rather than decreased.
Iron Cleft Weakness – Only Gulp deals damage; otherwise, damage is nullified.

This covers the entire damage calculation process from beginning to end; hopefully this addresses any misconceptions or ambiguities around the matter!