Magia Record damage mechanics

The last time I wrote this page, I titled it "Everything I know about MagiReco mechanics", which was a blatant lie because it wasn't everything I knew about it even at the time of writing, and definitely wasn't two years later after I totally left it to rot for a year and a half. So this time around I'm restricting the scope quite a lot. This page expands a bit on the old content and covers more recent additions to the game (spirit enhancement bonuses!), but I've omitted the appendix of effect descriptions, which after all never got finished and some of its comments are a bit outdated now too.

I might write up those later anyway, on a different page.

My explanations might sometimes be unclear, and sometimes I make mistakes, so either email me or hunt me down on Ducksnort if you have questions or corrections, after which I might or might not get around to actually updating this damn page. Judging by my track record, more likely not.

Provenance

Two major versions of this document were previously published on my rice subdomain: the original translations from the Japanese aruma wiki, and my long-standing elaboration.

This whole project would never have left the ground without the efforts of @chemblueP and @minagirusakage, who were doing the research before I ever entered the scene, and @sarami171122 and @goma_sio_huri, who were curating the results at aforementioned wiki.

It is requested that this information not be reproduced to matome sites (particularly eapmedia), and especially not without attribution. (This is limited relevance for an English reference, but I will say it.) Otherwise, if you're creating derivative works: you're quite welcome to, so long as you convey the appropriate attributions.

Overview

This page covers the Magia Record damage formula in enough detail to calculate damage to within an unavoidable 6% due to intentional randomness. It is a bit of a work in progress (and will perhaps never cease to be a work in progress) and as such may fall a bit short of that ideal, but it should be quite close, and certainly more accurate and far more precise than any other resource I've seen.

At a high level, the damage calculations proceed roughly as follows:

Base Damage = (Effective ATK × ATK buff) − (Effective DEF × DEF buff)/3

Minimum is 500.

Adjusted Damage = Base × Disc × Modifiers × Magia × Attribute

Minimum is 250.

Final Damage = Adjusted × Random[0.95,1.05]

Maximum is 9999999.

Base = (ATK × ATK buff) − (DEF × DEF buff)/3

At the core of the formula, the attacker's ATK is reduced by one-third of the defender's DEF, to a minimum of 500.

Concretely, the base damage can be interpreted as the average damage which would be dealt by non-Puella Accele disc with no other applicable modifiers.

When the DEF Ignored effect is activated, the DEF term is ignored (i.e. it is not subtracted; treat it as zero).

Effective ATK/DEF = (Base × (100 + Awakening)% + Memoria) × Formation

An effective base ATK and DEF is computed for each character when entering a battle, based on the team composition, and does not change in battle. (Only the buff/debuff multipliers change during the battle.)

• Base ATK/DEF is inherent to the girl by rarity and level.
• Awakening bonus is the percentage reported when the corresponding awakening material is set, otherwise zero. Only the card-inherent base stat is multiplied by the awakening bonus, so the increase is essentially fixed for a given character*rarity*level.
• Equipped memoria and spirit enhancements provide the ATK/DEF stats reported in their descriptions. Normally, only ability (passive) memoria have nonzero ATK, and only skill (active) memoria have nonzero DEF. These are not affected by the awakening bonus.
• Formations multiply the entire sum above on some of their tiles.

The astute may note that the calculation above bears little relation to the stat values reported in the team-building interface, which is simply Base + Memoria + Spirit enhancement, as it is impossible to calculate either from the other without looking up the card-inherent base stat and awakening modifiers. The team-building interface's figure is apparently total nonsense that doesn't reliably correspond to the stats actually used in battle.

Formation bonus

The last few of these are obviously not ATK/DEF modifiers, but are included for completeness to list all the formation figures in the same place. Note that many (most) formations restrict their bonuses to girls of a specific attribute and in specific positions.

ATK/DEF buff

ATK and DEF values are modified in battle only by an attacker's ATK buffs and a defender's DEF buffs. ATK and DEF buffs are clamped between −95.0% (0.05×) and +100.0% (2×), a property they in fact share with all buffs.

Minimum Base Damage

The base damage is clamped to a minimum of 500; there is no hard maximum reachable by players, as the base damage cannot exceed ATK after buffs, and thus is limited by the base stats of girls released.

Adjusted = Base × Disc × Modifiers × Magia × Attribute

The damage to be dealt is multiplied by various factors, to a minimum of 250.

The above division of terms is not entirely principled, and the order is kind of arbitrary due to associativity and does not reflect code execution order. However, I've made an effort to group terms where they are known to have joint limits. Notably, effects do not add or subtract flat amounts of damage from attacks outside the ATK/DEF base damage calculation.

Disc factors = Base × (100 + Awakening)% × Charge

The amount of damage dealt by an attack varies with the type of disc used to initiate it, as well as combos and other ambient factors. Moreover, they differ somewhat between quests (PvE) and Mirrors, so see also that section for more detail.

Awakening bonus

The awakening bonus for a particular disc type stacks additively with disc damage bonuses from spirit enhancement and is applied together as a percentage of damage dealt; e.g. an awakening bonus of +5% Charge disc damage and two spirit enhancement bonuses of +3% Charge disc damage together provide +11%. (This value is in fact computed before battle and reported in the battle data.)

Base disc factors

Blast discs

Blast discs are unreasonably special:

• Base factor is 60.0%
• Puella and Blast combos each add +30.0%
• Multiply by a position factor:

  Disc	Factor
  1st	1.0×
  2nd	1.1×
  3rd	1.2×

In summary:

Magia/Doppel discs

Magia and Doppel discs don't have a fixed damage multiplier. Instead, they have attack effects (or, in one case, a non-damaging dummy effect) and have their damage computed using the attack effect's effect value (if any) as the disc damage factor.

It's worth noting that Magia and Doppel discs don't count toward puella combos or connect points, so even you have the same girl use a magia and attack twice, the attacks will not receive the puella combo bonus, and the magia obviously won't either.

When using Magia/Doppel discs consecutively within a turn, the subsequent discs' damage increases:

Note that, unlike with Blast discs, this bonus is based on consecutive usage, not position. For example, it does not apply when using Magia/Doppel discs only in the 1st and 3rd positions with a standard disc in between, and using Magia/Doppel discs only in the second and third positions result in only 1x1× on the third-disc magia. Magia and Doppel discs are interchangeable for this purpose, though.

Selected attack effects

No subtype

The standard damage-dealing effect does nothing special; it deals its listed damage plus its growth for each magia level beyond 1; for example, an attack effect with effectValue=3700 and growPoint=100 deals 370.0% damage at magia level 1, and 410% at magia level 5. The base damage on this type is generally higher than on the other types.

A reference damage [Ⅰ] (All) magia effect deals 300.0% damage with 10.0% magia level growth; each successive Roman numeral typically increases the base damage by 10.0%; thus, for example, Damage [Ⅳ] (All) typically has 330% base damage.

A reference damage [Ⅰ] (Target) magia effect deals 600.0% damage, +20.0% per Roman numeral, but still only has a 10.0% growth. Effects which deal damage to random enemies general deal total base damage very roughly close to the base damage calculated this way divided over the number of hits with have a 10.0% growth which is applied separately to the damage multiplier for each hit, but the actual numbers are very slightly higher and I have no idea what's up with that, so just look it up.

Doppel damage is generally exactly 2.2× that of a hypothetical magia with the same effect and Roman numeral. That is, a hypothetical reference doppel damage [Ⅰ] (All) effect would deal 660.0% damage with 22.0% growth (but no actual doppel has a damage effect that low, because in practice doppel damage effects are assigned with a Roman numeral 2 higher than the corresponding rarity 5 magia). Tsuruno's doppel is misentered and instead has growth 10.0%, and Ikumi's doppel only has 1320.0% base damage, because apparently these figures are typed in manually or something.

Attribute-strengthened damage (ALIGNMENT)

Deals damage, and does 2× damage if the target's attribute is weak to the user's. This does not replace standard attribute effectiveness, it'll actually do 3× (or 3.6× with certain status effects) as much damage on a weakness as on neutral targets. Reference damage [Ⅰ] (All) deals 275.0%, +10.0% per Roman numeral, with 10.0% growth, except that Rika is buggy and has 10.0% more. Reference damage [Ⅰ] (Target) deals 460.0%, +20.0% per roman numeral, with 10.0% growth. Tsukuyo's doppel only has growth 10.0%.

Damage up for each status condition (DAMAGE_UP_BADS)

Holy Mami's magia/doppel effect, which deals damage increased by parameter for each distinct type of status condition active on the target. On the magia, the parameter is about one-fourth of the base damage; hypothetical reference damage [Ⅰ] (All) deals 275.0%, +10.0% per Roman numeral, with 10.0% growth (same as attribute-strengthened, in fact), with parameter 68.8%, +2.5% per Roman numeral. The doppel instead has parameter 80.0%, which, by the way, is actually lower than the corresponding magia parameter (which is 83.8%), because consistency is totally overrated.

Damage up as HP down (LINKED_DAMAGE)

Ren's magia/doppel effect, which deals damage increased by lost hp fraction of parameter; i.e. add ((1−hp/maxhp) × parameter) to the disc factor. On magia, the parameter is equal to the base damage; hypothetical reference damage [Ⅰ] (Target) deals 460.0%, +20.0% per roman numeral, with 10.0% growth (same as attribute-strengthened, in fact), with parameter 460.0%, +20.0% per roman numeral. The doppel has parameter 600.0%, which, by the way, is exactly the same as the corresponding magia parameter, because consistency is totally overrated.

DUMMY

Doesn't do damage, thanks Mitama. Or anything at all, even. The game actually works just fine if you remove this effect from her magia effect list. I don't know why this effect code exists.

Charge = Charge bonus × Charge buff

When using Accele or Blast discs while charged, any charge is consumed and damage is multiplied according to final disc type and charge count. (Accele discs also have their MP gain multiplied, but the multipliers follow yet another table not listed below.)

The following table is reproduced from aruma. I have never explicitly verified it, and it seems like it'd be a pain, but they seem to check out at least in the common cases.

It has been alleged that the charge multiplier tables have been changed in the past, but if so it must have happened before June 2018.

Charged Damage buff

When an Accele or Blast disc is used while charged, consuming the charge, the attacker's Charged Damage buff applies. Just like ATK and DEF buffs (and indeed all buffs), the Charged Damage buff is clamped between −95.0% (0.05×) and +100.0% (2×). Otherwise, the Charged Damage buff is 1×.

There is a 5.5× limit apparently between the Charge bonus and buff. This is not normally achievable without at least a +10.0% Charge buff, and even the maximum (+100.0%) Charge buff will not run into the limit without at least 7 charges, though... (It's unclear why this limit exists except that the developers really hate Charge for some reason and make up reasons for it to be gratuitously worse.)

Disc factors (Mirrors)

The disc modifiers are a bit different in mirrors.

In particular, all standard discs deal 0.7× as much damage, except for Blast, which is particularly special again and does and strangely more than that; and Magia (and Doppel) disc damage is 0.5×.

Base disc factors

Blast discs

• Base factor is 70.0%
• Puella and Blast combos each add +30.0%
• Multiply by the position factor given above.
• Multiply by 0.7× as with the other standard discs.

Equivalently, start with 49.0% add 21.0% for each type of combos.

Magia/Doppel discs

Magia and Doppel discs instead deal 0.5× their usual damage (rather than 0.7×).

Charged Damage

In addition to the usual charge effects and the Charged Damage buff, all charged attacks deal 0.9× damage in Mirrors.

This does, in fact, mean that 1-charge Accele deals 0.99× base damage, less than uncharged Accele. (While the damage figures are indistinguishable about 90% of the time due to randomness, the attack will occasionally do just below the minimum 95% of damage computed for a 1× disc just under 10% of the time.)

I'm not going to say this isn't stupid.

Attribute matchup factor

When attacking a defender suffering a status condition which increases damage from weakness with its weakness, increase damage 1.2× (i.e. 1.5× → 1.8×).

The effect of an attribute-strengthened magia (see above) further increases damage 2×.

Modifiers = Total + Critical

Total = 100.0% + Damage buffs + Damage Up effects − Damage Cut effects

This is a set of damage modifiers which all add to and subtract from each other, and, apart from Critical, share bounds separate from their individual bounds.

Damage buffs

Buff/debuff pairs which affect "damage", except magia damage, are accumulated additively:

• The attacker's Damage buff applies to all damage.
• The attacker's Blast Damage buff applies when the selected disc was a Blast disc.
• The attacker's Charge Disk Damage buff applies when the selected disc was a Charge disc. (This particular buff is rather rare, and thus far has only been applied by a few spirit enhancement cells. The much more common Charged Damage buff does not apply to Charge discs at all, and is multiplied in separately.)

Like all buffs, the Damage buff is clamped between −95.0% (0.05×) and +100.0% (2×).

Damage Up conditions

Unlike the buffs above, conditions have no caps per se. When activated, the bonus from the attacker's Damage Up condition applies to all damage.

• When activated, the attacker's Damage Up effect applies to all damage.
• When activated, the attacker's Damage Up Bad effect applies when the defender is afflicted with abnormal status. Note that when a status condition is applied to a multi-space bosses, only one space is considered afflicted with status conditions, usually the center tile.

Typically, Damage Up condition is defined with a 100.0% activation rate, and thus always activates. However, as with all other conditions, Damage Up (and Damage Cut) can have an activation probability. In particular, the pendulum witch and its familiars often appear with chance Damage Up and Damage Cut effects.

Conditions have no proper cap to their effects per se; they are only subject to the general 300.0% maximum on damage modifiers. Under normal circumstances, this means only +200.0% of Damage Up effect can be useful, although any excess will help to neutralize debuffs and Damage Cut effects before the cap is applied. This is most often observed where the AI rumour appears with the skill that does enough damage to instantly kill a player character: its Damage Up condition effect value is set so high that the first 100.0% of Damage Cut won't appear to have any effect.

Damage Cut conditions

The counterpart of the Damage Up conditions, the defender's Damage Cut effect values are subtracted from the damage modifier when activated:

• When activated, the defender's Damage Cut effect applies to all damage.
• When activated, the defender's Blast Damage Cut effect applies when the selected disc was a Blast disc.
• When activated, the defender's Magia Damage Cut effect applies when damage is dealt by a magia or doppel effect. (This is distinct from the Magia Damage DOWN debuff, which is applied separately.)

Like the Damage Up conditions above, Damage Cut conditions have an activation rate (but it's usually 100.0%); in addition, it is possible for the attacker to have immunity to Damage Cut, which can activate on a Damage Cut activation and ignore the activation.

These effects don't have a cap per se either; however, they are subject to the general -70.0% minimum on damage modifiers.

Bounds on total damage modifier

The sum of above damage modifiers is clamped between 30.0% (0.3×) and 300.0% (3×).

Critical bonus

When the Critical effect is is activated, the Critical bonus is equal to the total damage modifier, to a maximum of 100.0%.

That is, when the total damage modifier is over 100.0%, Critical will only add +100.0% damage. However, if the total damage modifier is less then 100.0%, Critical will not more than double the damage to be dealt.

Magia buff

The attacker's Magia Damage buff applies when the selected disc was a Magia disc. Like all buffs, Magia Damage is clamped between −95.0% (0.05×) and +100.0% (2×).

Bounds on adjusted damage

The adjusted damage is clamped to a minimum of 250 before being randomized.

Final = Adjusted Damage × Random[0.95,1.05]

The adjusted damage is then multiplied by a random factor between 0.95× and 1.05×. The distribution seems to be roughly uniform, modulo the limits of digital numeral representation...

The maximum final damage is 9999999, i.e. 10^7−1. This is occasionally reachable with setup nowadays!

Somewhat related links (mostly Japanese)

• probably the best resource you're going to get for MP mechanics, at least until I do my write-up; it's Japanese, but you can probably use the tables even if you're illiterate.
• 2ch wiki, which apparently still has people with the willpower to keep data and quest tables up to date.
• English wiki, which some people find useful and is usually pretty good at having pictures of things
• a mistake and a must-read for, ahem, “““gentlemen”””