Character statistics

In the Innocence Seekers video games, character statistics, or stats for short, are numerical determiners of a character's proficiency in battle.

Statistics
There are a number of stats a character has.

Experience level
 * Main article: Level

A character's experience level, or simply level, is a general measure of the character's skill, power and experience. In general, a higher level means higher stats. Level can be increased by earning experience points.

Experience points
 * Main article: Experience Points

A character's experience points, often abbreviated EXP, is a measure of the character's experience. If a character earns enough EXP, he/she will gain a level. EXP can be obtained by defeating enemies, using certain items, or via quest rewards.

Health points
 * Main article: Health Points

A character's health points, often abbreviated HP, is a measure of the character's vitality. It decreases as the character takes damage, and increases as the character is healed. If a character's HP reaches zero, he/she is considered to be incapacitated and is no longer able to battle unless revived. A character's maximum HP can be increased by levelling up or by using items. It may be temporarily increased by certain buffs.

Mana points
 * Main article: Mana Points

A character's mana points, often abbreviated MP, is a measure of the character's mana reserves. Using any spell or technique will consume MP, while items can be used to restore it. MP is a prerequisite for casting spells and using technique; if a character has too few MP (or none), he/she cannot use the spell/technique without significant consequences. A character's maximum MP does not increase per level unlike other stats; instead, it remains fixed until the character reaches certain level thresholds, at which point maximum MP is increased by one.

Attack
 * Main article: Attack (stat)

A character's attack, often shortened to ATK, is a measure of the character's physical power. A higher attack means he/she can deal more damage via physical attacks.

Defence
 * Main article: Defence

A character's defence, often shortened to DEF, is a measure of the character's ability to blunt physical attacks. A higher defence will decrease the amount of physical damage received, sometimes down to zero.

Intelligence
 * Main article: Intelligence

A character's intelligence, often shortened to INT, is a measure of the character's magical power. A higher intelligence means he/she can deal more damage via magic attacks.

Resistance
 * Main article: Resistance

A character's resistance, often shortened to RES, is a measure of the character's ability to resist magical attacks, as well as the strength of the character's healing spells. A higher resistance will decrease the amount of magical damage received, sometimes down to zero. A higher resistance also means that the character's healing spells are more potent.

Hit
 * Main article: Hit

A character's hit, often denoted in all-capitals as HIT, is a measure of the character's ability to reliably hit his/her target. A higher hit means that the character's attacks have higher accuracy. Some physical and magic attacks run partially off the hit stat (such as attacks using bows), while some physical attacks only use the hit stat (such as attacks using guns).

Speed
 * Main article: Speed

A character's speed, often shortened to SPD, is a measure of the character's agility. A higher speed means that the character is able to take turns more quickly and has a higher chance of evading attacks.

Elemental resistances

A character's elemental resistances determine how much damage they take from elemental attacks. A positive percentage below 100 per cent denotes partial resistance to the element, 100 per cent denotes total resistance to the element, a percentage higher than 100 per cent denotes the ability to absorb attacks of that element, and a negative percentage denotes weakness to the element.

Status resistances

A character's status resistances determine the probability of not being inflicted by a status effect.

Stat equations
None of these stats (other than MP, and only up to level 300) increase linearly with level. To determine the actual stats (without taking equipment into account), several equations are used.

Experience points

The following cubic equation is used to determine the total amount of EXP (denoted as E) needed to reach level x:


 * $$E = \frac{50x^3}{3} - 25x^2 + \frac{175x}{3} - 50$$

HP, ATK, DEF, INT, RES, HIT, SPD

Each of these stats has a base value (which does not need to be an integer), which differs between characters. Regardless of the base stat, the following equation is used to determine the actual stat (denoted S):


 * $$S = \left \lfloor \frac{B(L^2 + 34L + 189)}{200} \right \rfloor $$

L is the level of the character and B is the base stat. The final value is rounded down to the nearest integer.

MP

MP does not increase in the same way as normal stats. Enemies do not have MP, and player characters have a base MP of between six and fourteen (without taking into account items which boost stats permanently). The player's maximum MP increases based on the following equation:


 * $$S = \left \lfloor \frac{B(100 + 3L)}{100} \right \rfloor$$

A player character's MP stops increasing at level 300.

Stat caps
For all stats, there are artificial limits as to how large they can be. These caps depend on the stat in question.

The level cap is 65535, meaning the highest amount of EXP one can earn in total is 4,690,927,499,673,450 (to get from level 1 to level 65,535). To get from level 65,534 to level 65,535 requires 214,735,257,850 EXP, which is more than the amount of EXP required to reach level 2,344 from level 1 (which is 214,508,171,350). Note that it is not expected to reach such high levels before completion of a game's main story, which typically expects the player to be at around level 100 at the end. In comparison, some superbosses require the player characters' levels to be at or close to the cap.

HP is capped at 40,000,000,000 for player characters, while ATK, DEF, INT, RES, HIT and SPD are capped at 9,999,999,999 for both player characters and enemies. No character can have more than 200 MP without equipment (base MP of 14 plus the maximum of six Mana Seeds which increase base MP by one, and level 300+; with equipment, one can theoretically have as many as 1,400 MP, given that the most amount of MP given by any accessory module is 300). The amount of stat-boosting items a single character can use is limited; up to six Mana Seeds and up to 18 of each of the other Seeds (Vitality Seeds boost base HP by 20 each, while other Seeds increase their respective base stat by 5 each).

When taking into account stat boosts from Seeds, as well as assuming the highest possible base stat, the highest amount of HP a character can have without equipment (at level 65,535) is 26,212,094,084 (a base stat of 860+360=1,220), while for other stats it is 6,553,023,521 (a base stat of 215+90=305).

Trivia
If stats were not capped, then one would eventually reach nonsensical values as a consequence of the limitations of the data structures used to hold them. For example, if level were not capped at 65,535, then the amount of EXP required will eventually overflow and reach a low number, which may lead to an infinite level-up loop. Alternatively, stats may overflow and become unusually low values.

The following effects can be observed:
 * If level increases above 717,216, then the total amount of EXP required to reach that particular level will become an unusually low value. This is because one of the intermediate values used in the calculation will overflow. The amount of EXP obtained from this calculation is capped at 6,148,914,691,236,517,205 (or (264 - 1)/3, over 1,310 times higher than the amount needed to reach level 65,535). To reach level 717,216, one requires 6,148,904,524,057,632,750 EXP. Getting to level 717,217 requires 6,148,930,243,997,165,600 EXP (or 25,719,939,532,850 from level 717,216, which is more than that required to reach level 11,556 from level 1, which is 25,716,684,939,250), higher than the cap given. The software will give an erroneous value of 15,552,760,648,394 EXP required (which, if obtained at level 1, will increase one's level to 9,772, which requires 15,550,074,397,850 EXP).
 * If any stat other than HP were to exceed 92,233,720,368,547,758 (or floor((261)/25)), then an intermediate value in the calculation will overflow, which may result in absurdly low stats. At what level this occurs depends on the base stat, but is always higher than level 65,535 (with the level cap, base stats can safely be at the maximum of 65,535).
 * It is actually safe for base HP to be at 18,446,744,073,709,551,615, as HP will never overflow even at level 65,535, reaching a value of 396,334,255,090,920,406,107,637,677 (a 128-bit unsigned integer has a maximum value of 340,282,366,920,938,463,463,374,607,431,768,211,455, around 12 orders of magnitude larger than the number given). In the intermediate calculation, no value can exceed 1,701,411,834,604,692,317,316,873,037,158,841,057, and this value can only be reached by exceeding the level cap.
 * If, for some reason, level is set to zero, the amount required to reach such a level is erroneously calculated to be 6,148,914,691,236,517,155 (or (264 - 1)/3 - 50).

Base stats
Stats which increase with level have an associated base stat, which differs between characters. While enemy base stats vary by a lot, player character base stats are denoted using a letter ranking system. The following table denotes the actual values of each rank: