# Stats

A detailed explanation of how the stats are implemented in the game ** Updated as of: 0.17 Hotfix #3**

# Primary and Secondary Stats

There are four primary stats and eight secondary stat. Each primary stat has a base value of 10.0 which can be increased/decreased through item enchantments and traits (e.g. Slender, Body Height, etc). Each secondary stat has a base value which depends on its corresponding primary stat, secondary stats can also be increased/decreased through item enchantments and traits, but are also affected by their corresponding primary stat.

### Strength

[math]\displaystyle{ \text{Base Body} = \text{Strength} * 50 }[/math]

[math]\displaystyle{ \text{Base Action} = \text{Strength} / 3 }[/math]

### Dexterity

[math]\displaystyle{ \text{Base Hit} = \text{Dexterity} }[/math]

[math]\displaystyle{ \text{Base Evasion} = \text{Dexterity} }[/math]

### Intelligence

[math]\displaystyle{ \text{Base Mind} = \text{Intelligence} * 50 }[/math]

[math]\displaystyle{ \text{Base Spell} = \text{Intelligence} / 3 }[/math]

### Willpower

[math]\displaystyle{ \text{Base Penetration} = \text{Willpower} }[/math]

[math]\displaystyle{ \text{Base Resistance} = \text{Willpower} }[/math]

# Explanation of Stats

## Simple Explanation

Each point in a secondary stat increases a player's power by 10% - points in offensive secondary stats increase their offensive power by 10%, likewise points in defensive secondary stats increase their defensive power by 10%. As such, points in a primary stat increase both their offensive power and defensive power by 10%.

All of the stats are balanced around that 10% number and no stat is inherently stronger than any other stat (Intelligence/Spell is a minor exception as spell slots have primarily RP and tactical combat applications (through inflicting harmful transformations) and they do not affect a player's pure damage output nor survivability).

As such to maximize a player's combat potential, try to maximize the values on your items' enchantments without worrying too much about what the exact enchantments grant. Alternatively, because all the stats are balanced, pick whatever stats suit your RP goals without having to worry about ending up with a weak build.

## Complicated Explanation

When advantage on an attack is positive (advantage equals hit minus evasion or penetration minus resistance, see the following sections for more details on advantage) then the attack gets a linearly scaling percent increase in damage equal to the advantage multiplied by 10%. For example if the attack has 15 hit against 10 evasion, that attack will do an average of 50% extra damage. If the attack has 15 penetration against 10 resistance, that is again an advantage of 5 for a 50% increase in damage.

When advantage on attack is negative, then the attack's damage is decreased at a hyperbolically scaling rate. Hyperbolic scaling is calculated by pretending advantage is positive to calculate the multiplier, but then rather than multiplying the attack's damage by that multiplier, you divide the attacks damage by that multiplier. For example, if an attack has 10 penetration against 15 resistance, then divide the attack's damage by 1.5 rather than multiplying it by 1.5.

This has the effect that if an attack has 15 hit against 10 evasion, for an advantage of 5 in the dex based stats, but 10 penetration against 15 resistance for an advantage of -5 in the will based stats, then that attack will get multiplied by 1.5, then divided by 1.5, canceling each other out for a net damage modifier of zero.

Therefore:

- Each point in
**Strength**:- (
**Action**) Increases number of actions per turn by 10% (10% more actions = 10% more damage per turn) - (
**Body**) Increases body by 20% (Strength alone technically only increases body by 10%, but most all sources of strength are accompanied with an additional 10% increase to body, it is doubled to offset the fact that there are two hp stats that can be targeted)

- (
- Each point in
**Dexterity**:- (
**Hit**) Increases the hit chance, crit chance, and glance chance in such a way that average damage increases by 10% (the formulas are complicated, the exact details are in the following sections) - (
**Evasion**) Decreases the opponent's hit chance, crit chance, and glance chance in such a way that their average damage decreases by 10%

- (
- Each point in
**Intelligence**:- (
**Spell**) Increases the number of spell slots by 10% - (
**Mind**) Increases mind by 20% (Because spell slots are not as frequently used in duels, a purely dueling focused build may want to focus on getting points in mind from secondary enchantments rather than intelligence)

- (
- Each point in
**Willpower**:- (
**Penetration**) Increases the damage multiplier for outgoing spells by 10% - (
**Resistance**) Decreases the damage multiplier for incoming spells by 10%

- (

### Hard/Soft Caps and Floors

There are no hard caps on any of the stats. There is a soft cap on hit as an advantage of 10 yields a 0% miss and glance rate with a 100% critical hit rate, so any additional points in hit past the 10 point advantage are wasted. Although in practice getting a ten point advantage in hit is exceedingly rare.

As fumble chance is greater than zero for hit values below 11, it is recommended to invest at least 1 point in hit/dex to remove the fumble chance.

## Very Complicated Explanation

Read on below.

# Derived Stats

During a fight there are five additional statistics that are calculated using your stats and your opponent's stats:

- Fumble Chance
- Hit Chance
- Crit Chance
- Glance Chance
- Damage Multiplier

## Non-Advantage Based

Fumble chance is calculated using only your stats.

### Fumble Chance

[math]\displaystyle{ \text{Fumble Chance: } (11 - \text{hit}) / 20 }[/math]

## Advantage Based

The remaining four are calculated using the "advantage" one player has over the other in a given stat. For dexterity advantage equals attacker's hit minus defender's evasion, for willpower advantage equals attacker's penetration minus defender's resistance. A fumbled attack has the caster as the attacker and defender, so their penetrations is compared against their own resistance.

Denote advantage as:

- [math]\displaystyle{ \text{Advantage: } a }[/math]

The game calculates these values using several internal constants:

- [math]\displaystyle{ \text{Stat Power: } S = 0.10 }[/math]
- [math]\displaystyle{ \text{Glance Decay: } D_g = 0.5 }[/math]
- [math]\displaystyle{ \text{Miss Decay: } D_m = 0.5 }[/math]
- [math]\displaystyle{ \text{Base Glance: } B_g = 0.1 }[/math]
- [math]\displaystyle{ \text{Base Miss: } B_m = 0.1 }[/math]
- [math]\displaystyle{ \text{Base Crit: } B_c = 0.05 }[/math]
- [math]\displaystyle{ \text{Crit Multiplier: } c = 1.75 }[/math]
- [math]\displaystyle{ \text{Glance Multiplier: } g = 0.4 }[/math]
- [math]\displaystyle{ \text{Glance Growth Rate: } R_g = 0.1 }[/math]

Additionally the game calculates derived constants:

- [math]\displaystyle{ B_h = 1 - B_m }[/math]
- [math]\displaystyle{ B_d = B_h\Big(1 + (c-1)\frac{B_c}{B_h} + (g-1)\frac{B_g}{B_h}\Big) }[/math]

The values then depend on whether advantage is positive or negative. Advantage equals hit minus evasion for calculating hit/glance/crit chances and advantage equals penetration minus resistance for calculating the pen-res damage multiplier.

## [math]\displaystyle{ \text{Advantage } \geq 0 }[/math]

### Glance Chance ([math]\displaystyle{ P_g }[/math])

[math]\displaystyle{ P_g = B_g(D_g)^a }[/math]

### Hit Chance ([math]\displaystyle{ P_h }[/math])

[math]\displaystyle{ P_h = 1- B_m(D_m)^a }[/math]

### Crit Chance ([math]\displaystyle{ P_c }[/math])

[math]\displaystyle{ P_c = \frac{1}{c-1}\Bigg(\frac{B_d (1 + aS)}{P_h}-1+(1-g)P_g\Bigg) }[/math]

### Pen-Res Damage Multiplier ([math]\displaystyle{ W }[/math])

[math]\displaystyle{ W = 1 + aS }[/math]

## [math]\displaystyle{ \text{Advantage } \lt 0 }[/math]

### Crit Chance ([math]\displaystyle{ P_c }[/math])

[math]\displaystyle{ P_c = B_c }[/math]

### Glance Chance ([math]\displaystyle{ P_g }[/math])

[math]\displaystyle{ P_g = 1 - \frac{1}{1+R_g\Big(-a + \frac{B_g}{R_g(1-B_g)}\Big)} }[/math]

### Hit Chance ([math]\displaystyle{ P_h }[/math])

[math]\displaystyle{ P_h = \frac{B_d}{(1-aS)(1+(c-1)P_c + (g-1)P_g)} }[/math]

### Pen-Res Damage Multiplier ([math]\displaystyle{ W }[/math])

[math]\displaystyle{ W = \frac{1}{1-aS} }[/math]

# Attack Procedure

When attacking first the fumble chance is rolled. If the spell is fumbled then the player hits themselves. If the spell is not fumbled then the hit chance is rolled. If the spell hits then there is one final roll to determine if the spell crits, glances, or is a normal hit so that the probability of a crit is [math]\displaystyle{ P_c }[/math], the probability of a glance is [math]\displaystyle{ P_g }[/math] and the probability of a normal hit it [math]\displaystyle{ 1 - P_c - P_g }[/math]

## Damage Calculation

Damage calculation for an attack has four components:

- [math]\displaystyle{ \text{Pen-Res Multiplier: } W }[/math]
- [math]\displaystyle{ \text{Base Attack Damage: } B = 40.0 }[/math]
- [math]\displaystyle{ \text{Attack Type Multiplier: } M }[/math]
- [math]\displaystyle{ \text{Damage Roll: } R }[/math]

And the damage the attack does is taken by multiplying the four components together. [math]\displaystyle{ W }[/math] is calculated as described in the previous section and [math]\displaystyle{ B }[/math] is a constant.

[math]\displaystyle{ M }[/math] has the following values:

- If the attack is a fumble, [math]\displaystyle{ M = \frac{2}{3} }[/math]
- If the attack is a miss, [math]\displaystyle{ M = 0 }[/math]
- If the attack is a crit, [math]\displaystyle{ M = 1.75 }[/math]
- If the attack is a glance, [math]\displaystyle{ M = 0.4 }[/math]

Finally [math]\displaystyle{ R }[/math] is a random value uniformly distributed over the range [math]\displaystyle{ \Big(\frac{5}{6},\frac{7}{6}\Big) }[/math]