Stats and Attributes

Stats & Attributes Design

This document details the character stats, base attributes, and mathematical systems designed to prevent lopsided “stat-maxing” and encourage balanced, strategic character builds.

---

📊 Attributes Overview

CROSS uses a two-tier stat model consisting of Base Attributes (which players allocate points into) and Derived Stats (which determine actual combat and crafting outcomes).

graph TD
    subgraph Base Attributes
        STR[Strength]
        AGI[Agility]
        INT[Intelligence]
        VIT[Vitality]
    end

    subgraph Derived Secondary Stats
        AP[Attack Power]
        AS[Attack Speed]
        CR[Crit Rating]
        CS[Casting Speed]
        MN[Max Mana]
        HP[Max Health]
        MC[Mana Cost]
        SR[Stamina Recovery]
    end

    STR --> AP
    STR & AGI --> AS
    STR & AGI --> CR
    AGI & INT --> CS
    INT --> MN
    INT --> MC
    VIT --> HP
    VIT & INT --> SR

---

1. Base Attributes

Players allocate points (earned on level-up or from gear) into four base attributes:

1. Strength (STR): Measures physical brawn. Increases melee/ranged attack power and physical block value.
2. Agility (AGI): Measures speed, reflexes, and coordination. Increases base movement speed, attack speed, dodge rate, and critical strike chance.
3. Intelligence (INT): Measures mental capacity and magical attunement. Increases spell damage, healing power, maximum mana pool, and crafting success rates.
4. Vitality (VIT): Measures bodily health and physical constitution. Increases maximum health pool, physical defense, and maximum stamina.

---

⚖️ Anti-Maxing Mechanics (Encouraging Balanced Builds)

If players can simply dump all their points into a single stat (e.g. all Strength for a Warrior, all Intellect for a Mage) to get the best build, the gameplay gets boring and itemization becomes flat. We use three mathematical design layers to prevent this:

1. Multiplicative Synergy Stats

Important combat outcomes (Secondary Stats) require a balance of two base attributes. Maxing one while ignoring the other yields inferior results.

• Critical Damage Multiplier (Physical):
  • Concept: A critical hit requires both precision (AGI) to find the weak spot and power (STR) to break through armor.
  • Formula: $\text{Crit Multiplier}=1.5+\left(\frac{\text{AGI}\times \text{STR}}{\text{AGI}+\text{STR}}\right)\times 0.01$
  • Impact: If a player has $90$ AGI and $10$ STR (total 100), their multiplier is $1.5+9\times 0.01=1.59x$. If they balance it to $50$ AGI and $50$ STR (total 100), their multiplier is $1.5+25\times 0.01=1.75x$. Balance is mathematically rewarded.
• Casting Speed (Magical):
  • Concept: Casting spells quickly requires both mental memory/comprehension (INT) and physical somatic execution speed (AGI).
  • Formula: $\text{Casting Speed Bonus (\%)}=\sqrt{\text{INT}\times \text{AGI}}\times 2.0$
  • Impact: Maxing INT ($100$) while keeping AGI at $0$ gives $0\%$ casting speed bonus. Splitting points evenly yields a high, stable casting speed reduction.

2. Logarithmic Diminishing Returns

Stats that affect probabilities (Dodge Rate, Critical Strike Chance, Crafting Success) use a logarithmic growth scale. As a stat increases, each additional allocated point yields a smaller benefit.

$\text{Stat Benefit}=\text{Cap}\times \left(1-e^{-k\times \text{Attribute}}\right)$

• Agility $\to$ Dodge Chance: Capped at $40\%$. The first 30 points of Agility easily give $20\%$ dodge. The next 30 points only push it to $30\%$. Above 80 points, AGI yields negligible dodge increases, making it wiser to invest points in VIT (health pool) or STR (counter-damage).
• Intelligence $\to$ Crafting Success: Capped at $95\%$ (there is always a $5\%$ risk of failure). The return curve drops off sharply after 60 INT, encouraging crafters to put remaining points into Stamina (VIT) to increase their total crafting queue size.

3. Non-Linear Penalty Scaling (The Mana/Stamina Drain)

While higher stats increase output, they also increase input costs non-linearly if uncompensated.

• The Spell Burnback:
  • Higher Intelligence increases spell damage, but it also increases the Mana Cost of those spells.
  • If a Mage maxes INT but ignores Vitality/Intellect recovery stats, they will cast one or two devastating spells, drain their entire mana pool instantly, and stand uselessly.
• The Weight Penalty:
  • Strength increases attack power, but wielding heavy weapons slows attack speed:
  • $\text{Weapon Attack Interval (Seconds)}=\text{Base Speed}+\left(\frac{\text{Weapon Weight}}{\text{AGI}}\right)-\left(\text{STR}\times 0.005\right)$
  • If STR is high and AGI is ignored, heavy weapons strike extremely slowly, ruining DPS.