Math of Balance

Why does 100 armor in LoL always give +100% EHP, and not +50% at first and +10% at 500 armor? The answer lies in the diminishing returns formula, which elegantly solves the scaling problem.

• **League of Legends** - armor/(armor+100) guarantees linear EHP scaling at any amount of armor
• **World of Warcraft** - periodic rebalancing of armor formulas with each expansion to combat power creep
• **Counter-Strike** - armor reduces damage by a fixed %, creating predictable TTK breakpoints

DPS - Damage Per Second

**DPS (Damage Per Second)** - the basic damage metric for a weapon or character. It's not just 'damage per hit', but damage normalized over time. DPS lets you compare weapons with different attack speeds.

**DPS - theoretical maximum.** Actual damage depends on uptime (how long you're attacking), positioning, and misses. Practical DPS is often 60-80% of the theoretical value.

**DPS components:** - **Base damage** - damage per hit - **Attack speed** - attacks per second - **Crit chance** - chance of a critical hit - **Crit multiplier** - crit damage multiplier - **Armor penetration** - ignoring defenses

TTK - Time To Kill

**TTK (Time To Kill)** - the time to kill a target. Unlike DPS, TTK accounts for enemy health and gives a practical metric: 'how quickly will the opponent die?'

**TTK determines the game's pace.** Short TTK (< 1 sec) = tactical shooters (CS2). Long TTK (5+ sec) = RPG, MMO. Arcade shooters - in between (2-3 sec).

**TTK impacts gameplay:** - **Short TTK:** positioning matters more than aim, one mistake = death, slower pace - **Long TTK:** skill expression through tracking, room for counter-play and outplays

EHP - Effective HP

**EHP (Effective HP)** - how much 'real' damage is needed to kill a target accounting for defenses. If a tank has 1000 HP and 50% damage reduction, their EHP = 2000. You need to deal 2000 damage to kill them.

**EHP vs raw HP:** a tank with 3000 HP and 0 armor vs a tank with 1500 HP and 50% reduction have the same EHP (3000). But the second is vulnerable to armor penetration!

**Applying EHP:** - Comparing builds: HP vs Armor vs Dodge - Evaluating gold value: how much EHP does 1000 gold buy on HP vs armor - Breakpoints: when armor penetration becomes better than raw damage

Damage Formulas

Different games use different damage calculation formulas. The choice of formula determines the feel of the combat system and the complexity of balancing.

**Diminishing returns - the industry standard.** The formula armor/(armor+K) guarantees: 1) armor is always useful, 2) never grants immunity, 3) each point of armor gives the same EHP.

**Choosing a formula:** - **Subtractive:** for 'breakpoints' - clear defense thresholds - **Percentage:** simple to understand, predictable - **Diminishing:** balanced, standard for RPGs - **Multiplicative:** power fantasy, complex meta

Key Ideas

• **DPS = Damage × Speed × Crit modifiers** - a normalized damage metric for comparing weapons
• **TTK = HP / DPS** - a practical metric that determines the pace and feel of the combat system
• **EHP = HP / (1 - reduction)** - real survivability accounting for defenses, the key to tank vs damage balance

Related Topics

Math of balance is the foundation for quantitative systems analysis:

• What is Balance — Theory (types of balance) + practice (formulas)
• Game Economy — The same principles apply to economic systems

Вопросы для размышления

• What TTK does your favorite game have? How does it affect gameplay?
• If you were balancing an RPG, which damage formula would you choose and why?
• Calculate the EHP of a character in a game you know. How much gold does 1000 EHP cost?

Связанные уроки

• prob-02-combinatorics