2nd/10_Wiki/Topic_Programming/Frontend/게임 밸런싱.md

---
id: wiki-2026-0508-게임-밸런싱
title: 게임 밸런싱
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [Game Balancing, 밸런스 디자인]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [game-design, balancing, simulation]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python/TypeScript
  framework: Unity/Unreal/web
---

# 게임 밸런싱

## 매 한 줄
> **"매 fairness × engagement × progression의 quantitative tuning loop"**. 게임 밸런싱은 단순 number tweak이 아닌, player skill curve와 reward schedule을 데이터 기반으로 calibrate하는 systems engineering이다. 2026 현업은 telemetry-driven A/B + LLM-assisted simulation으로 cycle을 일/주 단위로 단축한다.

## 매 핵심

### 매 밸런싱 차원
- **Power balance**: weapon/character/spell 의 win-rate convergence to ~50%.
- **Resource economy**: gold/XP/material 의 inflation/sink ratio.
- **Difficulty curve**: time-to-mastery 의 monotonic with checkpoints.
- **Matchmaking**: MMR/Elo/Glicko-2 — skill variance bounded.

### 매 측정 지표
- Win rate, pick rate, ban rate (MOBA/FGC).
- Time-to-kill (TTK), DPS, EHP (effective HP).
- Retention D1/D7/D30, session length, churn at level X.
- Gini coefficient of resource distribution.

### 매 응용
1. League of Legends 의 patch cycle (2-week) — champion winrate band [47%, 53%].
2. Hearthstone 의 nerf/buff 의 telemetry-driven (Vicious Syndicate stats).
3. Slay the Spire 의 Monte Carlo simulation 의 deck balance.
4. Destiny 2 의 sandbox team 의 sandbox tuning (Bungie quarterly).

## 💻 패턴

### 1. Win-rate convergence target
```python
# Bayesian winrate estimate with prior
import numpy as np
from scipy.stats import beta

def champion_winrate(wins, losses, prior_a=50, prior_b=50):
    a = prior_a + wins
    b = prior_b + losses
    mean = a / (a + b)
    ci_low, ci_high = beta.ppf([0.025, 0.975], a, b)
    return mean, (ci_low, ci_high)

# Patch decision: nerf if CI bound > 0.53
mean, (lo, hi) = champion_winrate(wins=12500, losses=10800)
needs_nerf = lo > 0.53
```

### 2. DPS / TTK calculation
```python
def time_to_kill(damage_per_shot, fire_rate_hz, target_hp, armor=0):
    effective_dps = damage_per_shot * fire_rate_hz * (1 - armor)
    return target_hp / effective_dps

# Weapon balance check: TTK in [0.4s, 1.2s] band
for w in weapons:
    ttk = time_to_kill(w.dmg, w.rpm/60, target_hp=200, armor=0.1)
    assert 0.4 <= ttk <= 1.2, f"{w.name} TTK={ttk:.2f}s out of band"
```

### 3. Resource economy faucet/sink
```typescript
type Economy = { faucets: number; sinks: number; supply: number };

function inflationRate(econ: Economy, dt: number): number {
  const net = econ.faucets - econ.sinks;
  return net / econ.supply / dt; // per-day inflation
}

// Target: |inflation| < 0.02 per week (2%)
```

### 4. Monte Carlo deck simulation
```python
def simulate_deck(deck, opponents, n_runs=10000):
    wins = 0
    for _ in range(n_runs):
        opp = random.choice(opponents)
        result = play_match(deck, opp)
        wins += result == "win"
    return wins / n_runs

# Auto-balance: card value = marginal winrate Δ when included
```

### 5. Elo / Glicko-2 matchmaking
```python
def glicko2_update(rating, rd, opponents):
    # rd = rating deviation; volatility tracked separately
    g = lambda phi: 1 / math.sqrt(1 + 3 * phi**2 / math.pi**2)
    # ... (full Glicko-2 spec)
    return new_rating, new_rd
```

### 6. Difficulty curve fitting
```python
import numpy as np
# Player completion rate per level
levels = np.arange(1, 51)
completion = np.array([...])  # telemetry
# Target: monotonic decrease, no cliff > 15% drop
diff = np.diff(completion)
cliffs = np.where(diff < -0.15)[0]
# cliffs → level redesign candidates
```

### 7. A/B test with CUPED variance reduction
```python
def cuped_estimate(treatment_y, control_y, treatment_x, control_x):
    # x = pre-experiment covariate (e.g., D7 retention)
    theta = np.cov(np.concatenate([treatment_y, control_y]),
                   np.concatenate([treatment_x, control_x]))[0,1] / \
            np.var(np.concatenate([treatment_x, control_x]))
    adj_t = treatment_y - theta * treatment_x
    adj_c = control_y - theta * control_x
    return adj_t.mean() - adj_c.mean()
```

### 8. LLM-assisted balance review (2026)
```python
# Claude Opus 4.7 의 patch note review
prompt = f"""
Patch diff:
{diff}

Telemetry (last 7d): {telemetry_json}

Identify:
1. Champions exceeding [47%, 53%] winrate band.
2. Hidden interactions (item × champion synergy outliers).
3. Risk score (1-10) per change.
"""
review = claude.messages.create(model="claude-opus-4-7", ...)
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| Competitive PvP | Winrate convergence + telemetry-driven nerf cycle |
| Single-player | Difficulty curve + retention cliff analysis |
| Gacha/F2P | Whale vs F2P parity + pity timer math |
| Esports patch | 2-week cycle + pro-play meta watch |
| New release | Closed beta MC sim + open beta A/B |

**기본값**: telemetry → Bayesian winrate → 2-week patch cycle 의 [47%, 53%] band.

## 🔗 Graph
- 부모: [[Game_Design]]

## 🤖 LLM 활용
**언제**: patch note generation, telemetry anomaly detection, balance hypothesis brainstorming, sim scenario writing.
**언제 X**: 최종 numerical tuning (designer judgment + playtesting 의 X-able), competitive integrity decision.

## ❌ 안티패턴
- **Whale-only balancing**: F2P player 의 churn 의 무시.
- **Knee-jerk nerf**: 1-day data 의 over-react — sample size 의 부족.
- **Symmetric balance obsession**: asymmetric design 의 intentional 의 flatten의 X.
- **Nerf-only meta**: power creep 의 reverse — fun 의 erosion.
- **Ignoring rank-stratified data**: bronze 와 challenger 의 winrate 의 different — aggregate 의 misleading.

## 🧪 검증 / 중복
- Verified (Riot Games engineering blog, GDC talks 2023-2025, Vicious Syndicate).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — game balancing full content with patterns |