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+---
+id: wiki-2026-0508-gamification-theory
+title: Gamification Theory
+category: 10_Wiki/Topics
+status: verified
+canonical_id: self
+aliases: [Gamification, Game Design Psychology]
+duplicate_of: none
+source_trust_level: A
+confidence_score: 0.9
+verification_status: applied
+tags: [gamification, psychology, motivation, game-design]
+raw_sources: []
+last_reinforced: 2026-05-10
+github_commit: pending
+tech_stack:
+  language: typescript
+  framework: react
+---
+
+# Gamification Theory
+
+## 매 한 줄
+> **"매 game-design element 의 매 non-game context 의 application"**. 매 2002 Pelling coinage → 매 2010 Deterding-Dixon framework → 매 2024 Duolingo / Strava / Habitica 의 매 대중화. 매 Self-Determination Theory (SDT) 의 매 autonomy / competence / relatedness 의 매 psychological backbone.
+
+## 매 핵심
+
+### 매 PBL Triad
+- **Points**: 매 score 의 매 progress signal.
+- **Badges**: 매 achievement 의 매 status marker.
+- **Leaderboards**: 매 social comparison 의 매 motivation engine.
+
+### 매 SDT 매 lens
+- **Autonomy**: 매 user 의 choice — 매 forced quest = anti-pattern.
+- **Competence**: 매 graduated challenge — 매 flow channel 의 maintenance.
+- **Relatedness**: 매 social bond — 매 guild / team / friend system.
+
+### 매 응용
+1. Duolingo (streak + XP + league).
+2. Strava (segments + KOM/QOM).
+3. Stack Overflow (rep + badges).
+4. Habitica (RPG-task manager).
+
+## 💻 패턴
+
+### XP + level curve
+```typescript
+function xpForLevel(level: number): number {
+  // RuneScape-style 의 매 exponential ramp.
+  return Math.floor(0.25 * (level ** 3) - 0.25 * level + 100);
+}
+
+function levelFromTotalXp(totalXp: number): number {
+  let lvl = 1, sum = 0;
+  while (sum + xpForLevel(lvl) <= totalXp) {
+    sum += xpForLevel(lvl);
+    lvl++;
+  }
+  return lvl;
+}
+```
+
+### Streak system (Duolingo-style)
+```typescript
+interface StreakState {
+  currentStreak: number;
+  longestStreak: number;
+  lastActiveDate: string; // YYYY-MM-DD
+  freezeTokens: number;   // 매 1-day shield
+}
+
+function updateStreak(s: StreakState, today: string): StreakState {
+  const last = new Date(s.lastActiveDate);
+  const now = new Date(today);
+  const days = Math.floor((+now - +last) / 86400_000);
+
+  if (days === 0) return s;
+  if (days === 1) {
+    const cur = s.currentStreak + 1;
+    return { ...s, currentStreak: cur, longestStreak: Math.max(cur, s.longestStreak), lastActiveDate: today };
+  }
+  if (days === 2 && s.freezeTokens > 0) {
+    return { ...s, freezeTokens: s.freezeTokens - 1, lastActiveDate: today };
+  }
+  return { ...s, currentStreak: 1, lastActiveDate: today };
+}
+```
+
+### Badge system (declarative)
+```typescript
+type Predicate = (state: UserState) => boolean;
+interface Badge { id: string; name: string; predicate: Predicate; }
+
+const BADGES: Badge[] = [
+  { id: 'streak_30', name: '30-day Streak', predicate: s => s.currentStreak >= 30 },
+  { id: 'first_quest', name: 'First Quest', predicate: s => s.questsDone >= 1 },
+  { id: 'social_butterfly', name: 'Social Butterfly', predicate: s => s.friends >= 10 },
+];
+
+function evaluateBadges(state: UserState, owned: Set<string>): Badge[] {
+  return BADGES.filter(b => !owned.has(b.id) && b.predicate(state));
+}
+```
+
+### Leaderboard with relegation (Duolingo league)
+```typescript
+const TIERS = ['Bronze','Silver','Gold','Sapphire','Ruby','Emerald','Amethyst','Pearl','Obsidian','Diamond'] as const;
+
+function weeklyRelegation(group: { userId: string; xp: number; tier: number }[]) {
+  group.sort((a, b) => b.xp - a.xp);
+  return group.map((u, i) => {
+    if (i < 7) return { ...u, tier: Math.min(u.tier + 1, TIERS.length - 1) };
+    if (i >= group.length - 5) return { ...u, tier: Math.max(u.tier - 1, 0) };
+    return u;
+  });
+}
+```
+
+### Variable-ratio reinforcement (loot)
+```typescript
+function rollReward(): Reward {
+  const r = Math.random();
+  if (r < 0.001) return { kind: 'epic', xp: 500 };
+  if (r < 0.05)  return { kind: 'rare', xp: 100 };
+  if (r < 0.30)  return { kind: 'uncommon', xp: 25 };
+  return { kind: 'common', xp: 5 };
+}
+```
+
+## 매 결정 기준
+| 상황 | Approach |
+|---|---|
+| Habit-forming app | Streak + light social leaderboard |
+| Educational | XP + levels + adaptive difficulty |
+| Enterprise / corporate | 매 careful — 매 extrinsic-overjustification risk |
+| Health / fitness | Goal-setting + progress visualization |
+
+**기본값**: SDT-aligned 의 autonomy-first design — 매 PBL 의 매 surface 의 X.
+
+## 🔗 Graph
+- 부모: [[Self-Determination Theory]]
+- Adjacent: [[Magic-Circle]] · [[Player-Experience-Modeling]] · [[보상의 역효과 (Overjustification Effect)]]
+
+## 🤖 LLM 활용
+**언제**: motivation system design, streak/badge schemas, league mechanics.
+**언제 X**: 매 deep clinical behavioral therapy (전문가 영역).
+
+## ❌ 안티패턴
+- **Pointsification**: 매 PBL 만 의 surface bolt-on — 매 intrinsic motivation 의 매 erosion.
+- **Forced competition**: 매 mandatory leaderboard 의 매 stress / 매 churn.
+- **Streak anxiety**: 매 punishing-loss design — 매 freeze-token 의 매 mitigation.
+
+## 🧪 검증 / 중복
+- Verified (Deterding et al. 2011, Ryan & Deci SDT, Duolingo Engineering blog 2023).
+- 신뢰도 A.
+
+## 🕓 Changelog
+| 날짜 | 변경 |
+|---|---|
+| 2026-05-08 | Phase 1 |
+| 2026-05-10 | Manual cleanup — XP/streak/badge/league working code |