🏓 Initial ServeSync demo build

- FastAPI backend with PostgreSQL + Redis
- 4 core features: Registration, Courts, Matchmaking, Tournament
- Double elimination tournament with bracket visualization
- ELO-based matchmaking (Stage 1 Open, Stage 2 Skill-Based)
- Real-time WebSocket updates
- TV Screen display for courts
- Vue 3 + Tailwind CSS frontend
- Seed data: 12 players, 4 courts, active matches, tournament in progress
- Docker compose stack with Nginx reverse proxy

backend/app/services/elo.py

@@ -0,0 +1,53 @@
+"""ELO Rating System for ServeSync"""
+
+K_FACTOR = 32  # Standard K-factor
+
+
+def expected_score(rating_a: float, rating_b: float) -> float:
+    """Calculate expected score for player A vs player B"""
+    return 1 / (1 + 10 ** ((rating_b - rating_a) / 400))
+
+
+def calculate_elo_change(winner_rating: float, loser_rating: float) -> tuple[float, float]:
+    """
+    Calculate ELO changes after a match.
+    Returns (winner_change, loser_change)
+    """
+    expected_winner = expected_score(winner_rating, loser_rating)
+    expected_loser = expected_score(loser_rating, winner_rating)
+
+    winner_change = K_FACTOR * (1 - expected_winner)
+    loser_change = K_FACTOR * (0 - expected_loser)
+
+    return round(winner_change, 2), round(loser_change, 2)
+
+
+def calculate_team_elo(player1_rating: float, player2_rating: float = None) -> float:
+    """Calculate team ELO (average for doubles)"""
+    if player2_rating is None:
+        return player1_rating
+    return (player1_rating + player2_rating) / 2
+
+
+def get_tier_from_elo(elo: float) -> str:
+    """Get membership tier based on ELO rating"""
+    if elo < 1000:
+        return "bronze"
+    elif elo < 1200:
+        return "silver"
+    elif elo < 1500:
+        return "gold"
+    elif elo < 1800:
+        return "platinum"
+    else:
+        return "elite"
+
+
+def is_valid_match(player_elo: float, match_min_elo: float, match_max_elo: float) -> bool:
+    """Check if player is within ELO range for skill-based match"""
+    return match_min_elo <= player_elo <= match_max_elo
+
+
+def get_elo_range(player_elo: float, tolerance: float = 200) -> tuple[float, float]:
+    """Get valid ELO range for matching"""
+    return (max(0, player_elo - tolerance), player_elo + tolerance)