Database Design Documentation

Complete database schema design and architecture decisions for the Worms Math Game.

Overview

The database uses PostgreSQL (via Supabase) with 6 main tables:

users - User accounts (students and teachers)
quiz_questions - Pre-loaded quiz questions for 5. klasse matematik
quiz_attempts - Student quiz performance tracking
match_results - Completed game matches
match_participants - Player performance in matches
match_teams - Team information (for team-based matches)

Table Schemas

1. Users Table

Stores user accounts with rating and statistics.

CREATE TABLE users (
  id UUID PRIMARY KEY DEFAULT uuid_generate_v4(),
  username TEXT UNIQUE NOT NULL,
  role TEXT DEFAULT 'student' CHECK (role IN ('student', 'teacher')),

  -- Rating and stats
  rating INTEGER DEFAULT 1000,
  matches_played INTEGER DEFAULT 0,
  matches_won INTEGER DEFAULT 0,
  total_kills INTEGER DEFAULT 0,
  total_damage INTEGER DEFAULT 0,

  -- Timestamps
  created_at TIMESTAMP DEFAULT NOW(),
  last_played_at TIMESTAMP
);

Design Decisions:

UUID Primary Key: Allows distributed ID generation, better for scaling
Username Only Auth (MVP): No passwords for simplicity. Production would add auth.
Role Enum: student | teacher for permission differentiation
Starting Rating: 1000 (standard ELO starting point)
Denormalized Stats: matches_played, matches_won, etc. cached for performance
last_played_at: Track user engagement

Indexes:

CREATE INDEX idx_users_rating ON users(rating DESC);  -- Leaderboard queries
CREATE INDEX idx_users_role ON users(role);           -- Filter by role
CREATE INDEX idx_users_username ON users(username);   -- Login lookups

2. Quiz Questions Table

Pre-loaded questions for Danish 5. klasse matematik.

CREATE TABLE quiz_questions (
  id UUID PRIMARY KEY DEFAULT uuid_generate_v4(),
  subject TEXT DEFAULT 'matematik',
  topic TEXT NOT NULL CHECK (topic IN ('division', 'brøker', 'geometri', 'problemregning', 'grundlæggende', 'blandet')),
  grade_level INTEGER DEFAULT 5,

  -- Question content
  question TEXT NOT NULL,
  options JSONB NOT NULL,  -- ["Option A", "Option B", "Option C", "Option D"]
  correct_answer INTEGER NOT NULL CHECK (correct_answer BETWEEN 0 AND 3),

  -- Optional metadata
  difficulty TEXT DEFAULT 'medium' CHECK (difficulty IN ('easy', 'medium', 'hard')),
  explanation TEXT,

  created_at TIMESTAMP DEFAULT NOW()
);

Design Decisions:

JSONB for Options: Flexible, indexable, supports Danish characters
Integer for Correct Answer: 0-3 index (simple and fast)
Topic Categories: Aligned with Danish curriculum (division, brøker, geometri, problemregning)
Difficulty Levels: easy, medium, hard for adaptive difficulty
Optional Explanation: For teacher view / student feedback

Why JSONB?

Native PostgreSQL support
Efficient storage
Can query/filter by option content if needed
Supports arrays of any length

Indexes:

CREATE INDEX idx_quiz_questions_topic ON quiz_questions(topic);
CREATE INDEX idx_quiz_questions_difficulty ON quiz_questions(difficulty);

Sample Data: 60 questions pre-loaded (15 per topic):

Division (15 questions)
Brøker/Fractions (15 questions)
Geometri (15 questions)
Problemregning/Word Problems (15 questions)

3. Quiz Attempts Table

Tracks student performance for teacher dashboard.

CREATE TABLE quiz_attempts (
  id UUID PRIMARY KEY DEFAULT uuid_generate_v4(),
  user_id UUID REFERENCES users(id) ON DELETE CASCADE,
  question_id UUID REFERENCES quiz_questions(id) ON DELETE CASCADE,

  -- Attempt data
  answer_given INTEGER CHECK (answer_given BETWEEN 0 AND 3),
  is_correct BOOLEAN NOT NULL,
  time_spent INTEGER,  -- seconds

  -- Context
  match_id UUID,  -- Optional: link to match if during gameplay

  created_at TIMESTAMP DEFAULT NOW()
);

Design Decisions:

Foreign Keys with CASCADE: Delete user = delete their attempts
is_correct Boolean: Pre-calculated for fast queries
time_spent: Optional metric for analysis
match_id: Optional link to game context

Indexes:

CREATE INDEX idx_quiz_attempts_user ON quiz_attempts(user_id);
CREATE INDEX idx_quiz_attempts_question ON quiz_attempts(question_id);
CREATE INDEX idx_quiz_attempts_created_at ON quiz_attempts(created_at DESC);

Use Cases:

Student progress tracking
Teacher dashboard analytics
Topic mastery analysis
Time-per-question analysis

4. Match Results Table

Stores completed matches.

CREATE TABLE match_results (
  id UUID PRIMARY KEY DEFAULT uuid_generate_v4(),
  match_type TEXT NOT NULL CHECK (match_type IN ('ffa', '1v1', '2v2', '3v3', '4v4')),

  -- Match metadata
  duration_seconds INTEGER,
  total_turns INTEGER,

  created_at TIMESTAMP DEFAULT NOW(),
  ended_at TIMESTAMP
);

Design Decisions:

Match Type Enum: Supports FFA and team modes
Duration & Turns: Optional metadata for statistics
Separate timestamps: created_at (match start) vs ended_at (match end)

Indexes:

CREATE INDEX idx_match_results_created_at ON match_results(created_at DESC);
CREATE INDEX idx_match_results_type ON match_results(match_type);

5. Match Participants Table

Links users to matches with performance data.

CREATE TABLE match_participants (
  match_id UUID REFERENCES match_results(id) ON DELETE CASCADE,
  user_id UUID REFERENCES users(id) ON DELETE CASCADE,

  -- Team info (NULL for FFA)
  team_id INTEGER CHECK (team_id BETWEEN 1 AND 4),

  -- Performance
  placement INTEGER NOT NULL,  -- 1 = winner, 2 = second, etc.
  kills INTEGER DEFAULT 0,
  damage_dealt INTEGER DEFAULT 0,
  turns_taken INTEGER DEFAULT 0,

  -- Rating changes
  rating_before INTEGER NOT NULL,
  rating_after INTEGER NOT NULL,
  rating_change INTEGER NOT NULL,

  PRIMARY KEY (match_id, user_id)
);

Design Decisions:

Composite Primary Key: (match_id, user_id) ensures one entry per player per match
team_id NULL for FFA: Flexible for different game modes
Placement: 1 = winner, supports ties (multiple rank 1)
Rating Snapshot: Store before/after/change for history
Performance Metrics: kills, damage, turns for leaderboard

Indexes:

CREATE INDEX idx_match_participants_user ON match_participants(user_id);
CREATE INDEX idx_match_participants_match ON match_participants(match_id);

Why Store Rating Changes?

Historical accuracy (user's rating at time of match)
Audit trail for rating calculations
Can recalculate/verify ELO algorithm

6. Match Teams Table

Team information for team-based matches.

CREATE TABLE match_teams (
  match_id UUID REFERENCES match_results(id) ON DELETE CASCADE,
  team_id INTEGER CHECK (team_id BETWEEN 1 AND 4),

  -- Team info
  team_name TEXT NOT NULL,
  team_color TEXT NOT NULL,
  won BOOLEAN NOT NULL,

  -- Team stats
  total_kills INTEGER DEFAULT 0,
  total_damage INTEGER DEFAULT 0,

  PRIMARY KEY (match_id, team_id)
);

Design Decisions:

Only for Team Matches: NULL in match_results for FFA
team_id 1-4: Supports up to 4 teams
Danish Team Names: "Rødt Hold", "Blåt Hold", etc.
Aggregate Stats: Total kills/damage per team

Example Team Colors:

Team 1: #FF0000 (Red)
Team 2: #0000FF (Blue)
Team 3: #00FF00 (Green)
Team 4: #FFFF00 (Yellow)

Relationships

users (1) ----< (N) match_participants
match_results (1) ----< (N) match_participants
match_results (1) ----< (N) match_teams
users (1) ----< (N) quiz_attempts
quiz_questions (1) ----< (N) quiz_attempts

Cascading Deletes:

Delete user → delete their attempts and match participation
Delete match → delete all participants and teams
Delete question → delete all attempts (rare)

ELO Rating System

Algorithm Choice

Standard ELO with modifications for FFA and teams.

Rating Calculation

1v1 Formula:

New Rating = Old Rating + K * (Actual Score - Expected Score)
Expected Score = 1 / (1 + 10^((Opponent Rating - Player Rating) / 400))
Actual Score = 1 (win) or 0 (loss)
K-factor = 32 (standard)

FFA Formula:

Compare each player against all others
Average rating change across all comparisons
K-factor = 24 (lower for multi-opponent)

Team Formula:

Calculate team average rating
Apply standard ELO between teams
Same rating change for all team members
K-factor = 32 for 2 teams, 28 for 3+ teams

K-Factor Values

Match Type	K-Factor	Reason
1v1	32	Standard ELO
2v2	32	Clear winner/loser
3v3, 4v4	32	Team-based
FFA	24	Multiple opponents, lower volatility
Multi-team	28	Balanced for 3+ teams

Starting Rating

1000 - Standard ELO midpoint

Rating Floor

0 - Ratings cannot go below 0

Performance Optimizations

1. Indexes

All foreign keys indexed for JOIN performance:

-- User lookups
CREATE INDEX idx_users_rating ON users(rating DESC);
CREATE INDEX idx_users_username ON users(username);

-- Quiz queries
CREATE INDEX idx_quiz_attempts_user ON quiz_attempts(user_id);
CREATE INDEX idx_quiz_questions_topic ON quiz_questions(topic);

-- Match history
CREATE INDEX idx_match_participants_user ON match_participants(user_id);
CREATE INDEX idx_match_results_created_at ON match_results(created_at DESC);

2. Denormalized Stats

User stats cached in users table:

matches_played
matches_won
total_kills
total_damage

Trade-off:

✅ Fast leaderboard queries (no COUNT needed)
✅ No JOINs for user profile
❌ Must update on each match (handled by API)

3. JSONB for Options

Quiz options stored as JSONB:

✅ Native PostgreSQL type
✅ Indexable (GIN index if needed)
✅ Flexible array length
✅ Supports Unicode (Danish characters)

4. Composite Primary Keys

match_participants and match_teams use composite keys:

✅ Enforces uniqueness
✅ No extra index needed
✅ Fast lookups

Data Integrity

Constraints

-- Role validation
CHECK (role IN ('student', 'teacher'))

-- Match type validation
CHECK (match_type IN ('ffa', '1v1', '2v2', '3v3', '4v4'))

-- Answer range validation
CHECK (correct_answer BETWEEN 0 AND 3)
CHECK (answer_given BETWEEN 0 AND 3)

-- Team ID validation
CHECK (team_id BETWEEN 1 AND 4)

-- Difficulty validation
CHECK (difficulty IN ('easy', 'medium', 'hard'))

Foreign Keys

All relationships enforced with foreign keys:

quiz_attempts.user_id → users.id
quiz_attempts.question_id → quiz_questions.id
match_participants.match_id → match_results.id
match_participants.user_id → users.id
match_teams.match_id → match_results.id

Unique Constraints

-- Username must be unique
UNIQUE (username)

-- One entry per player per match
PRIMARY KEY (match_id, user_id)

-- One entry per team per match
PRIMARY KEY (match_id, team_id)

Scalability Considerations

Current Design (MVP)

Single region: Denmark/EU-Central
Estimated load: 100-500 users
Supabase free tier: 500 MB database, unlimited API requests

Future Scaling

If scaling needed:

Read Replicas: Leaderboard queries from replica
Partitioning: Partition quiz_attempts by date
Caching: Redis for leaderboard (TTL 60s)
Connection Pooling: PgBouncer (Supabase includes this)
Archiving: Move old matches to cold storage

Current indexes support:

Leaderboard: O(log N) with B-tree on rating
User lookup: O(1) hash on username
Match history: O(log N) with B-tree on created_at

Sample Queries

Get Top 10 Leaderboard

SELECT username, rating, matches_played, matches_won
FROM users
WHERE role = 'student'
ORDER BY rating DESC
LIMIT 10;

Get User Win Rate

SELECT
  username,
  rating,
  matches_played,
  matches_won,
  ROUND(100.0 * matches_won / NULLIF(matches_played, 0), 1) as win_rate
FROM users
WHERE id = 'user_id_here';

Get Quiz Accuracy by Topic

SELECT
  qq.topic,
  COUNT(*) as attempts,
  SUM(CASE WHEN qa.is_correct THEN 1 ELSE 0 END) as correct,
  ROUND(100.0 * SUM(CASE WHEN qa.is_correct THEN 1 ELSE 0 END) / COUNT(*), 1) as accuracy
FROM quiz_attempts qa
JOIN quiz_questions qq ON qa.question_id = qq.id
WHERE qa.user_id = 'user_id_here'
GROUP BY qq.topic;

Get Match History with Details

SELECT
  mr.match_type,
  mp.placement,
  mp.kills,
  mp.damage_dealt,
  mp.rating_before,
  mp.rating_after,
  mp.rating_change,
  mr.created_at
FROM match_participants mp
JOIN match_results mr ON mp.match_id = mr.id
WHERE mp.user_id = 'user_id_here'
ORDER BY mr.created_at DESC
LIMIT 10;

Security Considerations

MVP (Current)

No Row Level Security (RLS): All data readable by anyone
Username-only auth: No passwords
API validation: Server-side validation only

Production Recommendations

Enable RLS:

-- Users can only update their own stats
CREATE POLICY "Users update own" ON users
  FOR UPDATE USING (auth.uid() = id);

-- Anyone can read quiz questions
CREATE POLICY "Public quiz" ON quiz_questions
  FOR SELECT USING (true);

-- Users can only read their own attempts
CREATE POLICY "Users read own attempts" ON quiz_attempts
  FOR SELECT USING (auth.uid() = user_id);

Add Authentication:

Supabase Auth (email/password)
Session tokens
JWT validation

API Rate Limiting:

Prevent spam signups
Limit quiz question fetches

Input Validation:

Sanitize usernames
Validate JSON payloads
Prevent SQL injection (use parameterized queries)

Migration Strategy

Version 1 (Current)

Users with username-only auth
60 pre-loaded quiz questions
FFA and team match support
ELO rating system

Future Versions

V2: Authentication

Add users.password_hash
Add users.email
Enable Supabase Auth

V3: Social Features

Add friend_requests table
Add user_achievements table
Add chat_messages table

V4: Advanced Analytics

Add daily_stats aggregate table
Add skill_ratings per topic
Add match_replays JSONB column

Migration Process:

Write migration SQL
Test on staging database
Backup production
Run migration with transaction
Verify data integrity

Backup & Recovery

Supabase Automatic Backups

Daily backups: Automatic on all plans
Point-in-time recovery: Pro plan feature
Retention: 7 days (free), 30 days (pro)

Manual Backup

# Export database
pg_dump -h db.xxxxx.supabase.co -U postgres -d postgres > backup.sql

# Restore database
psql -h db.xxxxx.supabase.co -U postgres -d postgres < backup.sql

Critical Tables Priority

users - User accounts (CRITICAL)
match_results + match_participants - Game history (HIGH)
quiz_attempts - Student progress (HIGH)
quiz_questions - Can be re-seeded (MEDIUM)

Conclusion

The database design balances:

✅ Simplicity: Easy to understand and maintain ✅ Performance: Indexed queries, denormalized stats ✅ Flexibility: Supports FFA and team modes ✅ Scalability: Can handle 100-500 users easily ✅ Education: Tracks student progress for teachers ✅ Fairness: ELO rating system for balanced matchmaking

Total Tables: 6 Total Indexes: 11 Sample Data: 60 quiz questions Starting Rating: 1000 ELO

Ready for production deployment!

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Database Design Documentation

Overview

Table Schemas

1. Users Table

2. Quiz Questions Table

3. Quiz Attempts Table

4. Match Results Table

5. Match Participants Table

6. Match Teams Table

Relationships

ELO Rating System

Algorithm Choice

Rating Calculation

K-Factor Values

Starting Rating

Rating Floor

Performance Optimizations

1. Indexes

2. Denormalized Stats

3. JSONB for Options

4. Composite Primary Keys

Data Integrity

Constraints

Foreign Keys

Unique Constraints

Scalability Considerations

Current Design (MVP)

Future Scaling

Sample Queries

Get Top 10 Leaderboard

Get User Win Rate

Get Quiz Accuracy by Topic

Get Match History with Details

Security Considerations

MVP (Current)

Production Recommendations

Migration Strategy

Version 1 (Current)

Future Versions

Backup & Recovery

Supabase Automatic Backups

Manual Backup

Critical Tables Priority

Conclusion