📊 Data Source

Dataset: All International Football Results — 49,296 completed matches from 1872 to June 2026. Downloaded via kagglehub (martj42/international_results mirror).

⚡ Elo Rating System

Every match updates both teams’ Elo ratings using the standard formula, with modifications:

• K = 40 for competitive matches, 20 for friendlies
• Home advantage: +100 Elo points for non-neutral venues
• Goal difference multiplier: 1.0 (≤1 GD), 1.5 (2 GD), 1.75 (3 GD), scaling beyond
• Base Elo: 1000 for all teams at initialization

📈 Recent Form

Last 5 matches for each team, weighted by result: Win = 3 pts, Draw = 1 pt, Loss = 0 pts. Normalized to [0, 1] scale. Friendlies and competitive matches both count equally for form.

⚽ Goal Difference Trend

Average signed goal difference over last 10 matches. Positive = net scoring, negative = net conceding. Used as a proxy for attack/defense balance.

🎯 Composite Score & Win Probability

Match win probability uses a composite-adjusted Elo rather than raw Elo:

Draw probability set at ~25% for group stage; knockout rounds are winner-takes-all.

🎲 Monte Carlo Simulation

100,000 independent tournament simulations. Each run: simulate group stage → qualify top 2 + 8 best 3rd-place teams per group → bracket knockout rounds (R32 → R16 → QF → SF → Final). Win probability = fraction of simulations where a team lifts the trophy.

⚠️ Limitations

• Squad injuries and suspensions not modeled
• Recent pre-tournament friendlies are included but downweighted (K=20)
• Group stage draw structure taken from dataset — some group assignments may shift
• Model is statistical; upsets are inherent to football