Score Sensei combines historical match analysis with an Elo rating system and Monte Carlo simulation to generate match probabilities and season forecasts. Our approach uses two complementary models — one tuned for near-term match predictions and another optimized for end-of-season projections — each data-driven and continuously validated.

1. Building the Dataset

Everything starts with data. We maintain a historical database of over 60,000 club matches spanning more than a decade, covering the top European leagues and continental competitions. New results are merged in as they happen, and team names are harmonized across sources so that a club's full history is always connected.

For international tournaments like the FIFA World Cup, we use a separate dataset of 8,000+ international matches to build nation-level predictions.

2. Elo Ratings

At the core of our model is an Elo rating system — a method originally developed for chess that has become a standard for measuring team strength in sports. Every team starts at a baseline rating, and after each match their rating is updated based on the result, the margin of victory, and the strength of the opponent.

Stronger opponents are worth more: beating the league leader moves your rating up more than beating a relegation side. We also factor in competition importance — a Champions League match carries more weight than a friendly — and apply a small annual regression to prevent ratings from drifting too far from reality over time.

The result is a single number per team that captures their overall quality, updated chronologically through every match in our database.

3. Rolling Performance Signals

Elo captures long-term quality, but football is also about form, momentum, and context. Alongside Elo, we compute several rolling performance metrics for every team:

• Global averages — a team's weighted scoring and conceding rates across their full recent history, with stronger opponents counting more
• Recent form — scoring patterns from the last handful of matches, capturing hot streaks and slumps
• Home and away splits — some teams are significantly stronger at home; this signal captures that venue effect

Each metric is weighted by opponent quality and competition importance, so scoring three goals against a top-four side counts more than doing the same against a bottom-half team.

4. Dual Prediction Model

We use a dual-model approach because different signals matter at different time horizons:

• Near-term model (next few weeks): emphasizes Elo and recent form — when predicting tomorrow's match, current momentum matters most
• Simulation model (season projections): emphasizes Elo and global averages — for end-of-season forecasts, long-run quality is more predictive than a two-match hot streak

Both models combine their signals into expected goals for each team, then apply a Dixon-Coles correction — a well-known statistical adjustment that improves the modeling of low-scoring outcomes like 0-0 and 1-1 draws. The final output is a probability distribution over all possible scorelines.

5. Monte Carlo Simulation

For league tables and tournament brackets, we go beyond single-match probabilities. We run 10,000 Monte Carlo simulations of the remaining season, randomly sampling goal totals from Poisson distributions for each unplayed match.

Each simulation produces a complete final table. By counting how often each team finishes in each position across all 10,000 simulations, we get probabilities for winning the title, qualifying for continental competition, or being relegated. For knockout tournaments like the Champions League and World Cup, we simulate the full bracket — using actual fixtures and results where available, and modeling unplayed matches from there.

6. International Tournaments

For the FIFA World Cup and other international competitions, we use a dedicated model built on the Dixon-Coles framework — a statistical model that simultaneously estimates attack and defense parameters for every national team using maximum likelihood estimation. This approach naturally handles the challenge of varying opponent quality in international football, where teams play far fewer matches than clubs and face opponents from different confederations.

Tournament simulations follow the official format, including group stages, third-place advancement rules, and bracket constraints.

Competitions We Cover

Score Sensei provides predictions for the following competitions:

• European 1st division: Premier League, La Liga, Ligue 1, Serie A, Bundesliga, Primeira Liga, Eredivisie, Belgian Pro League
• European 2nd division: EFL Championship, 2. Bundesliga, Ligue 2, Serie B, Segunda División
• European cups: UEFA Champions League, UEFA Europa League, UEFA Conference League
• International: FIFA World Cup 2026, CONMEBOL World Cup Qualifying, Copa América, UEFA European Championship

Model Performance

We evaluate our model using calibration analysis: when the model predicts a 30% chance of something happening, does it actually happen about 30% of the time? The calibration plot below shows our predicted probabilities against actual outcomes across thousands of matches. Points close to the diagonal line indicate well-calibrated predictions.

Leagues Included in the Calibration

• La Liga
• Ligue 1
• Premier League
• Serie A
• Primeira Liga
• Bundesliga
• Eredivisie
• Belgian Pro League
• 2. Bundesliga
• Ligue 2
• EFL Championship
• Serie B
• Segunda División

Changelog

v0.4 — April 2026

• Introduced Elo rating system for both club and international models, computed from 60,000+ historical matches.
• Implemented dual prediction model: separate near-term and simulation weight configurations, each independently optimized.
• Added Dixon-Coles correction for improved low-score probability modeling.
• Switched to vectorized Monte Carlo simulation (10,000 iterations) for faster league and tournament projections.
• Added FIFA World Cup 2026 predictions with full group stage and knockout bracket simulation.
• International model rebuilt using Dixon-Coles maximum likelihood estimation on 8,000+ matches.

v0.3 — September 2024

• Added more weight to the 5 most recent matches for improved form sensitivity.
• Included Belgian and Dutch leagues.

v0.2 — June 2024

• Fixed home advantage calculation for neutral-ground matches.
• Added team and league strength ratings.