Methodology
Every technique, step by step. The data, the models, the math behind every prediction.
913 International Matches
The training dataset spans matches played between November 16, 2023 and June 11, 2026. We intentionally exclude the 2022 World Cup to prevent the model from developing an overwhelming "champion bias" towards Argentina, ensuring predictions are based purely on current form across continental tournaments, qualifiers, and friendlies.
Not all matches are equal. A Euro Championship or Copa America match holds much more weight than a friendly. Every match is mathematically weighted by both competition importance and recency.
Euros & Copa America
0.9xOther Continental
0.7xWC Qualifiers
0.7xNations League
0.6xFriendlies
0.3xSample Training Data
913 Matches · Showing 15 of them
| Date | Home | Away | Score | ||
|---|---|---|---|---|---|
| 2023-11-16 | Luxembourg | vs | Bosnia & Herz. | 4 – 1 | Euro Qualification0.7x |
| 2024-01-12 | Sweden | vs | Estonia | 2 – 1 | Friendlies0.3x |
| 2024-03-21 | Australia | vs | Lebanon | 2 – 0 | WC Qual. Asia0.7x |
| 2024-03-21 | Portugal | vs | Sweden | 5 – 2 | Friendlies0.3x |
| 2024-06-08 | Cameroon | vs | Cape Verde Isl. | 4 – 1 | WC Qual. Africa0.7x |
Starting from Zero
How Elo Works
This model is never told that some team (such as Spain) are strong. It learns the hierarchy from thousands of matches.
If an underdog beats a giant, they steal a lot of rating points. If the giant wins, they gain very few. Try it out:
Top teams by attack vs defense on a log-scale
Dixon-Coles MLE
Imagine each team has two hidden numbers: Attack (alpha) and Defense (beta). Spain has the highest alpha, which means they score a lot. Ecuador has the highest beta, meaning they rarely concede.
These values are found using Maximum Likelihood Estimation via the Newton-Raphson optimization algorithm, reverse-engineering team strength from historical goals.
Why Dixon-Coles over plain Poisson? Standard Poisson under-predicts low-scoring draws (like 0-0 and 1-1). Dixon-Coles adds a rho (ρ) dependency parameter to artificially inflate the probability of these realistic outcomes, which is crucial for international football where teams often play cautiously.
Poisson Regression (GLM)
Goals are count events, meaning you can score 0, 1, 2, but not 1.7. The Poisson distribution is built exactly for counting events. A Generalized Linear Model (GLM) estimates expected goals (λ) based on attacking/defending multipliers.
Goal Probability Curve (λ = 2.0)
Time-Decay Weighting
EWMA Form Tracker
A match played yesterday carries more signal than a match played 3 years ago. An Exponentially Weighted Moving Average is used to aggressively discount historical data, ensuring the model reflects a team's current form.
Why add an EWMA layer? Traditional models (like static Elo) can be too slow to react when a historically dominant team enters a sudden slump, or when a "golden generation" emerges for a mid-tier nation. EWMA ensures the model prioritizes recent momentum over ancient history.
Why This Ensemble?
Each model covers a different blind spot. Using only one would leave critical gaps.
Correctly models the shape of the entire goal distribution, especially the true frequency of 0-0 and 1-1 draws that plain Poisson misses.
Acts as a sanity check. When Dixon-Coles produces extreme parameter estimates for teams with sparse data, the GLM pulls the ensemble back toward a stable center.
Dixon-Coles and GLM train on all history equally. EWMA corrects this by aggressively weighting recent matches, catching a team on a sudden hot streak or slump.
The EWMA contribution is confidence-weighted: teams with fewer than 20 recent matches have their EWMA signal progressively down-weighted to prevent noise from sparse data distorting the final prediction.
What each model contributes to a single match prediction
Parameter Decisions
Every hyperparameter was chosen for a specific reason. None are arbitrary defaults.
MLE-fitted from 913 matches, matching the original Dixon & Coles (1997) reported range of -0.1 to -0.15. Corrects systematic Poisson undercount of 0-0 and 1-1 draws.
Dixon & Coles, JRSS 1997
Traditional World Football Elo uses 100 pts. WC2026 spans 3 host nations across neutral-ish venues, so advantage is reduced to 75%. Hosts receive half (37.5 pts) during simulation as they share venues.
World Football Elo Methodology
World Cup matches have the highest competitive stakes and information content. A 5-0 WC win should move ratings far more than a 5-0 friendly win. K=55 is the highest tier in the scale.
Calibrated vs backtest accuracy
Friendlies are low-stakes with squad rotation. Retained for sparse-data teams but given minimal weight so an anomalous friendly doesn't corrupt ratings.
Calibrated vs backtest accuracy
A match from 18 months ago gets 0.5× weight. From 3 years ago, ~0.25×. This reflects how quickly football team rosters and form change at international level.
Exponential decay: weight = 0.5^(age/18)
70% calibrated + 30% prior. Bayesian regularization: prevents a team with only 8 matches in training data from having their rating swung 40+ pts by a single anomalous result.
Standard in sparse-data Elo systems
The Ensemble Matrix
All three models' expected goals are averaged to get an ensemble lambda. This is used to generate a scoreline probability matrix, which is a grid of every possible score from 0-0 to 5-5 with exact probabilities.
Try dragging the sliders to see how the expected goals shift the probability distribution.
Lime = home win. Blue = away win. White = draw.
Calibration curve to verify accuracy
A perfectly calibrated model follows the dashed diagonal. Our lime curve tracks very close to perfect.
Monte Carlo & Accuracy
The model is tested using a walk-forward backtest: each match is predicted using only data from matches that happened before it. No cheating.
Backtest Results (vs Historical)
Once calibrated, the engine doesn't just predict a single outcome. The entire 2026 World Cup is played out 50,000 times in a Monte Carlo simulation. By analyzing the variance across all possible realities, the true fractional probability of every team's destiny is derived.
Simulated 50,000 Outcomes
Model Justification & Tuning
Why use an Ensemble of Statistical Models (Dixon-Coles, Poisson, Elo) rather than Machine Learning (like Random Forest, XGBoost) or Deep Learning?
- Data Sparsity & Overfitting: International football teams play very few matches a year. Deep learning and complex tree-based models thrive on massive datasets but will severely overfit on this sparse data, learning noise instead of true team strength.
- The Nature of Football: Football is low-scoring. Poisson distribution naturally models the count of discrete events (goals) occurring in a fixed time frame.
- Interpretability: Statistical models output explicit "Attack" and "Defense" parameters. If a model predicts a team will win, we can mathematically pinpoint exactly why, unlike black-box ML models.
How is the model tuned and weighted?
- Home Advantage: Host nations (USA, Mexico, Canada) receive a dedicated statistical boost during simulations. Other matches are treated as neutral venue games.
- Low-Scoring Dependency: Tuned to
rho = -0.13to accurately inflate the probability of 0-0 and 1-1 draws. - Match Importance (K-Factors): In Elo calibration, World Cup matches carry a massive weight (
K=55), whereas friendlies carry significantly lower weight. - Recency Decay: EWMA and Elo models feature time-decay. Matches played 2 years ago matter exponentially less than matches played last month.
- Goal Difference Multipliers: A 5-0 win boosts a rating more than a 1-0 win, but uses a logarithmic multiplier so anomalous blowouts don't break the model.