Probability Calculation Logic | 2026 World Cup Prediction Platform · Algorithmic Foundations

Probability Calculation Logic Whitepaper

Win/Draw/Loss Probabilities · Advancement Odds · Score Simulation · Kelly Value · Multi-Model Ensemble

Algorithm Version: 2026.06 · World Cup Edition
Win/Draw/Loss Probability Calculation ELO Difference + Correction Factors

⚡ Core Formula

P(Home Win) = 1 / (1 + 10^((ELO_away - ELO_home + HFA)/400))

HFA = Home advantage constant (0 for neutral World Cup venues, but group stage tweaked ±8 points for host nation factors)

Draw probability derived from Poisson correction: P(Draw) = 2 × √(P_win × P_loss) × draw adjustment coefficient (η)

ELO Difference → Win Rate Mapping (example)
ELO advantage 100 pts → Win Rate ≈64%

📊 Typical Probability Distribution

A "draw shrink factor" (η=0.85 for knockout stage, η=0.92 for group stage) is applied. Additionally, draw probability is fine-tuned by ±3% based on team tactical style (counter-attack vs possession).
Advancement Probability Calculation Monte Carlo Simulation + Bayesian Dynamic Update

🎲 Algorithm Workflow

1. Based on current group standings and remaining fixtures, generate 10,000 Monte Carlo simulations

2. Each simulation randomly decides match outcomes using ELO-derived win probabilities, then computes final group rankings

3. Count how many times each team finishes in the top 2 of its group → P(Advance)

P(Advance) = (Number of advancement simulations) / Total simulations

For knockout stages, the full path is simulated to obtain tournament win probabilities.

📈 Example: Group Stage Advancement Probability

Monte Carlo simulations are updated daily and automatically converge as real match results are ingested. Confidence interval width narrows as the group stage progresses (±8% error after MD1, ±3% before MD3).
Score Simulation Logic Poisson Distribution + xG Expectation Adjustment

⚽ Goal Distribution Model

Each team's goal count follows an independent Poisson distribution: Home team ~ Poisson(λ_home), Away team ~ Poisson(λ_away)

λ_home = avg xG_home × opponent defensive coefficient × form correction factor

Average xG is derived from the xG model; opponent defensive coefficient = league_avg / opponent average xGA. Score probabilities are computed via convolution.

For knockout stage matches tied after regular time, a "penalty shootout simulator" (based on historical penalty data) generates the final score.

📉 Single-Match Score Probability Distribution Example

A co-integration correction is applied to the Poisson distribution: empirical probability calibration for common scores (0-0, 1-0, etc.) ensures the simulated distribution passes the Kolmogorov–Smirnov test against historical real data (p>0.05).
Kelly Value & Expected Value Kelly Criterion + Marginal Edge

💰 Kelly Stake Fraction

f* = (p × b - q) / b

p = model true probability, b = decimal odds - 1, q = 1-p

When model probability > market implied probability, a positive expectation arises, and the system outputs a "Value Index" (0~100).

Kelly Fraction Suggested Thresholds
f* > 0.02 → Low value | 0.05~0.10 → High value

📊 Value Deviation Monitoring

Value calculation blends multiple odds sources (average market price + exchange data) and applies a volatility smoothing factor to avoid extreme Kelly fractions.
Multi-Model Ensemble Framework Weighted Voting + Bayesian Averaging

🧠 Ensemble Architecture

Final Probability = 0.40 × ELO base probability + 0.35 × xG simulated probability + 0.25 × market-calibrated probability

Weights are tuned based on historical backtesting (ELO weight increases to 0.45 for knockout stages). After fusion, a "softmax calibration" ensures probabilities sum to 1.

P_final = softmax( w_i × log(P_i) )

📈 Dynamic Model Weight Adjustment

Compared to a single ELO model, the ensemble model improves accuracy by 9.7% and reduces log loss by 14% in backtesting on the 2018-2022 World Cups.
Calculation Transparency & Reproducibility

▪ All probability formulas are publicly documented in the platform's technical docs. Core Python code is open-sourced (see GitHub repository).
▪ Daily probability snapshots and raw ELO/xG data are available via API (API key required).
▪ Monte Carlo simulations use deterministic random seeds, enabling third-party replication and verification.
▪ Any algorithmic changes undergo A/B testing and are recorded in the change log.

Probability calculation logic documentation is continuously updated. Core parameters and validation metrics are recalibrated after each round of matches. Detailed implementation can be found in the platform's GitHub repository.