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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.