Probability Models for Match Outcomes

Elo Rating Model

Originally developed by Arpad Elo for ranking chess players, the Elo system has been successfully adapted to football and other sports.

Core Concept

Each team is assigned a numerical rating that reflects its strength. After every match, ratings are updated based on the result, the expected outcome, and the match importance.

Football-Specific Adjustments

To better reflect football dynamics, the model includes:

  • Home advantage — usually +100 rating points for the home team
  • Goal margin — bigger wins yield larger rating changes
  • Match type — friendlies vs. qualifiers vs. finals affect the K-factor
  • Tournament weight — World Cup matches carry more impact than regular games

Use Cases

  • Team strength evaluation — more accurate than traditional rankings
  • Match outcome prediction — probability-based forecasting
  • Form tracking — monitor team performance trends
  • Cross-team comparisons — objective, data-driven insights

Poisson Distribution Model in Football

The Poisson distribution is a statistical method used to estimate the probability of a number of events (like goals) occurring in a fixed interval — such as a football match.

How It’s Used in Football

Estimate Expected Goals (xG) for each team using:

  • Team’s average goals scored/conceded
  • Opponent’s defensive/attacking strength
  • Home/away adjustments

Apply Poisson formula to calculate the probability of each scoreline (e.g., 0–0, 1–0, 2–1, etc.)

Build full match probability matrix to:

  • Predict win/draw/loss probabilities
  • Identify value bets
  • Simulate tournament outcomes

Limitations

  • Assumes goals are independent events (not always true in football)
  • Doesn’t account for red cards, injuries, or tactical shifts

  • Works best for low-scoring sports like football

Logistic Temporal Model in Football Analytics

A logistic temporal model combines logistic regression with time-aware features to predict binary outcomes (like win/loss) while accounting for how performance evolves over time.

Core Components:

Logistic Regression: Estimates the probability of a binary outcome (e.g., win vs. not win) based on input features.

Temporal Features: Includes time-based variables such as:

  • Recent form (e.g. last 5 matches)
  • Player fatigue or rotation
  • Match timing (e.g. weekday vs weekend)
  • Seasonal trends or momentum

Application in Football:

  • Predict match outcomes using historical data with time decay (recent matches weighted more heavily).
  • Model team performance trajectories across a season.
  • Detect turning points — when a team’s form shifts significantly.
  • Combine with event data (e.g. goals, cards, substitutions) to model in-match dynamics.

Upcoming Models