Methodology

Football ELO uses a Davidson 3-way probability model to rate individual players. Unlike traditional team-level ELO systems, our model decomposes match outcomes into individual player contributions, producing a unique rating for every player who participates.

The Davidson model extends classic ELO by explicitly modeling three possible outcomes — home win, draw, and away win — as a function of the combined ratings of both lineups. This produces more accurate probability estimates than binary win/loss models, which is critical in football where draws are common.

After each match, every participating player receives a rating update based on the difference between the predicted and actual outcome, weighted by their position and minutes played. Players on the winning side of an upset gain more, while players in expected victories gain less.

Coaches are rated using the same ELO framework as players. Each coach is treated as an additional participant in every match, with the highest positional weight of any role. This reflects their outsized influence on tactical setup, substitution timing, and overall team performance.

This makes Football ELO the only system that produces individual ELO ratings for football coaches, enabling direct comparisons between managers across different leagues and eras.

Home advantage varies significantly across leagues. A home team in South American football enjoys a much larger advantage than one in the English Premier League. Our model calibrates a per-league home advantage parameter from historical data, producing more accurate predictions in every competition.

The model has been trained and validated on 249,006 matches across 176 competitions. We validate our probability estimates against professional bookmaker odds, ensuring our model produces well-calibrated predictions.

Model parameters are optimized using gradient-free optimization against held-out match data, minimizing log-loss to produce the most accurate probability estimates possible.