FIFA ranking: Evaluation and path forward

TL;DR

This paper critically evaluates FIFA's ranking algorithm, identifies its limitations, and proposes a probabilistic model-based improvement that enhances predictive accuracy by incorporating home advantage, draw modeling, and goal differential weighting.

Contribution

It provides a formal probabilistic framework for FIFA's ranking, critiques the current importance parameter, and suggests modifications for better predictive performance.

Findings

The current importance parameter reduces predictive accuracy.

Incorporating home-field advantage improves predictions.

Modeling draws explicitly enhances the algorithm's effectiveness.

Abstract

In this work we study the ranking algorithm used by F\'ed\'eration Internationale de Football Association (FIFA); we analyze the parameters it currently uses, show the formal probabilistic model from which it can be derived, and optimize the latter. In particular, analyzing the games since the introduction of the algorithm in 2018, we conclude that the game's "importance" (as defined by FIFA) used in the algorithm is counterproductive from the point of view of the predictive capability of the algorithm. We also postulate the algorithm to be rooted in the formal modelling principle, where the Davidson model proposed in 1970 seems to be an excellent candidate, preserving the form of the algorithm currently used. The results indicate that the predictive capability of the algorithm is notably improved by using the home-field advantage and the explicit model for the draws in the game. Moderate, but notable improvement may be attained by introducing the weighting of the results with the goal differential, which although not rooted in a formal modelling principle, is compatible with the current algorithm and can be tuned to the characteristics of the football competition.