  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.
