In this work, we study the ranking algorithm used by Fédération Internationale de Football Association (FIFA); we analyze the parameters that it currently uses, show the formal probabilistic model from which it can be derived, and optimize the latter. In particular, analyzing games since the introduction of the algorithm in 2018, we conclude that game`s "importance" (defined by FIFA and used by the algorithm) is counterproductive from the point of view of the predictive capacity of the algorithm. We also postulate that the algorithm should be rooted in the formal modeling 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 capacity of the algorithm is considerably improved by using the home-field advantage (HFA), as well as the explicit model for the draws in the game. Moderate but notable improvement may be achieved by introducing the weighting of the results with the goal differential, which, although not rooted in a formal modeling principle, is compatible with the current algorithm and can be tuned to the characteristics of the football competition.
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