This work uses a statistical framework to present and evaluate the ranking algorithm that has been used by F\'ed\'eration Internationale de Volleyball (FIVB) since 2020. The salient feature of the FIVB ranking is the use of the probabilistic model, which explicitly calculates the probabilities of the games to come. This explicit modeling is new in the context of official ranking, and we study the optimality of its parameters as well as its relationship with the ranking algorithm as such. The analysis is carried out using both analytical and numerical methods. We conclude that, from the modeling perspective, the use of the home-field advantage (HFA) would be beneficial and that the weighting of the game results is counterproductive. Regarding the algorithm itself, we explain the rationale beyond the approximations currently used and explain how to find new parameters which improve the performance. Finally, we propose a new model that drastically simplifies both the implementation and interpretation of the resulting algorithm.

The Elo algorithm, renowned for its simplicity, is widely used for rating in sports tournaments and other applications. However, despite its widespread use, a detailed understanding of the convergence characteristics of the Elo algorithm is still lacking. Aiming to fill this gap, this paper presents a comprehensive (stochastic) analysis of the Elo algorithm, considering round-robin tournaments. Specifically, analytical expressions are derived describing the evolution of the skills and performance metrics. Then, taking into account the relationship between the behavior of the algorithm and the step-size value, which is a hyperparameter that can be controlled, design guidelines and discussions about the performance of the algorithm are provided. Experimental results are shown confirming the accuracy of the analysis and illustrating the applicability of the theoretical findings using real-world data obtained from SuperLega, the Italian volleyball league.

In this work, we deal with the problem of rating in sports, where the skills of the players/teams are inferred from the observed outcomes of the games. Our focus is on the online rating algorithms which estimate the skills after each new game by exploiting the probabilistic models of the relationship between the skills and the game outcome. We propose a Bayesian approach which may be seen as an approximate Kalman filter and which is generic in the sense that it can be used with any skills-outcome model and can be applied in the individual-as well as in the group-sports. We show how the well-know algorithms (such as the Elo, the Glicko, and the TrueSkill algorithms) may be seen as instances of the one-fits-all approach we propose. In order to clarify the conditions under which the gains of the Bayesian approach over the simpler solutions can actually materialize, we critically compare the known and the new algorithms by means of numerical examples using the synthetic as well as the empirical data. In this work we are interested in the rating algorithms that can be systematically derived from the probabilistic models which describe i) how the the skills affect the outcomes of the games, as well as ii) how the skills evolve in time, i.e., characterize the skills dynamics. Using the probabilistic models, the forecasting of the game outcomes is naturally derived from the rating.