Daniel Gomes de Pinho Zanco

Daniel Gomes de Pinho Zanco, Leszek Szczecinski, Eduardo Vinicius Kuhn et al.

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.

Salma Tenni, Daniel Gomes de Pinho Zanco, Leszek Szczecinski

This work presents and evaluates the ranking algorithm that has been used by Federation Internationale de Volleyball (FIVB) since 2020. The prominent feature of the FIVB ranking is the use of the probabilistic model, which explicitly calculates the probabilities of the future matches results using the estimated teams' strengths. Such explicit modeling is new in the context of official sport rankings, especially for multi-level outcomes, and we study the optimality of its parameters using both analytical and numerical methods. We conclude that from the modeling perspective, the current thresholds fit well the data but adding the home-field advantage (HFA) would be beneficial. Regarding the algorithm itself, we explain the rationale behind the approximations currently used and show a simple method to find new parameters (numerical score) which improve the performance. We also show that the weighting of the match results is counterproductive.

Daniel Gomes de Pinho Zanco, Leszek Szczecinski, Jacob Benesty

In this work, we consider the problem of regularization in the design of minimum mean square error (MMSE) linear filters. Using the relationship with statistical machine learning methods, using a Bayesian approach, the regularization parameter is found from the observed signals in a simple and automatic manner. The proposed approach is illustrated in system identification and beamforming examples, where the automatic regularization is shown to yield near-optimal results.