The issue of sparse networks in sports competitions: can Elo ratings efficiently compare football teams that never play a match?

This study assesses the accuracy of Elo-based rating models in sparse, fragmented networks of pairwise comparisons. Three different modifications to the standard Elo rating are introduced and combined to eight model variants which were tested on both real-world and artificially generated data from the domain of football. The first modification implements a noise-free input by replacing the match outcome with the matches betting odds. The second modification adapts the k-parameter to adhere for competition differences. The last introduces a league-consistent Elo adaptation. Forecasting accuracy, ranking quality, and comparison accuracy were assessed to compare model performance based on both a rich and a limited version of the dataset. Results show that Elo ratings are suitable for comparisons of teams that never meet in matches. Additionally, noise-free Elo continuously shows the best accuracy, while league-consistent Elo enhances accuracy when data availability is limited. The artificial dataset showed strong similarities to the real data, supporting its suitability for controlled experiments. Overall, the findings highlight the importance of the interplay of model choice and data availability, while demonstrating the general ability of Elo ratings to evaluate and compare teams, even in sparse network structures.