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In Natural Language Processing (NLP), the Elo rating system, originallydesigned for ranking players in dynamic games such as chess, is increasinglybeing used to evaluate Large Language Models (LLMs) through "A vs B" pairedcomparisons. However, while popular, the system's suitability for assessingentities with constant skill levels, such as LLMs, remains relativelyunexplored. We study two fundamental axioms that evaluation methods shouldadhere to: reliability and transitivity. We conduct extensive evaluation of Elobehaviour, illustrating that individual Elo computations exhibit volatility anddelving into the impact of varying the Elo rating system's hyperparameters. Weshow that these axioms are not always satisfied raising questions about thereliability of current comparative evaluations of LLMs. If the current use ofElo scores is intended to substitute the costly head-to-head comparison ofLLMs, it is crucial to ensure the ranking is as robust as possible. Guided bythe axioms, our findings offer concrete guidelines for enhancing thereliability of LLM evaluation methods, suggesting a need for reassessment ofexisting comparative approaches.

Elo Uncovered: Robustness and Best Practices in Language Model Evaluation