# All against the machine: the Solo score for rating skill in variable environments

arXiv: https://arxiv.org/abs/2610.04523 · HTML: https://mlsanity.com/paper/2610.04523/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 29 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 7 of 7)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains](https://mlsanity.com/paper/2406.12045/) (2024)
- [Chatbot Arena: An Open Platform for Evaluating LLMs by Human Preference](https://mlsanity.com/paper/2403.04132/) (2024)
- [tinyBenchmarks: evaluating LLMs with fewer examples](https://mlsanity.com/paper/2402.14992/) (2024)
- [Adding Error Bars to Evals: A Statistical Approach to Language Model Evaluations](https://mlsanity.com/paper/2411.00640/) (2024)
- [Luck, skill, and depth of competition in games and social hierarchies](https://mlsanity.com/paper/2312.04711/) (2023)
- [Ranking with multiple types of pairwise comparisons](https://mlsanity.com/paper/2206.13580/) (2022)

## Abstract (arXiv)

We propose a distribution-free metric to rate individual skill in ``player-versus-environment'' settings, where participants face heterogeneous tasks without direct opponents. Such settings are common in digital platforms, games, education, finance, and the benchmark evaluation of AI agents. They combine high randomness, tasks of widely varying difficulty, and unknown heterogeneity across individuals. Our metric maps each task outcome to a bounded performance score with zero population mean and variance bounded by 1/3, regardless of the outcome distribution, so that scores are directly comparable across tasks. Aggregating these scores over tasks yields an interpretable skill score for each individual (the ``Solo'' rating), and a reshuffling null model tests whether that score exceeds what chance alone would produce. We validate the approach on the progression of 2×105 players in the mobile games Candy Crush Saga and Bubble Witch 3 Saga. The metric identifies high- and low-skill players with high statistical confidence, their classification persists over hundreds of subsequent levels, and a windowed version of the score tracks changes in performance along progression.