Abstract
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 $2\times10^5$ 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.
Keywords
Subject
Publication details
- Journal
- Not available
- Open access
- Green open access
Cite this article
APA 7
Reguera, D., Hoffmann, X. R., Pérez, I., Colomer-de-Simón, P., Masoliver, M., Guardiola, X., Wedekind, J., & Boguñá, M. (2026). All against the machine: the Solo score for rating skill in variable environments. https://omanscience.com/en/articles/all-against-the-machine-the-solo-score-for-rating-skill-in-variable-environments
MLA 9
Reguera, David, et al. "All against the machine: the Solo score for rating skill in variable environments." https://omanscience.com/en/articles/all-against-the-machine-the-solo-score-for-rating-skill-in-variable-environments.
Chicago (author–date)
Reguera, David, Xavier R. Hoffmann, Irene Pérez, Pol Colomer-de-Simón, Miquel Masoliver, Xavier Guardiola, Jan Wedekind, and Marián Boguñá. 2026. "All against the machine: the Solo score for rating skill in variable environments." https://omanscience.com/en/articles/all-against-the-machine-the-solo-score-for-rating-skill-in-variable-environments.
Harvard
Reguera, D., Hoffmann, X. R., Pérez, I., Colomer-de-Simón, P., Masoliver, M., Guardiola, X., Wedekind, J. and Boguñá, M. (2026) 'All against the machine: the Solo score for rating skill in variable environments', Available at: https://omanscience.com/en/articles/all-against-the-machine-the-solo-score-for-rating-skill-in-variable-environments.
Vancouver
Reguera D, Hoffmann XR, Pérez I, Colomer-de-Simón P, Masoliver M, Guardiola X, et al. All against the machine: the Solo score for rating skill in variable environments. https://omanscience.com/en/articles/all-against-the-machine-the-solo-score-for-rating-skill-in-variable-environments
IEEE
D. Reguera, X. R. Hoffmann, I. Pérez, P. Colomer-de-Simón, M. Masoliver, X. Guardiola, J. Wedekind, and M. Boguñá, "All against the machine: the Solo score for rating skill in variable environments," https://omanscience.com/en/articles/all-against-the-machine-the-solo-score-for-rating-skill-in-variable-environments.