Run-to-Run Dispersion as Evidence about Interactive Evaluation

Authors

  • Adam Lawson Author
  • Scott Walters Author
  • Cole Gardner Author

Abstract

A configuration with higher average scores can also have more variable outcomes. Across 55 games in the released BBF files, the median within-game standard deviation on an inverse-hyperbolic-sine score scale is 0.151 for the main configuration and 0.103 for the file without resets. The corresponding mean standard deviations are 0.204 and 0.147. This is a descriptive dispersion comparison rather than a causal variance test. It shows why claims about reliable interaction should report the spread of repeated outcomes in addition to their location and should distinguish score variability from rendering instability.

References

  1. Meng, Zijie, et al. "Make a game: A novel paradigm for interactive game rendering." ICASSP 2026-2026 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE, 2026.
  2. White, Halbert. “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica, vol. 48, no. 4, 1980, pp. 817–838. https://doi.org/10.2307/1912934.
  3. Cameron, A. Colin, and Douglas L. Miller. “A Practitioner’s Guide to Cluster-Robust Inference.” Journal of Human Resources, vol. 50, no. 2, 2015, pp. 317–372. https://doi.org/10.3368/jhr.50.2.317.
  4. Greenland, Sander, Judea Pearl, and James M. Robins. “Causal Diagrams for Epidemiologic Research.” Epidemiology, vol. 10, no. 1, 1999, pp. 37-48. https://doi.org/10.1097/00001648-199901000-00008.
  5. Benjamini, Yoav and Yosef Hochberg. “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing.” Journal of the Royal Statistical Society Series B: Statistical Methodology, vol. 57, no. 1, 1995, pp. 289-300. https://doi.org/10.1111/j.2517-6161.1995.tb02031.x.
  6. Roberts, David R., et al. “Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure.” Ecography, vol. 40, no. 8, 2017, pp. 913-929. https://doi.org/10.1111/ecog.02881.
  7. Varma, Sudhir and Richard Simon. “Bias in error estimation when using cross-validation for model selection.” BMC Bioinformatics, vol. 7, no. 1, 2006. https://doi.org/10.1186/1471-2105-7-91.
  8. Wilkinson, Mark D., et al. "The FAIR Guiding Principles for Scientific Data Management and Stewardship." Scientific Data, vol. 3, 2016, article 160018. https://doi.org/10.1038/sdata.2016.18.
  9. Sculley, D., et al. "Hidden Technical Debt in Machine Learning Systems." Advances in Neural Information Processing Systems, vol. 28, 2015. https://papers.nips.cc/paper/2015/hash/86df7dcfd896fcaf2674f757a2463eba-Abstract.html
  10. Bland, J. Martin, and Douglas G. Altman. "Statistical Methods for Assessing Agreement between Two Methods of Clinical Measurement." The Lancet, vol. 327, no. 8476, 1986, pp. 307-310. https://doi.org/10.1016/S0140-6736(86)90837-8.
  11. Guo, Chuan, Geoff Pleiss, Yu Sun, and Kilian Q. Weinberger. “On Calibration of Modern Neural Networks.” Proceedings of the 34th International Conference on Machine Learning, PMLR, vol. 70, 2017, pp. 1321–1330. https://proceedings.mlr.press/v70/guo17a.html.
  12. Geifman, Yonatan, and Ran El-Yaniv. “Selective Classification for Deep Neural Networks.” Advances in Neural Information Processing Systems, vol. 30, 2017. https://arxiv.org/abs/1705.08500.
  13. Ovadia, Yaniv, et al. “Can You Trust Your Model’s Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shift.” Advances in Neural Information Processing Systems, vol. 32, 2019. https://arxiv.org/abs/1906.02530.
  14. Bellemare, Marc G., et al.. "The Arcade Learning Environment: An Evaluation Platform for General Agents" arXiv preprint arXiv:1207.4708, 2012. https://arxiv.org/abs/1207.4708.
  15. Agarwal, Rishabh, et al.. "Deep Reinforcement Learning at the Edge of the Statistical Precipice" arXiv preprint arXiv:2108.13264, 2021. https://arxiv.org/abs/2108.13264.
  16. Cobbe, Karl, et al.. "Leveraging Procedural Generation to Benchmark Reinforcement Learning" arXiv preprint arXiv:1912.01588, 2019. https://arxiv.org/abs/1912.01588.
  17. Brockman, Greg, et al.. "OpenAI Gym" arXiv preprint arXiv:1606.01540, 2016. https://arxiv.org/abs/1606.01540.
  18. Ha, David and Jürgen Schmidhuber. "World Models" arXiv preprint arXiv:1803.10122, 2018. https://arxiv.org/abs/1803.10122.
  19. Hafner, Danijar, et al.. "Dream to Control: Learning Behaviors by Latent Imagination" arXiv preprint arXiv:1912.01603, 2019. https://arxiv.org/abs/1912.01603.
  20. Micheli, Vincent, et al.. "Transformers are Sample-Efficient World Models" arXiv preprint arXiv:2209.00588, 2022. https://arxiv.org/abs/2209.00588.
  21. Alonso, Eloi, et al.. "Diffusion for World Modeling: Visual Details Matter in Atari" arXiv preprint arXiv:2405.12399, 2024. https://arxiv.org/abs/2405.12399.
  22. Valevski, Dani, et al.. "Diffusion Models Are Real-Time Game Engines" arXiv preprint arXiv:2408.14837, 2024. https://arxiv.org/abs/2408.14837.
  23. Bruce, Jake, et al.. "Genie: Generative Interactive Environments" arXiv preprint arXiv:2402.15391, 2024. https://arxiv.org/abs/2402.15391.
  24. Zhang, Richard, et al.. "The Unreasonable Effectiveness of Deep Features as a Perceptual Metric" arXiv preprint arXiv:1801.03924, 2018. https://arxiv.org/abs/1801.03924.
  25. Unterthiner, Thomas, et al.. "Towards Accurate Generative Models of Video: A New Metric & Challenges" arXiv preprint arXiv:1812.01717, 2018. https://arxiv.org/abs/1812.01717.
  26. Wang, Zhou, Alan C. Bovik, Hamid R. Sheikh, and Eero P. Simoncelli. "Image Quality Assessment: From Error Visibility to Structural Similarity." IEEE Transactions on Image Processing, vol. 13, no. 4, 2004, pp. 600-612. https://doi.org/10.1109/TIP.2003.819861.
  27. Schwarzer, Max, et al.. "Bigger, Better, Faster: Human-level Atari with human-level efficiency" arXiv preprint arXiv:2305.19452, 2023. https://arxiv.org/abs/2305.19452.
  28. Sutton, Richard S., and Andrew G. Barto. Reinforcement Learning: An Introduction. 2nd ed., MIT Press, 2018. http://incompleteideas.net/book/the-book-2nd.html.
  29. Levine, Sergey, Aviral Kumar, George Tucker, and Justin Fu. “Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems.” arXiv, 2020, arXiv:2005.01643. https://arxiv.org/abs/2005.01643.
  30. Kumar, Aviral, Aurick Zhou, George Tucker, and Sergey Levine. “Conservative Q-Learning for Offline Reinforcement Learning.” Advances in Neural Information Processing Systems, vol. 33, 2020, pp. 1179–1191. https://arxiv.org/abs/2006.04779.

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Published

2026-09-19

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Vol. 2 (2026): Archive issue of 2026-09-19

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Articles

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Copyright (c) 2026 Adam Lawson, Scott Walters, Cole Gardner

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This work is licensed under a Creative Commons Attribution 4.0 International License.