# When Guessing is Rewarded: Rethinking Language Model Evaluation with Distributional Uncertainty Scoring

arXiv: https://arxiv.org/abs/2510.04302 · HTML: https://mlsanity.com/paper/2510.04302/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 39 references that are in the map.
- First posted on arXiv 5 Oct 2025.

## Builds on (most cited first, 27 of 27)

- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [GPQA: A Graduate-Level Google-Proof Q&A Benchmark](https://mlsanity.com/paper/2311.12022/) (2023)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Crowdsourcing Multiple Choice Science Questions](https://mlsanity.com/paper/1707.06209/) (2017)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Gender Bias in Coreference Resolution](https://mlsanity.com/paper/1804.09301/) (2018)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [SciBench: Evaluating College-Level Scientific Problem-Solving Abilities of Large Language Models](https://mlsanity.com/paper/2307.10635/) (2023)
- [Do Large Language Models Know What They Don't Know?](https://mlsanity.com/paper/2305.18153/) (2023)
- [TheoremQA: A Theorem-driven Question Answering dataset](https://mlsanity.com/paper/2305.12524/) (2023)
- [Large Language Models Often Know When They Are Being Evaluated](https://mlsanity.com/paper/2505.23836/) (2025)
- [Unfamiliar Finetuning Examples Control How Language Models Hallucinate](https://mlsanity.com/paper/2403.05612/) (2024)
- [Detecting Hallucinations in Large Language Model Generation: A Token Probability Approach](https://mlsanity.com/paper/2405.19648/) (2024)
- [Hierarchical Autoregressive Transformers: Combining Byte- and Word-Level Processing for Robust, Adaptable Language Models](https://mlsanity.com/paper/2501.10322/) (2025)
- [Unveiling LLM Evaluation Focused on Metrics: Challenges and Solutions](https://mlsanity.com/paper/2404.09135/) (2024)
- [A comprehensive taxonomy of hallucinations in Large Language Models](https://mlsanity.com/paper/2508.01781/) (2025)
- [Exploiting Reasoning Chains for Multi-hop Science Question Answering](https://mlsanity.com/paper/2109.02905/) (2021)
- [Why and How LLMs Hallucinate: Connecting the Dots with Subsequence Associations](https://mlsanity.com/paper/2504.12691/) (2025)
- [Enhancing Hallucination Detection through Noise Injection](https://mlsanity.com/paper/2502.03799/) (2025)

## Abstract (arXiv)

Standard language model evaluation assigns scores to single predicted answers, rewarding high-confidence responses regardless of how residual probability mass is distributed over alternative options. This creates a systematic pressure toward overconfident guessing: under accuracy-based schemes, a model maximises its expected score by always committing to an answer rather than abstaining, even when its uncertainty is high. While penalty-based approaches partially address this by raising the confidence threshold for strategic guessing, they still treat all sub-threshold responses identically, ignoring a fundamental distinction in how models can express uncertainty - for example between hedging toward incorrect answers versus hedging toward "I don't know" responses. This paper introduces a novel evaluation metric to solve this problem of not considering a model's entire probability distribution over answer choices. The metric naturally distinguishes between harmful overconfidence in wrong answers and uncertainty expressed through abstention, providing scores in an interpretable default range. Through theoretical analysis and illustrative examples, the metric is shown to offer a more nuanced and aligned evaluation paradigm that incentivises models to express genuine uncertainty rather than guessing. Adapting 12 existing evaluation benchmarks to the metric's variants and measuring performance on six language models shows that for half of the tested benchmarks scores are negative across all tested models, indicating significant tendencies towards hallucination.