Question Difficulty Estimation for Large Language Models via Answer Plausibility Scoring

Accurate estimates of item difficulty are essential for valid assessment and effective adaptive learning. However, for newly created tasks, response data are typically unavailable. Pretesting and expert judgement can be costly and slow, while machine learning methods often require large labelled training datasets. Recent work suggests that large language models (LLMs) may help. However, there is limited evidence on the elicitation procedures and prompt configurations used to emulate experts for difficulty estimation. This study addresses this gap by evaluating three off-the-shelf LLMs as difficulty raters for newly created items without access to response data. Using an item bank from an online learning system, the study examined 6 domains of primary-school mathematics, with empirical difficulty estimates treated as empirical reference. The study used a full factorial design crossing three factors: judgement format (absolute vs pairwise), decision type (hard decisions vs token-probability-based estimates), and prompting strategy (zero-shot vs few-shot). LLM-derived difficulty estimates were compared with empirical difficulties using Spearman rank correlations. Across domains, LLM-based estimates exhibited moderate to strong positive correlations with empirical item difficulties. For simpler arithmetic tasks, some configurations approached the upper end of the accuracy range reported for human experts in previous research. Pairwise comparison consistently outperformed absolute judgement in the absence of additional refinements. However, when token-level probabilities were incorporated and examples of items with known empirical difficulty were provided, the absolute judgement configuration likewise demonstrated moderate-to-high alignment. The study positions LLMs as a promising tool for initial item calibration and offers insights into effective workflow configuration.

LLM benchmarks are increasingly dynamic: instead of containing a fixed set of questions, they define templates and parameters that can generate an effectively unlimited number of question variants. This flexibility is valuable, but it makes evaluation expensive -- especially when the goal is not just determining an average score, but reliably identifying a model's weak spots. This paper introduces a new methodology for identifying hard questions in dynamic benchmarks. It leverages COUP, a recent Bayesian optimization algorithm (Graham, Velez & Leyton-Brown, 2026), after introducing several substantive modifications to make the algorithm suitable for practical LLM pipelines. We also wrap it in a tool that supports flexible choices of datasets and utility functions, enabling users to target the kinds of questions they care about (e.g., low-accuracy questions; questions that are unusually hard relative to their measured complexity). In experiments across a range of benchmarks, we show that our method, dubbed $\texttt{QuickScope}$, discovers truly difficult questions more sample efficiently than standard baselines, while also reducing false positives from noisy outcomes.

Predicting human item difficulty is central to educational assessment, where reliable estimates support fairness and effective test construction. Existing methods often depend on costly human calibration or item-level textual representations, providing limited evidence about the cognitive processes that make items difficult. We argue that difficulty should be viewed not only as a property of item text, but also as an observable consequence of the problem-solving burden an item induces. Large Reasoning Models (LRMs) offer scalable process evidence through reasoning traces, but such evidence must be structured to support interpretable modeling. To this end, we introduce Epi2Diff (Episode to Difficulty), a framework that maps LRM reasoning traces into cognitively grounded episode sequences. These episodes group trace segments into functional problem-solving states, enabling difficulty to be modeled through reasoning scale, effort allocation, and state transitions. Epi2Diff extracts compact episode-dynamic features and combines them with semantic item representations for human difficulty prediction. Experiments on four real-world human difficulty datasets show that Epi2Diff consistently outperforms strong baselines, including fine-tuned small language models, LLM in-context learning, and supervised LLM adaptation. On SAT-derived classification benchmarks, Epi2Diff achieves an 8.1% average relative gain over supervised LLM fine-tuning baselines. Further analyses show that harder items induce more effortful, iterative, and implementation-centered episode dynamics, rather than merely longer responses. These results demonstrate that cognitive episodes in LRM reasoning traces provide a predictive and interpretable process representation for human item difficulty, offering a new lens for educational measurement with reasoning models.