# LLMs are Overconfident: Evaluating Confidence Interval Calibration with FermiEval

arXiv: https://arxiv.org/abs/2510.26995 · HTML: https://mlsanity.com/paper/2510.26995/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 6 references that are in the map.
- First posted on arXiv 30 Oct 2025.

## Builds on (most cited first, 2 of 2)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Benchmarking LLMs' Mathematical Reasoning with Unseen Random Variables Questions](https://mlsanity.com/paper/2501.11790/) (2025)

## Built on by (most cited first, 8 of 8)

- [CausalDS: Benchmarking Causal Reasoning in Data-Science Agents](https://mlsanity.com/paper/2607.08093/) (2026)
- [Allocate Marginal Reviews to Borderline Papers Using LLM Comparative Ranking](https://mlsanity.com/paper/2602.06078/) (2026)
- [SCATR: Simple Calibrated Test-Time Ranking](https://mlsanity.com/paper/2604.16535/) (2026)
- [Domain-Filtered Knowledge Graphs from Sparse Autoencoder Features](https://mlsanity.com/paper/2604.23829/) (2026)
- [Full Conformal Prediction under Stochastic Non-Conformity Measure](https://mlsanity.com/paper/2606.28730/) (2026)
- [Can VLMs Reliably Assess Sidewalk Accessibility Attributes from Pedestrian-Level Imagery?](https://mlsanity.com/paper/2609.17882/) (2026)
- [Multi-agent Scaling Across Disjunctive and Compensatory Tasks](https://mlsanity.com/paper/2609.31563/) (2026)
- [Jailbreaks for Black-Box Uncertainty Quantification in Large Reasoning Models](https://mlsanity.com/paper/2609.35350/) (2026)

## Abstract (arXiv)

Large language models (LLMs) excel at numerical estimation but struggle to correctly quantify uncertainty. We study how well LLMs construct confidence intervals around their own answers and find that they are systematically overconfident. To evaluate this behavior, we introduce FermiEval, a benchmark of Fermi-style estimation questions with a rigorous scoring rule for confidence interval coverage and sharpness. Across several modern models, nominal 99% intervals cover the true answer only 65% of the time on average. With a conformal prediction based approach that adjusts the intervals, we obtain accurate 99% observed coverage, and the Winkler interval score decreases by 54%. We also propose direct log-probability elicitation and quantile adjustment methods, which further reduce overconfidence at high confidence levels. Finally, we develop a perception-tunnel theory explaining why LLMs exhibit overconfidence: when reasoning under uncertainty, they act as if sampling from a truncated region of their inferred distribution, neglecting its tails.