Confidence Calibration in Large Language Models

Noam Michael; Daniel BenShushan; Jacob Bien; Don A. Moore

cs.AIApr 3, 2026

Confidence Calibration in Large Language Models

Authors: Noam Michael, Daniel BenShushan, Jacob Bien, Don A. Moore

Organizations: U.C. Berkeley · University of Southern California

Abstract

We investigate the calibration of large language models' (LLMs') confidence across diverse tasks. The results of our preregistered study show that the current crop of LLMs are, like people, too sure they are right: confidence exceeds accuracy, on average. Importantly, however, this tendency is moderated by a powerful hard-easy effect, wherein overconfidence is greatest on difficult tests; by contrast, easy tests actually show substantial underconfidence. We develop LifeEval, a test for evaluating model calibration across levels of difficulty.

Figures & tables

Figure 1: LifeEval, from left to right: The user provides the LLM with sex, minimum age and radius. The LLM responds with its best guess and its confidence that the actual age at death falls within that range. We score the model’s response based on its point estimate and the user’s conditions. Finally, we compare the true probability of the model’s response and the model’s stated confidence.

Question Set	Length	After Cleaning	Answer Fields	Context	Task Description
BoolQ	3270	2503	True, False	None	True or False trivia questions
SciQ	1000	995	A, B, C, D	None	Scientific trivia questions
LSAT-AR	230	86	A, B, C, D, E	Premise for logical question	Find optimal solution for complex situation
SAT-EN	206	173	A, B, C, D	Passage	Answering questions about a reading passage
HaluEval-QA	2000	1790	N/A	Short passage	Pre-generated Model responses to questions
LifeEval	808	751	Predicted age at death	Sex, Minimum Age	Estimate age at death given minimum age and sex

Table 1: The six question sets.

Model	Type	Score (%)	ECE	Conf. (%)	% Rnd	Hard-Easy	$N$
Claude-Sonnet-3.7	Reasoning	54.5	0.040	53.1	90.1	0.180	808
Claude-Sonnet-4	Reasoning	54.0	0.063	49.8	98.8	0.327	808
DeepSeek-R1	Reasoning	54.4	0.031	57.2	29.0	0.053	808
Gemini-2.5-Pro	Reasoning	53.8	0.025	53.4	18.0	0.092	808
GPT-o3	Reasoning	54.2	0.029	54.1	69.8	0.189	761
Reasoning models		54.2	0.037	53.5	61.1	0.168	751

Table 2: Performance metrics across various models on LifeEval split by model type. We report Mean Score, Expected Calibration Error (ECE), Mean Confidence, Percentage of Rounded outputs, Hard-Easy (the regression coefficient between difficulty and overconfidence), and number of completions (

N

). LifeEval has a mean Maximum Achievable Score (MAS) of 56.80%. We ran a regression comparing Overconfidence and question difficulty

(1-MAS_{question})

. A higher regression coefficient implies an increased Hard-Easy effect. Aggregate rows average within column, except for

N

which is the size of the subset of questions answered by all models (Reasoning & Chat). Score (%) is the mean score for each model on LifeEval . Our formula for question level scoring can be seen in Eq. 3

Figure 2: Aggregate calibration plots for each question set, showing accuracy conditional on confidence. Reasoning models in red and Non-Reasoning in black. Observations are averaged within confidence bins, [0,0.1),[0.1,0.2)…[0.9,1),[1].

Figure 3: Overconfidence by question set and Model.

Figure 4: Overconfidence as a function of model and radius; difficulty decreases with larger accuracy radius.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: LifeEval allows for the monotonic decrease in task difficulty given age, sex, and radius. As the Maximum Achievable Score (MAS) increases, the task difficulty decreases.

Figure 6: Best age to guess as a function of minimum age, sex, and radii. We see that the optimal age is constant until a certain minimum age is reached. Additionally, we see Female’s have slightly higher overall life expectancy.

Figure 7: Comparison between the calibration error of stated confidence versus token probability for models when available. In most cases, Stated ECE was lower than Token ECE. Given the nature of HaluEval, we did not get token probabilities from the models. Because of this, HaluEval is left out from this analysis.

Verdict	Count	%	Description
no_evidence	4,188	50.7	General demographic knowledge only
weak_evidence	2,225	26.9	Some specificity suggesting possible exposure
strong_evidence	1,846	22.3	Clear use of specific actuarial values

Appendix

Table 3: Distribution of LLM judge verdicts across all 8,261 LifeEval responses.

Model	no_evidence	weak_evidence	strong_evidence	Strong %
Claude Haiku 3	731	20	0	0.0
GPT-4o	706	45	0	0.0
Claude-Sonnet-3.7	692	58	1	0.1
Claude-Sonnet-4	483	266	2	0.3
DeepSeek-V3	709	37	5	0.7
Llama-3.1-70B	238	457	56	7.5

Appendix

Table 4: Distribution of contamination verdicts per model across all 751 LifeEval questions.

Figure 8: Overconfidence as a function of model and radius; difficulty decreases with larger accuracy radius. Specifically on the no_evidence subset.

Model	Type	Score (%)	ECE	Conf. (%)	% Rnd	Regression Coef.	$N$
Claude-Sonnet-3.7	Reasoning	54.3	0.037	52.7	91.9	0.177	692
Claude-Sonnet-4	Reasoning	46.4	0.071	47.3	98.6	0.264	483
DeepSeek-R1	Reasoning	46.7	0.034	47.7	44.4	0.053	45
Gemini-2.5-Pro	Reasoning	42.9	0.029	42.9	25.7	0.080	35
GPT-o3	Reasoning	42.1	0.050	45.7	77.8	0.412	36
Aggregate		46.5	0.044	47.2	67.7	0.197	3

Appendix

Table 5: Performance metrics on the LifeEval no_evidence subset (rows where the LLM judge found no evidence of SSA table memorization). Aggregate rows take mean of all columns except for

N

which is the number of questions where every model in the group received a no_evidence verdict.

Figure 9: Side by side plots of all models (rows) and all question sets (columns). GPT-4o, Llama-3.1-70B, and Llama-3.1-8B all display their token probabilities in red.

Figure 10: Each plot displays the relationship between Stated Confidence and actual Score for various model families. Each scatter plot illustrates how accurately a given family of models estimates their own performance to their true score. The prevalence of horizontal lines show the tendency for certain models to round their probability estimates.

Panel of Figure 11 — Figure 11: Accuracy for each model on all question sets. SAT-EN and SciQ had the highest performance while LSAT-AR saw the biggest variation between models.

		Claude-Sonnet-3.7	Claude-Sonnet-4	DeepSeek-R1	GPT-o3	Gemini-2.5-Pro
Question Set	Metrics
BoolQ	Accuracy	83.14	84.30	84.50	86.06	84.90
	Confidence	95.57	91.97	95.61	82.59	99.35
	ECE	0.12	0.08	0.11	0.04	0.15
	(%) Rounded	46.06	96.20	68.08	50.38	73.95
HaluEval	Accuracy	52.12	52.12	52.12	52.12	52.12

Appendix

Table 6: Performance of reasoning models across all question sets.

Provider	Google	OpenAI	Anthropic	Lambda	DeepSeek	Total
Spend (USD)	228.59	234.17	94.53	941.78	$7.41^{*}$	1,506.48

Appendix

Table 8: Total spend by provider. New users on Google’s platform receive

\

300

in compute credits which we did not surpass. Lambda generously provided us with a

$5,000$ research grant to cover our compute costs on their services. We ran both Llama models using one NVIDIA H100 GPU over a combined 283 hours. Recording token distributions for later analysis significantly slowed down TPS. We suggest avoiding this when replicating our results. We did not keep track of our total spend on DeepSeek but we estimate the price based on publicly available pricing and our input and output token counts.

Model	Publisher	Type	Model Card
Claude Haiku 3	Anthropic	Chat	Model Card
Claude Sonnet 3.7	Anthropic	Reasoning	Model Card
Claude Sonnet 4	Anthropic	Reasoning	Model Card
DeepSeek V3	DeepSeek	Chat	Model Card
DeepSeek R1	DeepSeek	Reasoning	Model Card
Gemini 2.5 Flash	Google	Chat	Model Card

Appendix

Table 9: Information about each model used.

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Language model calibration studies whether models’ confidence estimates match their actual accuracy across tasks, prompts, and deployment settings.

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Accurate confidence estimation is critical for reliable use of large language models (LLMs). Prior work on LLM calibration largely focuses on response-level confidence, which estimates the correctness of a single generated output. However, this formulation is misaligned with many practical settings where the central question is how likely a model is to solve a query overall. We show that this mismatch results from the stochastic nature of modern LLM decoding, under which single-response correctness fails to reflect underlying model capability. To address this issue, we introduce capability calibration, a new evaluation framework for measuring how well query-level confidence aligns with a model's expected accuracy on individual queries. We formally distinguish capability calibration (CC) from response calibration (RC) and show that the two differ both theoretically and empirically. We further show that CC is better suited than RC to applications like pass@k prediction and inference budget allocation. Finally, we evaluate common confidence estimation methods to understand the practical feasibility of CC.

Abstract

Language Model Calibration

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