The Illusion of AI Expertise Under Uncertainty: A Probabilistic Paradigm to Interpret Results Under Ground Truth Variation

Aparna Elangovan; Lei Xu; Mahsa Elyasi; Ismail Akdulum; Mehmet Aksakal; Enes Gurun; Brian Hur; Saab Mansour

cs.AIJan 9, 2026

The Illusion of AI Expertise Under Uncertainty: A Probabilistic Paradigm to Interpret Results Under Ground Truth Variation

Authors: Aparna Elangovan, Lei Xu, Mahsa Elyasi, Ismail Akdulum, Mehmet Aksakal, Enes Gurun, Brian Hur, Saab Mansour,

Organizations: Independent Researcher · Amazon · Gazi University · University of Colorado ·

Abstract

Benchmarking the capabilities of AI systems, including Large Language Models (LLMs) and Vision Models, typically ignores the impact of uncertainty in the underlying ground truth answers from experts. This ambiguity is not just limited to human preferences, but is also consequential even in safety critical domains such as medicine where uncertainty is pervasive. In this paper, we introduce a probabilistic paradigm to theoretically explain how high certainty in ground truth answers is almost always necessary for even an expert to achieve high scores. In contrast, in datasets with high variation in ground truth answers, the expert performance drops substantially resulting in almost no difference between a random labeller and an expert. This characteristic also manifests when comparing models, where uncertainty obfuscates differences between poor and high performing models. Therefore, ignoring uncertainty in ground truth evaluation data can result in the misleading conclusion that a non-expert has similar performance to that of an expert. Given ground truth answer variability and commonly used F1 and accuracy metrics, we bring forth a simple and explainable probabilistic coin toss model to estimate expected accuracyand expected F1 and compare the estimated scores with those that experts (human or model) achieve across multiple domains -- including radiology and models such as GPT-5 and Gemini-3. The results lead to the recommendation that stratification by the probability of the ground truth answer becomes critical when expert performance is relatively low. Under stratified evaluation, performance comparison becomes more reliable in high certainty bins, mitigating the effect of the key confounding factor --- uncertainty.

Figures & tables

	$N=100$		$N=10$
$p_{d}$	$r_{c}$	$P(Score>=r_{c})$	$r_{c}$	$P(Accurcy>=r_{c})$
$p_{d}=p_{r}=0.25$	Random labeller baseline for 4 classes
0.25	50	6.6e-8	5	0.08
0.25	80	1.2e-30	8	0.00
$p_{d}=p_{r}=0.5$	Random labeller baseline for 2 classes
0.5	50	0.54	5	0.62

Table 1: Examples of how given probability

p_{d}

of following the majority label, the corresponding probability of scores over 50% or 80% accuracy changes out of

N

100 vs. 10 examples.

$p_{d}$ (Expected Recall)	$m$	Expected Precision	Expected F1
$p_{d}=p_{r}=0.5$	Random labeller baseline for 2 classes
0.5	0.01	0.01	0.02
0.5	0.10	0.10	0.17
0.5	0.50	0.50	0.50
0.6	0.01	0.01	0.03
0.6	0.10	0.14	0.23

Table 2: Examples showing how given probability

p_{d}

following the majority label, the positive class ratio

m

, the expected precision and F1 increases with increasing

m

Figure 1: Simulated impact of agreement for the majority label (X axis). Y axis is the performance of a simulated human (H) who follows the majority label distribution (

p_{d}

) vs. the random labeler (R) performance across different positive label ratios

m\in{0.1,0.3,0.5}

. At low certainty, the difference between human labeler and random labeler is relatively low compared to high certainty. Recall and Accuracy are unaffected by the positive label ratio. The vertical bars indicate standard deviation.

Panel of Figure 2 — Figure 2: Comparison of theoretical vs. empirical performance of Models ( M ) and human ( H ) radiologists, compared against ground truth (majority label across 5 human radiologists). H is the average performance of additional 3 radiologists. Dashed lines are theoretical expected performance at given $p_{d}$ and $m$ according to equations 2 and 14 . Theoretical performance closely matches human expert performance ( $p_{d}\rightarrow 1.0$ is approximated as $p_{d}=0.97$ ). Humans achieve a relatively high F1-score ( $>0.8$ ) as $p_{d}\rightarrow 1.0$ , whereas $p_{d}\rightarrow 0.6$ the peak performance drops close to a random labeller baseline. At low positive class ratio ( $m<0.01$ ), even at $p_{d}\rightarrow 1.0$ (see Pneumonia and Consolidation), F1 is $<0.35$ . $\Delta=H-M$ is the vertical distance illustrated by the length of the vertical line connecting the human and the model performance. See Appendix Tables 8 and 11 for detailed results with sample size. Similar results for Gemini-2.5 & Gemini-3.1 are in Appendix Figure 10 and Tables 10 9 .

$\|GT\|=5,\|L\|$ =2				F1						Accuracy
Pathology	$p_{d}$	S	$m$	AI	H	$E$	$\Delta_{\text{H}-AI}$	$\Delta_{E-\text{H}}$	$\Delta_{E-M}$	AI	H	$E$	$\Delta_{\text{H}-AI}$	$\Delta_{E-\text{H}}$	$\Delta_{E-M}$
Gemini-3.0 Preview
Cardio- megaly	0.60	142	0.507	0.67	0.64 $\pm$ 0.10	0.60	-0.03	-0.04	-0.07	0.63	0.66 $\pm$ 0.03	0.60	0.03	-0.06	-0.03
	0.80	196	0.372	0.69	0.71 $\pm$ 0.04	0.75	0.02	0.04	0.06	0.72	0.79 $\pm$ 0.03	0.80	0.07	0.01	0.08
	1.00	162	0.037	0.35	0.70 $\pm$ 0.12	0.71	0.35	0.01	0.36	0.91	0.98 $\pm$ 0.02	0.97	0.07	-0.01	0.06
	All	500	0.302	0.66	0.68 $\pm$ 0.07	0.68	0.02	0.00	0.02	0.75	0.81 $\pm$ 0.03	0.80	0.06	-0.01	0.05

Table 3: Examples of models ( M ) Gemini-3.0 and GPT-5.1 performance variation when stratified by

p_{d}

compared to average human ( H ) performance of 3 radiologists and the corresponding standard deviation, sample size S . For Lung Opacity, the overall (

p_{d}=All

) performance is over 80%, and even at stratified

p_{d}

, the models achieves reasonable F1 and accuracy scores compared to humans. On the other hand, for Cardiomegaly and Support Devices the overall (

p_{d}=All

) performance falls below 80% and and Gemini even achieves a

\Delta=H-M

of just 2 points for Cardiomegaly, however as

p_{d}\rightarrow 1

, the

\Delta

is over 20 points. Expected ( E ) performance given

\langle p_{d},m\rangle

per equations 2 and 14 (note:

p_{d}\rightarrow 1.0

is approximated as

p_{d}=0.97

). Scores (Model or Human) over 0.80 are highlighted and they all occur at

p_{d}\in{0.8,1.0}

but never at

0.60

. Full results in Appendix Tables 8 , and 11 .

Panel of Figure 3 — Figure 3: (Left and Mid) Distribution of difference in Human vs. Model $\Delta=H-M$ : Each point $\Delta_{i,o,p_{d}}=H_{o,p_{d}}-M_{i,o,p_{d}}$ where $i\in\{\text{Gemini-3.1},\text{Gemini-3.0},\text{Gemini-2.5},\text{GPT-5.1}\}$ , $p_{d}\in\{0.6,0.8,1.0,\text{All}\}$ , $o\in\text{Pathologies}$ . $H_{o,p_{d}}$ is the human score (F1 or accuracy) against the pathology $o$ at $p_{d}$ . Similarly, $M_{i,o,p_{d}}$ is the performance of the model $i$ against the pathology $o$ at $p_{d}$ . Average $\Delta$ is generally higher as $p_{d}\rightarrow 1.0$ compared to $p_{d}\rightarrow 0.6$ where $\Delta$ F1 is close to zero. (Right) Distribution of absolute model accuracy: All 4 model accuracies (agnostic of $m$ ) across different $p_{d}$ . Empirical vs. (expected) mean annotated in text. Note: Significance Welch t-test for means ( $H_{0}$ Null hypothesis: there is no difference between the means) and Levene’s test (trimmed, proportion to cut=0.1) for variance ( $H_{0}$ : there is no difference in variance): **** ( $p<=0.0001$ ), *** ( $p<=0.001$ ), ** ( $p<=0.01$ ), * ( $p<=0.05$ ), ns (not significant). Blue : Indicates significance of variance.

$\|GT\|\in\langle 2,3\rangle$ , $\|L\|$ =2			F1						Accuracy (A)
$p_{d}$	S	$m$	AI	$\text{H}^{\prime}$	$E$	$\Delta_{\text{H}^{\prime}-AI}$	$\Delta_{E-\text{H}^{\prime}}$	$\Delta_{E-M}$	AI	$\text{H}^{\prime}$	$E$	$\Delta_{\text{H}^{\prime}-AI}$	$\Delta_{E-\text{H}^{\prime}}$	$\Delta_{E-M}$
0.67	15834	0.229	0.39	0.48 $\pm$ 0.0045	0.48	0.09	0.00	0.09	0.42	0.67 $\pm$ 0.0045	0.67	0.25	0.00	0.25
1.00	185245	0.029	0.11	1.00 $\pm$ 0.0000	1.00	0.89	-0.00	0.89	0.58	1.00 $\pm$ 0.0000	1.00	0.42	0.00	0.42
ALL	201079	0.045	0.15	0.75 $\pm$ 0.0000	0.75	0.60	-0.00	0.60	0.56	0.97 $\pm$ 0.0000	0.97	0.41	0.00	0.41

Table 4: Stratified performance on existing public results [ 5 ] on Mammogram. S is the sample size,

\text{H}^{\prime}

is simulated human performance based on GT distribution and hence matches expected performance.

\Delta_{E-M}

narrows as certainty lowers as shown when

p_{d}\rightarrow 0.67

compared to

p_{d}\rightarrow 1.0

Panel of Figure 4 — Figure 4: Model-2-Model comparison: Left and Mid: Strong (SM) vs. weak model (WM) : The mean of $\Delta_{SM-WM}$ is less than zero at $p_{d}\rightarrow 0.6$ , indicating that the weaker model is better than the stronger model, demonstrating the unreliability of comparison when ground truth is not certain. At $p_{d}\rightarrow 1.0$ , $\Delta_{SM-WM}$ of stronger model is higher than zero. Right: Comparison of 2 SMs: $p_{d}\rightarrow 1.0$ shows that there is only marginal difference between two models but $p_{d}\rightarrow 0.6$ is not a clear indicator as it is not any different to weak vs. strong model comparison. Paired Student’s T-test for statistical significance ( $H_{0}$ : No difference in performance between a pair of models). Note: Improvements may be marginal between models, hence not statistically significant.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Proportion of samples (CheXpert test set with 500 samples) by agreement level as annotated by 5 radiologists independently. The number of samples with 100% agreement ( $p_{d}=1.0$ ) on positive findings drops dramatically to less than 0.01 for 4 of 5 the pathologies. The exception is lung opacity, where the proportion of samples approximately remains the same regardless of agreement levels. Agreement level for all pathologies are in Appendix 6 .

Figure 6: Chest x ray agreement for binary classification across 13 labels. The agreement is across 5 radiologists. The x-axis shows the percentage agreement for the majority label ( yes/ no) and the corresponding y-axis indicate the total number of records with that agreement. For instance, for Atelectasis, 100% agreement ( 5 out of 5 radiologists) is observed for 32 records for a positive finding (yes), while 100% agreement for negative finding for 200 records.

Figure 7: MNLI Matched, MNLI Mismatched and SNLI performance (Accuracy) distribution by $p_{d}$ on 4 models - Mistral, Mistral Large, Sonnet and Llama 3.1. These are existing results from Elangovan et. al. [ 8 ] . The variation in scores is low when $p_{d}\rightarrow 0.6$ compared to $p_{d}\rightarrow 1.0$ , as demonstrated by the statistical significance using Levene’s test for variance. This shows the lack of differentiating capability between strong vs. weak models when $p_{d}\rightarrow 0.6$ . The mean performance at $p_{d}\rightarrow 1.0$ is also higher (statistically significant using Welch’s t-test) compared to $p_{d}\rightarrow 0.6$ Detailed tabular results are available in Table 5 .

Dataset	$p_{d}$	S	$E(A)$	$\text{H}^{\prime}$	$\Delta_{E\text{H}^{\prime}}$	Model	A	$\Delta_{EM}$
MNLI M $\langle$ GT = 5, L=3 $\rangle$	0.60	1599	0.60	0.61 $\pm$ 0.02	-0.01	Llama3.1	0.55	0.05
						Mistral	0.50	0.10
						Mistral-L	0.59	0.01
						Sonnet	0.61	-0.01
	0.80	2457	0.80	0.81 $\pm$ 0.01	-0.01	Llama3.1	0.68	0.12
						Mistral	0.63	0.17

Appendix

Table 5: Expected accuracy ( A ) vs empirical accuracy. Here M is the existing result on Models by Elangovan et al [ 8 ] . GT is the number of ground truth annotations and

L

is the number of labels. H ’ is the simulated performance of another Human.

\Delta_{EM}=E(A)-M

\Delta_{E\text{H}^{\prime}}=E(A)-\text{H}^{\prime}

. † Only 7 samples (in

p_{d}\rightarrow 0.75

) have 4 annotations in the SNLI dataset, the rest have 5.

Figure 8: Difference in expected vs. actual model performance of G-Eval original results [ 22 ] for 4 criteria - Coherence, relevance, consistency and fluency. Ground truth is the majority label. Model performance is the most frequent label from the model. $\Delta_{EM}$ is close to zero $p_{d}\rightarrow 0.33$ , the gap between expected and the model’s substantially lower performance becomes apparent as $p_{d}\rightarrow 1.0$ . Detailed tabular performance in Appendix Table 6 . Examples of differences between G-Eval and human experts are shown in Appendix Table 7 . Paired (expected vs. actual) T-test for significance.

Criteria	$p_{d}$	$S$	E(A)	Score	$\Delta_{EM}$
Coherence $\langle GT$ =3, L=5 $\rangle$	0.33	341	0.33	0.185	0.145
	0.67	1059	0.67	0.291	0.379
	1.00	200	1.00	0.165	0.835
Consistency $\langle GT$ =3, L=5 $\rangle$	0.33	19	0.33	0.368	-0.038
	0.67	241	0.67	0.241	0.429
	1.00	1340	1.00	0.305	0.695

Appendix

Table 6: Accuracy of GEval: Model performance is the most frequent label from the model. Human ground truth is also the majority label.

\Delta_{EM}

narrows down the most as

p_{d}\rightarrow 0.33

Id	ModelId	$p_{d}$	Experts	Model
dm-test-9b5a04b9879fe716a2dcd66dd331f99534603c16	M22	1.00	[5, 5, 5]	[’ 4’, ’ 4’, ’ 3’, ’ 4’, ’ 3’, ’ 4’, ’ 3’, ’ 4’, ’ 3’, ’ 4’, ’ 4’, ’ 3’, ’ 4’, ’ 4’, ’ 4’, ’ 4’, ’ 3’, ’ 3’, ’ 3’, ’ 4’]
dm-test-9beaaf73e4517d5bf1bc284f386485d571da96cf	M15	1.00	[5, 5, 5]	[’ 3’, ’ 3’, ’ 2’, ’ 3’, ’ 4’, ’ 3’, ’ 3’, ’ 3’, ’ 2’, ’ 3’, ’ 3’, ’ 3’, ’ 3’, ’ 3’, ’ 3’, ’ 3’, ’ 3’, ’ 4’, ’ 3’, ’ 3’]
dm-test-b255397ee863bd8faf9def57c0f76769153d905e	M9	1.00	[3, 3, 3]	[’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’, ’ 2’]

Appendix

Table 7: Examples of differences at GEval vs Human experts for coherence.

Panel of Figure 9 — Figure 9: Model-2-Model accuracy comparison: Paired Student’s T-test to measure the statistical significance where the null hypothesis ( $H_{o}$ )is there is no difference between the pair of models. Significance: * ( $p<=0.05$ ), ns (not significant). Left and Mid : Comparison of strong and weak model: Right : Comparison of 2 strong models.

				F1						Accuracy
Pathology	$p_{d}$	S	$m$	AI	H	$E$	$\Delta_{\text{H}-AI}$	$\Delta_{E-\text{H}}$	$\Delta_{E-M}$	AI	H	$E$	$\Delta_{\text{H}-AI}$	$\Delta_{E-\text{H}}$	$\Delta_{E-M}$
Atelectasis	0.60	130	0.500	0.57	0.66 $\pm$ 0.03	0.60	0.09	-0.06	0.03	0.53	0.60 $\pm$ 0.02	0.60	0.07	-0.00	0.07
	0.80	140	0.400	0.63	0.70 $\pm$ 0.03	0.76	0.07	0.06	0.13	0.67	0.73 $\pm$ 0.03	0.80	0.06	0.07	0.13
	1.00	230	0.139	0.67	0.74 $\pm$ 0.03	0.90	0.07	0.16	0.23	0.88	0.91 $\pm$ 0.02	0.97	0.03	0.06	0.09
	All	500	0.306	0.62	0.69 $\pm$ 0.02	0.73	0.07	0.04	0.11	0.73	0.78 $\pm$ 0.02	0.83	0.05	0.05	0.10
Cardio- megaly	0.60	142	0.507	0.67	0.64 $\pm$ 0.10	0.60	-0.03	-0.04	-0.07	0.63	0.66 $\pm$ 0.03	0.60	0.03	-0.06	-0.03

Appendix

Table 8: Performance of Gemini Pro 3.0 Preview ( GP ) model vs. human ( H ) radiologists, compared against ground truth (majority label across 5 human radiologists). The data is stratified by

p_{d}

probability of observed agreement among the 5 radiologists for the majority label. Size (S) is the number of samples corresponding to that

p_{d}

, positive class ratio is

m

. H is the average performance of additional 3 radiologists and the corresponding standard deviation. Humans achieve a peak F1-score of over 0.98 @

p_{d}=1.0

, while the best performance at

p_{d}=0.6

is 0.72 across all pathologies. Similar trend is seen for recall, precision and accuracy. At low positive class ratio (

m<0.01

), even at

p_{d}=1.0

(see Pneumonia and Consolidation), F1 is

<0.35

\Delta=H-GP

is the difference between the average of human performance and the model. All the scores (Model or Human) over 0.80 are highlighted and they all occur at

p_{d}\in{0.8,1.0}

but never at

0.60

given the sample size (

S

				F1						Accuracy
Pathology	$p_{d}$	S	$m$	AI	H	$E$	$\Delta_{\text{H}-AI}$	$\Delta_{E-\text{H}}$	$\Delta_{E-M}$	AI	H	$E$	$\Delta_{\text{H}-AI}$	$\Delta_{E-\text{H}}$	$\Delta_{E-M}$
Atelectasis	0.60	130	0.500	0.61	0.66 $\pm$ 0.03	0.60	0.05	-0.06	-0.01	0.52	0.60 $\pm$ 0.02	0.60	0.08	-0.00	0.08
	0.80	140	0.400	0.63	0.70 $\pm$ 0.03	0.76	0.07	0.06	0.13	0.63	0.73 $\pm$ 0.03	0.80	0.10	0.07	0.17
	1.00	230	0.139	0.58	0.74 $\pm$ 0.03	0.90	0.16	0.16	0.32	0.82	0.91 $\pm$ 0.02	0.97	0.09	0.06	0.15
	All	500	0.306	0.61	0.69 $\pm$ 0.02	0.73	0.08	0.04	0.12	0.69	0.78 $\pm$ 0.02	0.83	0.09	0.05	0.14
Cardio- megaly	0.60	142	0.507	0.43	0.64 $\pm$ 0.10	0.60	0.21	-0.04	0.17	0.62	0.66 $\pm$ 0.03	0.60	0.04	-0.06	-0.02

Appendix

Table 9: Performance on CheXpert using Gemini-3.1 pro

Panel of Figure 10 — Figure 10: Performance of Gemini-2.5, Gemini-3.1 ( M ) vs. human ( H ) radiologists, compared against ground truth (majority label across 5 human radiologists). H is the average performance of additional 3 radiologists who are different from the 5 radiologists used to determine the ground truth. The data is stratified by $p_{d}$ probability of observed agreement among the 5 radiologists for the majority label, corresponding positive class ratio is $m$ . Dashed lines are theoretical expected performance at given $p_{d}$ and $m$ according to equations 2 and 14 , ( $p_{d}\rightarrow 1.0$ is approximated as $p_{d}=0.97$ ). Humans are able to achieve a relatively high F1-score ( $>0.8$ ) as $p_{d}\rightarrow 1.0$ , whereas $p_{d}\rightarrow 0.6$ the peak performance drops close to a random labeller baseline. At low positive class ratio ( $m<0.01$ ), even at $p_{d}\rightarrow 1.0$ (see Pneumonia and Consolidation), F1 is $<0.35$ . $\Delta=H-M$ is the vertical distance illustrated by the length of the vertical line connecting the human and the model performance.

				F1						Accuracy
Pathology	$p_{d}$	S	$m$	AI	$\text{H}^{\prime}$	$E$	$\Delta_{\text{H}-AI}$	$\Delta_{E-\text{H}}$	$\Delta_{E-M}$	AI	H	$E$	$\Delta_{\text{H}-AI}$	$\Delta_{E-\text{H}}$	$\Delta_{E-M}$
Atelectasis	0.60	130	0.500	0.65	0.66 $\pm$ 0.03	0.60	0.01	-0.06	-0.05	0.52	0.60 $\pm$ 0.02	0.60	0.08	-0.00	0.08
	0.80	140	0.400	0.62	0.70 $\pm$ 0.03	0.76	0.08	0.06	0.14	0.53	0.73 $\pm$ 0.03	0.80	0.20	0.07	0.27
	1.00	230	0.139	0.40	0.74 $\pm$ 0.03	0.90	0.34	0.16	0.50	0.60	0.91 $\pm$ 0.02	0.97	0.31	0.06	0.37
	All	500	0.306	0.56	0.69 $\pm$ 0.02	0.73	0.13	0.04	0.17	0.56	0.78 $\pm$ 0.02	0.83	0.22	0.05	0.27
Cardio- megaly	0.60	142	0.507	0.69	0.64 $\pm$ 0.10	0.60	-0.05	-0.04	-0.09	0.56	0.66 $\pm$ 0.03	0.60	0.10	-0.06	0.04

Appendix

Table 10: Performance on CheXpert using Gemini-2.5 pro

				F1						Accuracy
Pathology	$p_{d}$	S	$m$	AI	H	$E$	$\Delta_{\text{H}-AI}$	$\Delta_{E-\text{H}}$	$\Delta_{E-M}$	AI	H	$E$	$\Delta_{\text{H}-AI}$	$\Delta_{E-\text{H}}$	$\Delta_{E-M}$
Atelectasis	0.60	130	0.500	0.49	0.66 $\pm$ 0.03	0.60	0.17	-0.06	0.11	0.54	0.60 $\pm$ 0.02	0.60	0.06	-0.00	0.06
	0.80	140	0.400	0.64	0.70 $\pm$ 0.03	0.76	0.06	0.06	0.12	0.74	0.73 $\pm$ 0.03	0.80	-0.01	0.07	0.06
	1.00	230	0.139	0.70	0.74 $\pm$ 0.03	0.90	0.04	0.16	0.20	0.93	0.91 $\pm$ 0.02	0.97	-0.02	0.06	0.04
	All	500	0.306	0.59	0.69 $\pm$ 0.02	0.73	0.10	0.04	0.14	0.77	0.78 $\pm$ 0.02	0.83	0.01	0.05	0.06
Cardio- megaly	0.60	142	0.507	0.59	0.64 $\pm$ 0.10	0.60	0.05	-0.04	0.01	0.56	0.66 $\pm$ 0.03	0.60	0.10	-0.06	0.04

Appendix

Table 11: Performance of GPT-5.1 on CheXpert

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Decomposing LLM-Judge Uncertainty to Target Expert Labels

Ryan Lail

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Annotator Disagreement LLM-as-a-Judge Uncertainty Quantification Human-in-the-Loop Annotation LLM Uncertainty Estimation Aleatoric Uncertainty+2

Open paper AskPDF arXiv

An LLM judge evaluates outputs at scale. Experts should label only where it is least sure. Its natural escalation signal conflates two uncertainties: aleatoric, real disagreement in the expert pool, which labels cannot reduce, and epistemic, the judge's ignorance, which labels do reduce. A small Bayesian model separates them: a regression on labels already collected learns how far to trust a black-box judge's prediction. Both components follow as simple formulas, with no sampling or further judge calls. The components isolate on a real LLM judge against exactly known truth, and stated confidence is no guide to its actual error. On real human disagreement (ChaosNLI) the epistemic ranking removes 83% more error than total uncertainty for the same expert labels, though simply escalating the least-labelled items does as well there. We demonstrate we can estimate where a judge is ignorant rather than where experts genuinely disagree, and propose using this to direct expert labelling. Code and data are available at https://github.com/composo-ai/judge-uncertainty-decomposition.

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