The Score Granularity Gap in Black-Box LLM Classification: A Comparative Study of Confidence Constructions

Abstract: LLMs are increasingly deployed as black-box classifiers in pipelines that automate confident decisions and route uncertain ones to human review. Such selective prediction needs a confidence score that an operator can threshold at a chosen risk level. Prior work asks whether LLM confidence is well calibrated or well ranked; we ask a complementary, deployment-oriented question that has been largely overlooked: at what resolution can the score be thresholded? We call the answer the score granularity gap. Through a controlled comparison of seven ways to build a confidence score, from a single verbalized number, to token probabilities, to querying the model many times and combining the answers, across 25 model-dataset pairs (9 LLMs, 3 benchmarks), we find that single-shot verbalized confidence, once correctly converted to a class probability, ranks cases surprisingly well, yet takes only a handful of distinct values. It therefore offers an operator only a few coarse thresholds, no matter how well it ranks. We show which constructions widen this gap, at what inference cost, and with what effect on ranking, notably that multi-query aggregation helps weak models but can degrade already-strong ones. We translate these trade-offs into concrete deployment guidance.

• The paper shows that single-shot verbalized confidence scores provide strong ranking but remain too coarse for fine-grained thresholding.
• It demonstrates that multi-signal aggregation and calibrated token log-probabilities can improve score granularity, albeit with mixed effects on performance in strong models.
• The study underscores the need for dual evaluation of ranking and granularity to ensure reliable and transparent deployment in regulated applications.

Score Granularity in Black-Box LLM Classification: Comparative Analysis of Confidence Constructions

Problem Motivation and Scope

Selective prediction with LLMs necessitates actionable confidence scores for threshold-based automation and human review routing. Classical metrics—calibration and ranking—are insufficient for deployment when the available score is constrained to only a few distinct values. The core issue addressed is the score granularity gap: even well-ranking LLM confidence scores may not permit fine-grained operational control due to their coarse score distributions. Binary classification on English datasets (BoolQ, MNLI, PubMedQA) and nine LLMs is selected to isolate the problem in its simplest form.

Confidence Score Construction and Granularity Metrics

The study systematically compares seven constructions for confidence scores:

• Single-shot: Direct verbalized confidence converted to class probability ("Verb"), token log-probabilities ("Verb-logprob"), and calibrated variants.
• Multi-signal: Aggregation of m=10 interpretable sub-task scores or m=10 paraphrased prompt confidences, combined by naïve averaging or learned logistic regression, optionally calibrated.

Crucial granularity metrics used for evaluation:

• G(f): Number of distinct score values (operating-point bound).
• H(f): Score entropy, quantifying distribution spread.
• M(f): Interior mass, fraction of scores away from extremes (0 and 1).

These metrics determine whether a score is thresholdable in practical deployment beyond just its ranking or calibration properties.

Empirical Findings: Ranking and Resolution Decoupling

Verbalized confidence, after conversion to class probability, achieves strong ranking (mean normalized PR-AUCN=0.80 across pairs), but is almost always too coarse for deployment. On average, Verb yields only 1–21 distinct score values (mean=9), with 45% of test cases sharing a single most common score. Entropy and interior mass are also low (H=1.2 nats, M=17%), confirming the staircase effect on the risk-coverage curve. Thus, operators are limited to a handful of thresholds, impeding fine coverage-risk control.

Multi-query aggregation (both sub-task and paraphrase ensembles) consistently expands resolution (mean G=138, H=2.8, M~45%) but improves ranking selectively, mainly for weaker models. For strong models (≥90% accuracy), aggregated scores can degrade global risk-coverage (AURC), driven by perturbations in already-well-separated confidence assignments.

Token log-probabilities, where available, are a favorable intermediate: calibration spreads scores efficiently, maintaining ranking and covering interior operating points. However, most commercial APIs do not expose token probabilities.

Attempts to synthetically increase score resolution by prompting for more decimals fail: yielded digits are noise, degrading ranking across all tested pairs.

Aggregation Mechanisms: Calibration, Averaging, and Learning

Ablation analysis confirms naïve averaging collapses performance on polarity-conflicted probe sets (e.g., MNLI, average PR-AUC .462), while learned logistic regression recovers signal (PR-AUC .912). Even manual polarity alignment is insufficient—regression is necessary for weighting conflicting, heterogeneous signals. Individual sub-tasks are weak classifiers, and only aggregation via learned weights achieves robust scores.

Calibration applied to regression outputs never changes ranking, only improves calibration and thresholdability, further supporting its orthogonal utility.

Interpretability and Deployment Properties

The interpretable sub-task variant, though not superior in ranking to the paraphrased ensemble, provides essential deployment properties: weight transparency, error attribution, and audit trails. These are necessary in regulated domains (medical triage, content moderation) for operational transparency. Failure modes of decomposition are made visible by auditability, unlike silent errors in paraphrased aggregation.

Practical Recommendations for Deployment

Deployment guidance emerges directly from empirical findings:

1. Always convert verbalized confidence to class probability.
2. If log-probabilities are available, calibrate for interior thresholds; otherwise, use multi-query aggregation for weak models (<85% accuracy).
3. For strong models (≥90% accuracy), Verb suffices unless fine control is explicitly required—aggregation may degrade performance.
4. For interpretability requirements, prefer the sub-task variant, accepting increased inference cost (10x) for operational transparency.

Reporting should include both ranking and granularity axes; a method with perfect ranking but few thresholds is not deployment-ready.

Implications and Future Directions

Theoretically, the score granularity gap mandates a shift in evaluation protocols: beyond calibration and ranking, thresholdability and operating-point count/distribution must be considered. Practically, the study demonstrates that increased model strength does not mitigate the granularity gap; strong models still yield coarse scores under black-box constraints. Efforts to manufacture granularity without semantic diversity are counterproductive.

Open questions remain for granular score construction in multi-class, heavily imbalanced, and generative settings, as well as multilingual contexts. Deep ensemble, semantic-entropy, and conformal wrappers warrant direct benchmarking. API design for token-probabilities and improved score aggregation mechanisms may enable better trade-offs in deployment scenarios.

Conclusion

This work formalizes and operationalizes the score granularity gap as a critical constraint for black-box LLM deployment in selective prediction, distinct from classical confidence ranking and calibration. Single-shot verbalized confidence is inherently coarse regardless of ranking quality; multi-signal aggregation and calibrated token-probabilities offer improved resolution but impose inference or API costs. Interpretation is essential for regulated deployment, and trade-off reporting across ranking and resolution is required for rigorous confidence score evaluation in future AI systems (2606.22179).