LLMs Exhibit Significantly Lower Uncertainty in Creative Writing Than Professional Writers

Peiqi Sui

cs.CLFeb 18, 2026

LLMs Exhibit Significantly Lower Uncertainty in Creative Writing Than Professional Writers

Authors: Peiqi Sui

Organizations: Department of English, McGill University

Abstract

We argue that uncertainty is a key and understudied limitation of LLMs' performance in creative writing, which is often characterized as trite and cliché-ridden. Literary theory identifies uncertainty as a necessary condition for creative expression, while current alignment strategies steer models away from uncertain outputs to ensure factuality and reduce hallucination. We formalize this tension by quantifying the ``uncertainty gap'' between human-authored stories and model-generated continuations. Through a controlled information-theoretic analysis of 28 LLMs on high-quality storytelling datasets, we demonstrate that human writing consistently exhibits significantly higher uncertainty than model outputs. We find that instruction-tuned and reasoning models exacerbate this trend compared to their base counterparts; furthermore, the gap is more pronounced in creative writing than in functional domains, and shows a consistent correlation with writing quality. Achieving human-level creativity requires new uncertainty-aware alignment paradigms that can distinguish between destructive hallucinations and the constructive ambiguity required for literary richness.

Figures & tables

Figure 1: The human–model uncertainty gap. Given a cumulative prefix $T_{1}$ from a New Yorker story, we compare the author’s next sentence $T_{2}$ against a model-generated continuation $\hat{T}_{2}$ , scoring both under the same model (e.g., OLMo-3.1-32B-Instruct ). The human continuation presents a plot twist that introduces genuine tension into the story, which is reflected on all uncertainty metrics; the model instead reduces the scene to a stock quotation.

	Base				Instruct				Thinking
Model	NLL	PPL	PMI	CPMI	NLL	PPL	PMI	CPMI	NLL	PPL	PMI	CPMI
OLMo-2-7B	2.18	3.62	-1.70	0.13	3.01	5.97	-1.89	0.01
OLMo-2-13B	2.19	3.48	-1.63	0.12	2.48	4.14	-1.77	0.10
OLMo-2-32B	2.15	3.19	-1.55	0.08	2.32	3.51	-1.64	0.07
OLMo-3-7B	2.20	3.95	-1.81	0.15	3.30	7.98	-2.20	0.09	2.74	6.07	-2.17	0.11
OLMo-3-32B	2.15	3.47	-1.66	0.09	2.99	5.59	-1.68	-0.43	2.78	5.06	-1.66	-0.40

Table 1: (Top) New Yorker, (Bottom) Tell-Me-A-Story. Values reported are medians. NLL and PPL are reported as ratios (human/model); PMI and CPMI as differences (human

-

model), negative

\Delta

PMI indicates higher human uncertainty. Cell colors represent human–model gap magnitude (green = small, red = large). Instruct and thinking models exhibit significantly larger gaps than their base variants.

Domain	NLL	PPL	PMI ( $\Delta$ )	CPMI ( $\Delta$ )
Essays	3.07	6.03	$-1.71$	$-0.09$
News (Reuters)	3.31	5.91	$-1.73$	$-0.10$
Creative Writing	3.11	6.60	$\mathbf{-2.15}$	$\mathbf{-0.28}$

Table 2: Uncertainty gap by domain. Values are medians aggregated across 8 instruct models on the Ghostbuster corpus. The domain gap is very pronounced on

\Delta

PMI and

\Delta

CPMI.

Source	Metric	$\rho$	Sig.	% Linear	Sweet Spot	% Diminishing
Human	NLL	$+0.072\pm 0.049$	56%	12%	34%	9%
	PPL	$+0.072\pm 0.049$	56%	5%	0%	25%
	PMI	$-0.106\pm 0.052$	75%	44%	2%	0%
Model	NLL	$+0.109\pm 0.062$	77%	28%	31%	19%
	PPL	$+0.109\pm 0.062$	77%	9%	31%	33%
	PMI	$-0.076\pm 0.040$	69%	45%	2%	0%

Table 3: Relationship between uncertainty metrics and writing quality.

\rho

: mean Spearman correlation

\pm

std; Sig.: % of models with significant correlation in the expected direction (positive for NLL/PPL, negative for PMI;

p<0.05

); Sweet Spot: % exhibiting a significant inverted-U (quadratic) relationship with peak in range.

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

UE Metric	Higher Value Indicates	Scope
Token Entropy	More uncertainty	Token
Perplexity	More uncertainty	Sequence
PMI	More predictable by context	Sequence
CPMI	Uncertainty at key positions	Sequence

Appendix

Table 4: Summary of uncertainty metrics and their interpretation.

New Yorker

Tell-Me-A-Story

Family

Variant

\Delta

PMI

\Delta

CPMI

\Delta\text{NLL}_{\text{abs}}

\Delta S

\frac{|\Delta S|}{|\Delta\text{PMI}|}

\Delta

PMI

\Delta

CPMI

\Delta\text{NLL}_{\text{abs}}

\Delta S

\frac{|\Delta S|}{|\Delta\text{PMI}|}

Localization

OLMo-2-7B

Base

-

1.70

+0.13

+1.29

-

1.14

0.67

-

1.55

+0.04

+1.15

-

1.08

0.70

filler

OLMo-2-7B

Instruct

-

1.89

+0.01

+1.79

-

1.79

0.95

-

1.85

+0.01

+1.70

-

1.70

0.92

uniform

OLMo-2-13B

Base

-

1.63

+0.12

+1.25

-

1.11

0.68

-

1.48

+0.03

+1.11

-

1.07

0.72

filler

OLMo-2-13B

Instruct

-

1.77

+0.10

+1.42

-

1.30

0.74

-

1.69

+0.05

+1.34

-

1.27

0.75

filler

OLMo-2-32B

Base

-

1.55

+0.08

+1.16

-

1.07

0.69

-

1.45

+0.01

+1.07

-

1.04

0.72

filler

Appendix

Table 5: Decomposition of the CPMI gap for every cell of Table 1 .

\Delta\text{NLL}_{\text{abs}}

is the absolute surprisal gap (human

-

model) and

\Delta S

is the decision-point component, which sums unconditional log-probabilities only at tokens whose conditional surprisal exceeds

\tau=2

nats. Per row,

\Delta\text{CPMI}=\Delta\text{NLL}_{\text{abs}}+\Delta S

. The ratio

|\Delta S|/|\Delta\text{PMI}|

localizes the gap, and the localization tag summarizes it: filler below

{\approx}0.9

, uniform near 1, decision points above

{\approx}1.05

. The tag agrees across both datasets for all 28 cells.

	New Yorker				Tell-Me-A-Story
Source	NLL	PPL	PMI	CPMI	NLL	PPL	PMI	CPMI
Human (ground truth)	3.11	22.53	1.31	$-$ 0.24	2.78	16.08	1.52	$-$ 0.21
Qwen3-4B-Instruct	2.85	17.29	1.73	0.09	2.56	12.95	2.05	0.25
OLMo-3-7B-Instruct	3.06	21.28	1.77	0.08	2.71	15.03	2.12	0.24
Gemma-3-4B-it	2.74	15.42	1.82	0.19	2.39	10.88	2.25	0.37
Gemma-3-12B-it	2.74	15.50	1.93	0.21	2.41	11.16	2.35	0.41

Appendix

Table 6: Medians under an independent Llama-3.1-8B-Instruct evaluator. Unlike Table 1 , values are raw per-source medians rather than human/model ratios or differences; the gap is the human row minus (or over) each model row. Human NLL and PPL exceed every model on both datasets, and human PMI/CPMI fall below every model, matching the direction of Table 1 .

Dataset	Total Stories	After Filtering	Sentences	Tokens	Writers	Data Source	Availability	Memorization Risk
New Yorker	504	70	9,144	201,199	Expert, some prize-winning	The New Yorker magazine	Private	Very Low
Tell_Me_a_Story ( Huot et al., 2025 )	230	226	23,218	500,452	Professional	Story workshop	Public (requires decryption)	Low
Ghostbuster ( Verma et al., 2024 )	299	298	10,010	213,749	Lay	Reddit (r/WritingPrompts)	Public	Medium

Appendix

Table 7: Dataset Statistics

		Essays				News (Reuters)				Creative Writing
Model	Size	NLL	PPL	PMI	CPMI	NLL	PPL	PMI	CPMI	NLL	PPL	PMI	CPMI
OLMo-2-Instruct	7B	3.45	7.14	$-1.66$	0.24	3.46	6.16	$-1.69$	0.20	3.46	7.43	$-2.13$	0.01
OLMo-2-Instruct	13B	2.85	5.11	$-1.58$	0.25	2.86	4.48	$-1.59$	0.20	2.68	4.85	$-1.95$	0.08
OLMo-3-Instruct	7B	3.30	7.32	$-1.92$	0.25	3.62	8.07	$-2.25$	0.26	3.51	8.94	$-2.33$	0.05
Llama-3.1-Instruct	8B	2.15	3.79	$-2.24$	$-0.19$	2.27	3.47	$-1.99$	$-0.34$	2.17	3.95	$-3.03$	$-0.26$
Qwen3-Instruct	4B	3.25	6.60	$-1.50$	0.34	3.51	6.92	$-1.47$	0.32	3.55	8.33	$-1.63$	0.21

Appendix

Table 8: Full domain comparison results. All values are medians. NLL and PPL are ratios (human/model); PMI and CPMI are differences (human

-

model).

Model	vs. Essays (%)	vs. News (%)
OLMo-2-7B-Instruct	+28.3	+26.0
OLMo-2-13B-Instruct	+23.4	+22.6
OLMo-3-7B-Instruct	+21.4	+3.6
Llama-3.1-8B-Instruct	+35.3	+52.3
Qwen3-4B-Instruct	+8.7	+10.9
Phi-4	+12.3	+16.0

Appendix

Table 9: Relative increase in PMI gap for creative writing compared to functional domains.

Target	Comparison	Metric	Sig. in expected dir.	Median $\|r_{rb}\|$
Human–model gap	Base $\rightarrow$ Instruct	NLL	18/22	1.00
Human–model gap	Base $\rightarrow$ Instruct	PPL	20/22	1.00
Human–model gap	Base $\rightarrow$ Instruct	PMI	14/22	0.75
Human–model gap	Base $\rightarrow$ Instruct	CPMI	12/22	0.80
Human–model gap	Base $\rightarrow$ Thinking	NLL	6/6	1.00
Human–model gap	Base $\rightarrow$ Thinking	PPL	6/6	1.00

Appendix

Table 10: Number of family

\times

dataset comparisons that are both significant (Holm-corrected

p<.05

) and in the hypothesized direction, out of 22 for base to instruct and 6 for base to thinking. Expected direction: NLL/PPL ratios increase (the gap widens),

\Delta

PMI and

\Delta

CPMI become more negative, and the model’s own NLL/PPL decrease.

Family	NLL	PPL	PMI	CPMI
New Yorker
OLMo-2-7B	$2.18\!\rightarrow\!3.02$ ∗∗∗	$3.67\!\rightarrow\!6.26$ ∗∗∗	$-1.71\!\rightarrow\!-1.87$ ∗∗∗	$0.15\!\rightarrow\!0.03$ ∗∗∗
OLMo-2-13B	$2.19\!\rightarrow\!2.50$ ∗∗∗	$3.66\!\rightarrow\!4.38$ ∗∗∗	$-1.64\!\rightarrow\!-1.80$ ∗∗∗	$0.14\!\rightarrow\!0.13$
OLMo-2-32B	$2.15\!\rightarrow\!2.32$ ∗∗∗	$3.38\!\rightarrow\!3.71$ ∗∗∗	$-1.56\!\rightarrow\!-1.67$ ∗∗∗	$0.11\!\rightarrow\!0.09$
OLMo-3-7B	$2.20\!\rightarrow\!3.33$ ∗∗∗	$4.10\!\rightarrow\!8.55$ ∗∗∗	$-1.80\!\rightarrow\!-2.22$ ∗∗∗	$0.17\!\rightarrow\!0.13$ ∗∗∗
OLMo-3-32B	$2.16\!\rightarrow\!3.00$ ∗∗∗	$3.52\!\rightarrow\!5.88$ ∗∗∗	$-1.69\!\rightarrow\!-1.67$	$0.11\!\rightarrow\!-0.37$ ∗∗∗

Appendix

Table 11: Human–model gap, base to instruct. Cells show base median

\rightarrow

instruct median ; stars denote a significant two-sided change on the Holm-corrected p-value (

{}^{***}p<.001

{}^{**}p<.01

{}^{*}p<.05

; no star = not significant), and the direction is read from the two medians. NLL/PPL widen for every family except Llama-3.1-8B , which is flat, and Mistral-Small-24B , which narrows slightly.

Family	NLL	PPL	PMI	CPMI
New Yorker
OLMo-3-7B	2.20 $\rightarrow$ 2.76 ∗∗∗	4.10 $\rightarrow$ 6.19 ∗∗∗	$-$ 1.80 $\rightarrow$ $-$ 2.18 ∗∗∗	0.17 $\rightarrow$ 0.15
OLMo-3-32B	2.16 $\rightarrow$ 2.78 ∗∗∗	3.52 $\rightarrow$ 5.25 ∗∗∗	$-$ 1.69 $\rightarrow$ $-$ 1.66	0.11 $\rightarrow$ $-$ 0.36 ∗∗∗
Qwen3-4B	2.22 $\rightarrow$ 3.35 ∗∗∗	4.16 $\rightarrow$ 8.37 ∗∗∗	$-$ 1.74 $\rightarrow$ $-$ 1.56 ∗∗∗	0.20 $\rightarrow$ 0.28 ∗∗∗
Tell-Me-A-Story
OLMo-3-7B	2.15 $\rightarrow$ 2.76 ∗∗∗	3.36 $\rightarrow$ 5.15 ∗∗∗	$-$ 1.66 $\rightarrow$ $-$ 2.03 ∗∗∗	0.06 $\rightarrow$ 0.05

Appendix

Table 12: Human–model gap, base to thinking, for the three families with an exact base–instruct–thinking triplet. Conventions as in Table 11 .

	New Yorker		Tell-Me-A-Story
Family	NLL	PPL	NLL	PPL
OLMo-2-7B	1.11 $\rightarrow$ 0.91 ∗∗∗	3.03 $\rightarrow$ 2.48 ∗∗∗	1.01 $\rightarrow$ 0.78 ∗∗∗	2.76 $\rightarrow$ 2.17 ∗∗∗
OLMo-2-13B	1.07 $\rightarrow$ 0.98 ∗∗∗	2.91 $\rightarrow$ 2.67 ∗∗∗	0.98 $\rightarrow$ 0.86 ∗∗∗	2.66 $\rightarrow$ 2.36 ∗∗∗
OLMo-2-32B	1.04 $\rightarrow$ 0.97 ∗∗∗	2.82 $\rightarrow$ 2.64 ∗∗∗	0.95 $\rightarrow$ 0.88 ∗∗∗	2.60 $\rightarrow$ 2.41 ∗∗∗
OLMo-3-7B	1.16 $\rightarrow$ 0.91 ∗∗∗	3.21 $\rightarrow$ 2.48 ∗∗∗	1.07 $\rightarrow$ 0.80 ∗∗∗	2.90 $\rightarrow$ 2.23 ∗∗∗
OLMo-3-32B	1.09 $\rightarrow$ 0.88 ∗∗∗	2.98 $\rightarrow$ 2.41 ∗∗∗	1.00 $\rightarrow$ 0.79 ∗∗∗	2.73 $\rightarrow$ 2.20 ∗∗∗

Appendix

Table 13: The model continuation’s own surprisal, base to instruct, which is the most literal reading of a “reduction in uncertainty”. It drops significantly for 9 of 11 families, with every story moving the same way (

|r_{rb}|\approx 1

). The two exceptions, Llama-3.1-8B and Mistral-Small-24B , show a small but significant increase : post-training did not reduce their uncertainty.

Family	Variant	NLL ratio	PPL ratio	PMI gap	CPMI gap
New Yorker
OLMo-2	Base	2.18 $\rightarrow$ 2.15 ∗ $r_{rb}\!=\!-.40$	3.67 $\rightarrow$ 3.38 ∗∗∗ $r_{rb}\!=\!-1.0$	$-$ 1.71 $\rightarrow$ $-$ 1.56 ∗∗∗ $r_{rb}\!=\!+.84$	+0.15 $\rightarrow$ +0.11 ∗ $r_{rb}\!=\!-.43$
OLMo-2	Instruct	3.02 $\rightarrow$ 2.32 ∗∗∗ $r_{rb}\!=\!-1.0$	6.26 $\rightarrow$ 3.71 ∗∗∗ $r_{rb}\!=\!-1.0$	$-$ 1.87 $\rightarrow$ $-$ 1.67 ∗∗∗ $r_{rb}\!=\!+.95$	+0.03 $\rightarrow$ +0.09 ∗∗∗ $r_{rb}\!=\!+.64$
OLMo-3	Base	2.20 $\rightarrow$ 2.16 ∗∗ $r_{rb}\!=\!-.47$	4.10 $\rightarrow$ 3.52 ∗∗∗ $r_{rb}\!=\!-1.0$	$-$ 1.80 $\rightarrow$ $-$ 1.69 ∗∗∗ $r_{rb}\!=\!+.85$	+0.17 $\rightarrow$ +0.11 ∗∗∗ $r_{rb}\!=\!-.69$
OLMo-3	Instruct	3.33 $\rightarrow$ 3.00 ∗∗∗ $r_{rb}\!=\!-1.0$	8.55 $\rightarrow$ 5.88 ∗∗∗ $r_{rb}\!=\!-1.0$	$-$ 2.22 $\rightarrow$ $-$ 1.67 ∗∗∗ $r_{rb}\!=\!+1.0$	+0.13 $\rightarrow$ $-$ 0.37 ∗∗∗ $r_{rb}\!=\!-1.0$
OLMo-3	Thinking	2.76 $\rightarrow$ 2.78 (ns)	6.19 $\rightarrow$ 5.25 ∗∗∗ $r_{rb}\!=\!-.97$	$-$ 2.18 $\rightarrow$ $-$ 1.66 ∗∗∗ $r_{rb}\!=\!+1.0$	+0.15 $\rightarrow$ $-$ 0.36 ∗∗∗ $r_{rb}\!=\!-1.0$

Appendix

Table 14: Per-variant scale effect. Cells show the median at the smallest size

\rightarrow

the median at the largest size, with stars on the Holm-corrected p-value (

{}^{***}p<.001

{}^{**}p<.01

{}^{*}p<.05

) and the matched-pairs rank-biserial effect size. Gemma-3 Base is the one case where the NLL ratio grows slightly with scale.

Family	NLL tax	PPL tax	PMI tax	CPMI tax
New Yorker
OLMo-2 (7B $\rightarrow$ 32B)	+0.83 $\rightarrow$ +0.16 ∗∗∗ $r_{rb}\!=\!-1.0$	+2.44 $\rightarrow$ +0.34 ∗∗∗ $r_{rb}\!=\!-1.0$	$-$ 0.19 $\rightarrow$ $-$ 0.10 ∗∗∗ $r_{rb}\!=\!+.50$	$-$ 0.11 $\rightarrow$ $-$ 0.01 ∗∗∗ $r_{rb}\!=\!+.78$
OLMo-3 (7B $\rightarrow$ 32B)	+1.12 $\rightarrow$ +0.86 ∗∗∗ $r_{rb}\!=\!-.98$	+4.22 $\rightarrow$ +2.22 ∗∗∗ $r_{rb}\!=\!-1.0$	$-$ 0.38 $\rightarrow$ $-$ 0.03 ∗∗∗ $r_{rb}\!=\!+.98$	$-$ 0.04 $\rightarrow$ $-$ 0.47 ∗∗∗ $r_{rb}\!=\!-1.0$
Gemma-3 (4B $\rightarrow$ 27B)	+1.72 $\rightarrow$ +1.26 ∗∗∗ $r_{rb}\!=\!-.98$	+5.15 $\rightarrow$ +2.92 ∗∗∗ $r_{rb}\!=\!-1.0$	+0.10 $\rightarrow$ $-$ 0.15 ∗∗∗ $r_{rb}\!=\!-.92$	$-$ 0.46 $\rightarrow$ $-$ 0.06 ∗∗∗ $r_{rb}\!=\!+1.0$
Tell-Me-A-Story
OLMo-2 (7B $\rightarrow$ 32B)	+1.08 $\rightarrow$ +0.28 ∗∗∗ $r_{rb}\!=\!-1.0$	+2.39 $\rightarrow$ +0.49 ∗∗∗ $r_{rb}\!=\!-1.0$	$-$ 0.29 $\rightarrow$ $-$ 0.10 ∗∗∗ $r_{rb}\!=\!+.84$	$-$ 0.03 $\rightarrow$ +0.02 ∗∗∗ $r_{rb}\!=\!+.53$

Appendix

Table 15: Alignment tax by scale, where the tax is the instruct gap minus the base gap. Cells show the per-story tax at the smallest size

\rightarrow

the tax at the largest size. All 24 tests are significant at Holm

p<.001

Setting	OLMo-2-7B	Llama-3.1-8B	Qwen3-4B	Gemma-3-4B
Gap in NLL (nats)
$T=0.6$	1.87 / 1.81	1.38 / 1.22	2.00 / 1.83	2.23 / 1.96
$T=1.0$	1.81 / 1.72	1.33 / 1.17	2.02 / 1.86	2.23 / 1.96
$T=1.5$	1.67 / 1.63	$-$ 0.33 / $-$ 0.29	1.81 / 1.67	2.08 / 1.82
VS	$-$ 0.10 / $-$ 0.25	$-$ 0.40 / $-$ 0.27	-	-
Gap in PMI (nats)

Appendix

Table 16: Median paired gap under bare-

T_{1}

scoring, reported per dataset as New Yorker / Tell-Me-A-Story. Note that the sign convention differs from Table 1 : these are gaps in nats, not ratios. A positive NLL gap means the model is more confident than the human; a negative PMI gap means model continuations depend on context more than human ones. PPL ratio equals

\exp

(NLL gap) and tracks NLL directly.

Dataset	Source	Metric	$n$	$\bar{\rho}$	$\sigma_{\rho}$	Sig.+	Sig.–	Sweet	$\bar{z}^{*}$	$\Delta R^{2}$
ghostbuster	Human	NLL	8	0.122	0.021	100%	0%	0%	–	0.0008
	Human	PMI	8	-0.077	0.025	0%	88%	12%	-0.68	0.0007
	Human	PPL	8	0.122	0.021	100%	0%	0%	–	0.0008
	Model	NLL	8	0.176	0.033	100%	0%	0%	–	0.0016
	Model	PMI	8	-0.031	0.030	0%	25%	0%	–	0.0009
	Model	PPL	8	0.176	0.033	100%	0%	0%	–	0.0046

Appendix

Table 17: Detailed correlation analysis between uncertainty metrics and writing quality, broken down by dataset.

\bar{\rho}

: mean Spearman correlation across models;

\sigma_{\rho}

: standard deviation; Sig.+/–: percentage of models with significant positive/negative correlation (

p<0.05

); Sweet: percentage exhibiting inverted-U relationship;

\bar{z}^{*}

: mean peak location in standardized units for sweet-spot cases.

	New Yorker		TellMeAStory		Ghostbuster
Model	Human	Model	Human	Model	Human	Model
Qwen3-4B-Base	0.029	0.018	0.130 ∗∗∗	0.121 ∗∗∗	–	–
Qwen3-4B-Instruct-2507	0.015	0.100 ∗∗	0.095 ∗∗∗	0.167 ∗∗∗	0.112 ∗∗∗	0.176 ∗∗∗
Qwen3-4B-Thinking-2507	0.017	0.064 ∗	0.090 ∗∗∗	0.109 ∗∗∗	–	–
OLMo-2-0325-32B	0.007	0.017	0.134 ∗∗∗	0.153 ∗∗∗	–	–
OLMo-2-0325-32B-Instruct	0.006	0.026	0.111 ∗∗∗	0.162 ∗∗∗	–	–

Appendix

Table 18: Per-model Spearman correlations between uncertainty (NLL) and writing quality. Significance:

{}^{***}p<0.001

{}^{**}p<0.01

{}^{*}p<0.05

Dataset	Source	Metric	$\bar{\beta}_{1}$	$\bar{\beta}_{2}$	Linear	Sweet Spot	Diminishing
ghostbuster	Human	NLL	0.055	-0.0038	100%	0%	0%
	Human	PMI	-0.036	-0.0015	75%	12%	0%
	Human	PPL	0.059	-0.0017	38%	0%	12%
	Model	NLL	0.077	-0.0014	75%	0%	12%
	Model	PMI	-0.021	0.0041	12%	0%	0%
	Model	PPL	0.092	-0.0091	25%	0%	75%

Appendix

Table 19: Quadratic regression analysis:

\text{Quality}=\beta_{0}+\beta_{1}x+\beta_{2}x^{2}

where

x

is standardized uncertainty. A significant negative

\beta_{2}

with peak within range indicates an inverted-U (sweet spot) relationship. Values averaged across models.

Source	Metric	Linear	Sweet Spot	Diminishing	U-Shape	Flat/NS
Human	NLL	8	22	6	0	28
	PPL	3	0	16	0	45
	PMI	28	1	0	0	35
Model	NLL	18	20	12	1	13
	PPL	6	20	21	0	17
	PMI	29	1	0	3	31

Appendix

Table 20: Distribution of relationship shapes between uncertainty and quality across all model-dataset combinations. Linear: significant linear term only; Sweet Spot: significant inverted-U with peak in range; Diminishing: inverted-U with peak outside range; U-Shape: significant positive quadratic term.

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