UnpredictaBench: A Benchmark for Evaluating Distributional Randomness in LLMs
Authors: Amirhossein Abaskohi, Amirhossein Dabiriaghdam, Liang Luo, Ellie Dingqiao Wen, Lele Wang, Giuseppe Carenini, Peter West
Organizations: University of British Columbia · 2Independent Researcher
Abstract
We introduce UnpredictaBench, an evaluation that tests the ability of large language models (LLMs) to capture true underlying distributions. As LLMs are increasingly used as substitutes for other entities (e.g., for humans in economic simulations), the tendency of many models to collapse towards a single plausible answer means a failure to capture the unpredictability of real systems. Recent work on improving output diversity is insufficient for this setting: simulation requires samples that are calibrated to a target distribution, not merely varied outputs. UnpredictaBench isolates a simplified but fundamental version of this problem: sampling outcomes from individual target distributions, including canonical statistical distributions, distributions induced by stochastic programs, and natural-language scenarios that describe random processes. We introduce 448 such problems together with KS@N, a general-purpose evaluation metric that quantifies how well a model outputs approximate black-box target distributions via the Kolmogorov-Smirnov statistical test. This is the rate at which we fail to reject model samples of size N against ground-truth samples, with larger N indicating greater difficulty. Tested across open and proprietary models, we find a large spread in distributional capabilities. For instance, when models generate samples of size 100 (KS@100, our standard metric), scores range from near 0 to over 20%. No model is able to achieve over 40% at KS@100, showing significant headroom in distributional sampling as a capability. Although adding reasoning can somewhat increase scores, we find no immediate solution for this issue. UnpredictaBench shows that even simple distributional simulation remains challenging, making it a necessary first step toward using LLMs as stand-ins for complex systems. Project website and resources are available at https://unpredictabenchmark.github.io/.
Large language models (LLMs) are increasingly used to simulate human behavior in business, economics, and the social sciences, offering a low-cost complement to laboratory experiments, field studies, and surveys. This paper evaluates how well LLMs replicate human behavior in operations management. Using nine published behavioral-operations experiments, we assess LLM performance along two dimensions: whether LLM-generated data reproduce the original hypothesis-test outcomes, and whether their full response distributions align with human data, measured by Wasserstein distance. We find that LLMs often replicate hypothesis-level effects, suggesting that they can capture salient decision biases and behavioral regularities. However, their response distributions frequently diverge from human data, even for strong proprietary models, with dispersion mismatch playing an important role. We also examine two lightweight mitigation strategies: chain-of-thought prompting and hyperparameter tuning. Both can reduce distributional misalignment, and appropriate tuning can sometimes allow smaller or open-source models to match or outperform larger proprietary systems.
LLMs are increasingly used to simulate human survey responses, but prior work has mainly evaluated replication using mean-level or aggregate agreement, offering limited insight into whether LLMs reproduce the variability of human behavior. We evaluate LLM-based survey replication at the distributional level using a non-public 2010 consumer choice experiment on Korean instant noodle purchases, a setting unlikely to overlap with model training data. We evaluate three response variables of differing statistical type: binary purchase incidence, categorical brand choice, and count purchase quantity. For each, we compare human and LLM responses at mean-level, pattern, and distributional alignment, and against reference baselines from the human data alone. LLMs reproduce condition-level patterns reasonably well but fail to capture distributional structure: for purchase quantity, no model beats a condition-insensitive baseline that simply matches the pooled human distribution. Because models that match human means well can still produce distributions further from humans than this baseline, mean-based evaluation alone can be actively misleading. Replication also varies with input configuration, with structured personas and multimodal inputs improving alignment while explicit reasoning prompting degrades it monotonically.
Existing benchmarks typically report accuracy for a single model on a single run. This systematically understates real-world LLM capabilities, particularly under heterogeneous data distributions: (i) different models get different questions correct according to their specializations, and (ii) given a budget, multiple generations can be sampled and selectively retained. To quantify this gap, we introduce the Capability Frontier: a Pareto frontier over a set of models that characterizes the best achievable performance at each cost level under optimal selection across models and generations (i.e., via an oracle). Our construction corrects for two opposing biases: underestimation from single-model evaluation and overestimation from taking maxima over noisy samples. We study 21 LLMs across 16 widely used benchmarks spanning coding, reasoning, medicine, factuality, instruction following, and agentic tasks, comparing Capability Frontier performance at matched cost to each benchmark's top-performing model. Correcting for single-model evaluation yields a 54% error rate reduction; additionally correcting for single runs yields an 82% improvement, with SOTA accuracy matched at 85% cost reduction. Complementing these empirical results, we use controlled probabilistic simulations to show that higher query topic entropy produces a near-monotonic increase in the performance gap between oracle routing and the best single model. Our findings suggest collective LLM capabilities are substantially underestimated, with implications for evaluation and deployment in data-heterogeneous, multi-domain settings.