Unsolvability Ceiling in Multi-LLM Routing: An Empirical Study of Evaluation Artifacts

Efficient routing across multiple LLMs enables cost-quality tradeoffs by directing queries to the cheapest capable model. Prior work attributes routing headroom to an "unsolvability ceiling", queries no model in the pool can solve. We present a large-scale study of multi-tier LLM routing with 206,000 query-model pairs across six benchmarks (MMLU, MedQA, HumanEval, MBPP, Alpaca, ShareGPT) using the Gemma 4 and Llama 3.1 families. Evaluating with both LLM-as-a-judge and exact-match metrics, we show that a substantial portion of reported unsolvability stems from evaluation artifacts: (i) systematic judge biases favoring verbosity over correctness, (ii) truncation under fixed generation budgets, and (iii) output format mismatches. Through dual-judge validation and exact-match grounding, we reduce measured unsolvability across tasks. We introduce a decomposition framework attributing failures to these artifacts, revealing consistent patterns across domains and model families. These artifacts also distort router training signals: standard routers collapse to majority-class prediction (~79% smallest-tier optimal), confirmed via random-feature and shuffled-label controls, incurring a 13-17 percentage point opportunity cost. We provide actionable recommendations including dual-judge validation, exact-match anchoring, and cost-sensitive objectives. Our findings suggest existing routing headroom estimates are substantially inflated, underscoring the need for reliable evaluation protocols in multi-LLM systems.