More Test-Time Compute Can Hurt: Overestimation Bias in LLM Beam Search

Wider beam search should improve LLM reasoning, but when should you stop widening? Prior work on beam width selection has focused on inference efficiency citepqin2025dsbd, freitag2017beam, without analyzing whether wider search can hurt output quality. We present an analysis, grounded in Extreme Value Theory, that answers this question. Beam selection over noisy scorer outputs introduces a systematic overestimation bias that grows with the candidate pool size, and we derive a maximum useful beam width hatk beyond which search degrades performance. This critical width depends on the signal-to-noise ratio of the scorer: hatk grows exponentially with (Delta/σ)2, where Delta > 0 is the quality advantage of correct paths over incorrect ones and σ is the scorer noise. We validate this theory by comparing perplexity-guided and PRM-guided beam search across three 7B-parameter models and ten domains on MR-BEN (5,975 questions). Perplexity scoring, with its high noise, yields hatk = 1: search provides no benefit at any width tested. PRM scoring, with lower noise, yields hatk ≥ 4, with gains of up to 8.9 percentage points. The same model, the same algorithm, but different scorers place hatk at opposite ends of the beam width range. Our analysis identifies the scorer's signal-to-noise ratio as the key quantity governing beam width selection, and we propose diagnostic indicators for choosing the beam width in practice.