arXiv:2611.05908v1 Announce Type: new Abstract: Second-stage neural rankers are commonly applied with a fixed re-ranking depth, assuming that retrieval effectiveness saturates as depth increases. Prior research has questioned the assumption that increasing the re-ranking depth yields linear performance gains, further suggesting that optimal re-ranking depth varies considerably from query to query. In the past, studying such phenomena was methodologically difficult given the scale of manual annotation required. With the advent of LLM-based relevance judgments we can now more easily undertake such studies, in this case to pinpoint the optimal re-ranking depth on a per-query basis. Using dense LLM-based relevance judgments over a typical re-ranking pipeline, we show that many queries exhibit a well-defined optimal re-ranking depth, beyond which effectiveness stagnates or degrades. We formulate re-ranking depth as a query-specific property and study whether it can be predicted a priori from first-stage retrieval characteristics. Through a large-scale analysis, we find that most standard query performance prediction (QPP) methods are ineffective for this task. In contrast, a predictor derived from LLM-assessed first-stage ranking quality, which we term IR-DCG@10, can reduce the average re-ranking depth by up to a factor of 3 while preserving overall effectiveness, depending on the specific first- and second-stage rankers used. Under oracle selection of optimal depths, we further show that retrieval effectiveness can improve by more than 7% while reducing the average re-ranking depth by a factor of 5 on the MSMARCO DEV collection. Given our promising preliminary findings, we would encourage the use of automatic judgments to facilitate research otherwise infeasible under manual annotation. Towards this point, we release relevance judgments, our codebase, and experimental artefacts to support reproducibility and further research.