Using large language models (LMs) for query or document expansion can improve generalization in information retrieval. However, it is unknown whether these techniques are universally beneficial or only effective in specific settings, such as for particular retrieval models, dataset domains, or query types. To answer this, we conduct the first comprehensive analysis of LM-based expansion. We find that there exists a strong negative correlation between retriever performance and gains from expansion: expansion improves scores for weaker models, but generally harms stronger models. We show this trend holds across a set of eleven expansion techniques, twelve datasets with diverse distribution shifts, and twenty-four retrieval models. Through qualitative error analysis, we hypothesize that although expansions provide extra information (potentially improving recall), they add additional noise that makes it difficult to discern between the top relevant documents (thus introducing false positives). Our results suggest the following recipe: use expansions for weaker models or when the target dataset significantly differs from training corpus in format; otherwise, avoid expansions to keep the relevance signal clear.