Learning from human feedback has enabled the alignment of language models (LMs) with human preferences. However, collecting human preferences is expensive and time-consuming, with highly variable annotation quality. An appealing alternative is to distill preferences from LMs as a source of synthetic annotations, offering a cost-effective and scalable alternative, albeit susceptible to other biases and errors. In this work, we introduce HyPER, a Hybrid Preference routER that defers an annotation to either humans or LMs, achieving better annotation quality while reducing the cost of human-only annotation. We formulate this as an optimization problem: given a preference dataset and an evaluation metric, we (1) train a performance prediction model (PPM) to predict a reward model's (RM) performance on an arbitrary combination of human and LM annotations and (2) employ a routing strategy that selects a combination that maximizes the predicted performance. We train the PPM on MultiPref, a new preference dataset with 10k instances paired with humans and LM labels. We show that the selected hybrid mixture of synthetic and direct human preferences using HyPER achieves better RM performance compared to using either one exclusively by 7-13% on RewardBench and generalizes across unseen preference datasets and other base models. We also observe the same trend in other benchmarks using Best-of-N reranking, where the hybrid mix has 2-3% better performance. Finally, we analyze features from HyPER and find that prompts with moderate safety concerns or complexity benefit the most from human feedback.