Dyadic regression models, which output real-valued predictions for pairs of entities, are fundamental in many domains (e.g. obtaining user-product ratings in Recommender Systems) and promising and under exploration in others (e.g. tuning patient-drug dosages in precision pharmacology). In this work, we prove that non-uniform observed value distributions of individual entities lead to severe biases in state-of-the-art models, skewing predictions towards the average of observed past values for the entity and providing worse-than-random predictive power in eccentric yet crucial cases; we name this phenomenon eccentricity bias. We show that global error metrics like Root Mean Squared Error (RMSE) are insufficient to capture this bias, and we introduce Eccentricity-Area Under the Curve (EAUC) as a novel metric that can quantify it in all studied domains and models. We prove the intuitive interpretation of EAUC by experimenting with naive post-training bias corrections, and theorize other options to use EAUC to guide the construction of fair models. This work contributes a bias-aware evaluation of dyadic regression to prevent unfairness in critical real-world applications of such systems.