Current AI models frequently exhibit epistemic sycophancy, endorsing claims to agree with a user. Existing evaluations typically measure this either by assessing what it takes to make a model shift a binary endorsement or by eliciting an explicit probability in a proposition. However, much user-facing sycophantic behavior is demonstrated through shifts in graded support expressed through ordinary language. We propose the AI Epistemic Deference Index (AEDI): a continuous, unidimensional score representing how sensitive the support expressed in a model's output is to the attitude expressed in a user's prompt. To generate AEDI, we provide a new protocol for estimating probabilities from natural language outputs, using LLMs-as-judges validated for consistency and correlation to human judgment. We deploy it on a new curated database of 500 propositions across diverse topics and 16,000 prompts varying in user attitude, testing eight prominent models. Every model exhibits substantial deference, though with large and systematic differences across providers, with Claude models demonstrating the least, and Grok and Gemini models the most. The effect is amplified in prompts requesting a written artifact, and concentrated on propositions where models hold weaker priors. We release AEDI as an easy-to-update benchmark and measurement pipeline for output-level sycophancy evaluation.