This paper proposes a novel framework for predict-then-optimize problems that characterizes expected loss as the covariance between costs and optimal decisions: E[Loss] =-cov(c, z opt (c)). This closed-form expression enables ex-ante loss estimation using simulated or historical data without requiring predictors. For polynomial cost structures c ∼ X deg , we prove that optimal decisions should be estimated using degree deg-1 predictors, exploiting the relationship ∂c/∂X ∝ X deg-1. We show linear decision functions minimize expected loss and provide rigorous conditions under which this framework applies. Our method requires solving N optimization problems once offline, achieving K× speedup over iterative methods like SPO+ (K = 10-100 iterations). Experiments on shortest path problems demonstrate that our approach matches or exceeds SPO+ performance. The framework provides practical tools including cross-validation for unknown polynomial degrees and robustness to model misspecification.