Win statistics provide clinically interpretable measures for comparing treatment groups with prioritized composite outcomes, but efficient covariate-adjustment methods for win statistics with right censored time-to-event outcomes remain limited. We develop a semiparametric framework for marginal win probability and win odds with prioritized time-to-event outcomes, including semi-competing risks, while also accommodating scalar survival outcomes as a special case. The estimand compares independent draws from the marginal distributions of the potential outcomes under treatment and control, which preserves a marginal causal interpretation. We derive the efficient influence function under conditional independent censoring, allowing censoring to depend on baseline covariates and predictable event history. The resulting cross-fitted one-step estimator incorporates covariate adjustment and censoring martingale augmentation, allows flexible estimation of nuisance parameters, and attains the semiparametric efficiency bound under suitable conditions on consistency and convergence rate of nuisance parameters. Simulation studies show that the estimator has small bias, accurate standard error estimation and confidence interval coverage, and substantial efficiency gain relative to the inverse-probability-of-censoring weighted (IPCW) estimator. An application to a randomized breast cancer trial comparing tamoxifen combined with radiotherapy against tamoxifen alone demonstrates improved precision, with an approximately 25\% reduction in estimated variance at five years.

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