A conceptually simple formulation is proposed for a new empirical sea state bias (SSB) model using information retrieved entirely from altimetric data. Nonparametric regression techniques are used, based on penalized smoothing splines adjusted to each predictor and then combined by a Generalized Additive Model. In addition to the significant wave height (SWH) and wind speed (U10), a mediator parameter designed by the mean wave period derived from radar altimetry, has proven to improve the model performance in explaining some of the SSB variability, especially in swell ocean regions with medium-high SWH and low U10. A collinear analysis of scaled sea level anomalies (SLA) variance differences shows conformity between the proposed model and the established SSB models. The new formulation aims to be a fast, reliable and flexible SSB model, in line with the well-settled SSB corrections, depending exclusively on altimetric information. The suggested method is computationally efficient and capable of generating a stable model with a small training dataset, a useful feature for forthcoming missions.