Additive main effect and multiplicative interaction (AMMI) and best linear unbiased prediction (BLUP) are popular methods for analyzing multi‐environment trials (MET). The AMMI has nice graphical tools for modeling genotype‐vs.‐environment interaction (GEI) but fails in some aspects, such as accommodating a linear mixed‐effect model (LMM) structure. The BLUP provides reliable estimates but new insights to deal graphically with a random GEI structure are needed. This article compares the predictive success of BLUP and AMMI, shows how to generate biplots for modeling GEI in MET analysis using LMM, and proposes a new quantitative genotypic stability measure called WAASB, which is the Weighted Average of Absolute Scores from the singular value decomposition of the matrix of BLUPs for the GEI effects generated by an LMM. We also introduced the theoretical basis of a superiority index that allows weighting between mean performance and stability, which was conveniently called WAASBY. The BLUP was found to outperform AMMI in the analysis of four real MET trials. The application of our indexes is illustrated using an oat (Avena sativa L.) MET dataset. It was shown that reliable measures of stability using WAASB may help breeders and agronomists to make correct decisions when selecting or recommending genotypes. In addition, the simultaneous selection index, WAASBY, will be useful when the selection should consider different weights for stability and mean performance. Some advantages over existing statistics are discussed. Finally, the implementation of the procedures of this article in future studies is facilitated by an R package containing all required functions.