Prediction formulae of a given synthetic variety are discussed from a fixed standpoint and from a random sample standpoint, taking into account both genetic and environmental conditions. In the former approach it appears that, for any ploidy level, the prediction using a linear relationship between vigor and parameters of the genetic structure is strictly valid only with homozygous parents and in the absence of epistasis. The concept of synthesizing or varietal ability is generalized and discussed in relation with the problem of prediction. The 2nd approach is a statistical one. Theoretical expressions of expected genetic gains are given for different predictors. A numerical application allows the study of the relative efficiencies of the predictors. A statistical index with the general combining abilities of the parents and their values under self-fertilization can efficiently select among synthesis in a 1st stage of selection. The theoretical results are discussed in relation with the known experimental results.