Our objective was to determine whether the response to selection (R) and predictive ability (rMP) in an A/B population are higher with a large training population that is used for all biparental crosses, or with a smaller ad hoc training population highly related to the A/B population. We studied 969 biparental maize (Zea mays L.) populations phenotyped at four to 12 environments. Parent–offspring marker imputation was done for 2911 single nucleotide polymorphism loci. For 27 A/B populations, training populations were constructed by pooling: (1) all prior populations with A as one parent (A/*, where * is a related inbred) and with B as one parent (*/B) [general combining ability (GCA) model]; (2) A/* or */B crosses only; (3) all */* crosses (same background model, SB); and (4) all */*, A/*, and */B crosses (SB + GCA model). The SB model training population was 450–6000% as large as the GCA model training populations, but the mean coefficient of coancestry between the training population and A/B population was lower for the SB model (0.44) than for the GCA model (0.71). The GCA model had the highest R and rMP for all traits. For yield, R was 0.22 Mg ha−1 with the GCA model and 0.15 Mg ha−1 with the SB model. We concluded that it is best to use an ad hoc training population for each A/B population.