In genomewide selection, the expected correlation between predicted performance and true genotypic value is a function of the training population size (N), heritability on an entry-mean basis (h2), and effective number of chromosome segments underlying the trait (Me). Our objectives were to (i) determine how the prediction accuracy of different traits responds to changes in N, h2, and number of markers (NM) and (ii) determine if prediction accuracy is equal across traits if N, h2, and NM are kept constant. In a simulated population and four empirical populations in maize (Zea mays L.), barley (Hordeum vulgare L.), and wheat (Triticum aestivum L.), we added random nongenetic effects to the phenotypic data to reduce h2 to 0.50, 0.30 and 0.20. As expected, increasing N, h2, and NM increased prediction accuracy. For the same trait within the same population, prediction accuracy was constant for different combinations of N and h2 that led to the same Nh2. Different traits, however, varied in their prediction accuracy even when N, h2, and NM were constant. Yield traits had lower prediction accuracy than other traits despite the constant N, h2, and NM. Empirical evidence and experience on the predictability of different traits are needed in designing training populations.