effect sizes are very small so that they are estimated with much error. One explanation of this apparent paradox is to consider the extreme case of a single variant when it is known that this variant is associated with the trait but the effect size is not known and needs to be estimated. Estimating its effect size will be unbiased across repeated samples from the same population and the standard error of estimation informs about the precision (standard error) of the estimate of effect size. This is the scenario analogous to our estimate of the variance explained by all SNPs. Now consider that, for each (unbiased) estimate of effect size, we make a prediction of phenotypes in an independent sample based upon the estimated effect size of the variant in the discovery sample. The correlation between predicted value and actual phenotype will depend on how well the variant has been estimated—the worse the estimate of the effect size of the variant in the discovery sample, the worse will be the variance explained by the predictor in the validation sample. This is the scenario analogous to our prediction analysis.
