Abstract Understanding how gene expression is translated to phenotype is central to modern molecular biology, but the success is contingent on the intrinsic tractability of the specific traits under examination. However, an a priori estimate of trait tractability from the perspective of gene expression is unavailable. Motivated by the concept of entropy in a thermodynamic system, we here propose such an estimate ( S T ) by gauging the number ( N ) of different expression states that underlie the same trait abnormality, with large S T corresponding to large N . By analyzing over 200 yeast morphological traits we show that S T is constrained by natural selection, which builds co-regulated gene modules to minimize the total number of possible expression states. We further show that S T is a good measure of the titer of recurrent patterns of an expression-trait relationship, predicting the extent to which the trait could be deterministically understood with gene expression data.