Shannon entropy is widely used to measure the complexity of DNA sequences but suffers from saturation effects that limit its discriminative power for long uniform segments. We introduce a novel metric, the entropy rank ratio R, which positions a target sequence within the full distribution of all possible sequences of the same length by computing the proportion of sequences that have an entropy value equal to or lower than that of the target. In other words, R expresses the relative position of a sequence within the global entropy spectrum, assigning values close to 0 for highly ordered sequences and close to 1 for highly disordered ones. DNA sequences are partitioned into fixed-length subsequences and non-overlapping n-mer groups; frequency vectors become ordered integer partitions and a combinatorial framework is used to derive the complete entropy distribution. Unlike classical measures, R is a normalized, distribution-aware measure bounded in [0,1] at fixed (T,n), which avoids saturation to log2 4 and makes values comparable across sequences under the same settings. We integrate R into data augmentation for convolutional neural networks by proposing ratio-guided cropping techniques and benchmark them against random, entropy-based, and compression-based methods. On two independent datasets, viral genes and human genes with polynucleotide expansions, models augmented via R achieve substantial gains in classification accuracy using extremely lightweight architectures.