Parser-based log compression, which separates static templates from dynamic variables, is a promising approach to exploit the unique structure of log data. However, its performance on complex production logs is often unsatisfactory. This performance gap coincides with a known degradation in the accuracy of its core log parsing component on such data, motivating our investigation into a foundational yet unverified question: does higher parsing accuracy necessarily lead to better compression ratio? To answer this, we conduct the first empirical study quantifying this relationship and find that a higher parsing accuracy does not guarantee a better compression ratio. Instead, our findings reveal that compression ratio is dictated by achieving effective pattern-based grouping and encoding, i.e., the partitioning of tokens into low entropy, highly compressible groups. Guided by this insight, we design DeLog, a novel log compressor that implements a Pattern Signature Synthesis mechanism to achieve efficient pattern-based grouping. On 16 public and 10 production datasets, DeLog achieves state-of-the-art compression ratio and speed.