One of the goals of molecular bioinformatics is decoding amino acid sequences to extract information on the principles of protein folding. However, this is difficult to perform with standard bioinformatics techniques such as multiple sequence alignment and so on. Thus, we propose a technique based on inter-residue average distance statistics to make predictions regarding the protein folding mechanisms of amino acid sequences. Our method involves constructing a kind of predicted contact map called an Average Distance Map (ADM) based on average distance statistics to pinpoint regions of possible folding nuclei for proteins. Only information on the amino acid sequence of a given protein is required for the present method. In this article, we summarize the results of studies using our method to analyze how specific protein sequences affect folding properties. In particular, we present studies on proteins in the phage lysozyme, such as the globin, fatty acid binding protein-like, and the cupredoxin-like fold families. In the present review, we characterize the 3D architectures of these proteins through the properties of the protein ADMs. Furthermore, we combine the information on the conserved residues within the regions predicted by the ADMs with our results obtained so far. Such information may help identify the folding characteristics of each protein. We discuss this possibility in the present review.