The problem of characterizing and detecting recurrent sequence patterns such as substrings or motifs and related associations or rules is variously pursued in order to compress data, unveil structure, infer succinct descriptions, extract and classify features, etc. In molecular biology, exceptionally frequent or rare words in bio-sequences have been implicated in various facets of biological function and structure. The discovery, particularly on a massive scale, of such patterns poses interesting methodological and algorithmic problems and often exposes scenarios in which tables and synopses grow faster and bigger than the raw sequences they are meant to encapsulate. In previous study, the ability to succinctly compute, store, and display unusual substrings has been linked to a subtle interplay between the combinatorics of the subword of a word and local monotonicities of some scores used to measure the departure from expectation. In this paper, we carry out an extensive analysis of s...