Simple Summary: Pain is one of the most common and debilitating symptoms in cancer patients. A clinical peculiarity of cancer pain is the breakthrough cancer pain (BTcP), which is defined as a temporary exacerbation of pain that “breaks through” a phase of adequate pain control by an opioid-based therapy. The NP-BTcP occurs in the absence of any specific activity. In this paper, we addressed the topic through a mathematical approach to provide many indications for identifying the diagnostic and therapeutic gaps in NP-BTcP management. Abstract: Breakthrough cancer pain (BTcP) is a temporary exacerbation of pain that “breaks through” a phase of adequate pain control by an opioid-based therapy. The non-predictable BTcP (NP-BTcP) is a subtype of BTcP that occurs in the absence of any specific activity. Since NP-BTcP has an important clinical impact, this analysis is aimed at characterizing the NP-BTcP phenomenon through a multidimensional statistical technique. This is a secondary analysis based on the Italian Oncologic Pain multiSetting—Multicentric Survey (IOPS-MS). A correlation analysis was performed to characterize the NP-BTcP profile about its intensity, number of episodes per day, and type. The multiple correspondence analysis (MCA) determined the identification of four groups (phenotypes). A univariate analysis was performed to assess differences between the four phenotypes and selected covariates. The four phenotypes represent the hierarchical classification according to the status of NP-BTcP: from the best (phenotype 1) to the worst (phenotype 4). The univariate analysis found a significant association between the onset time >10 min in the phenotype 1 (37.3%)’ vs. the onset > 10 min in phenotype 4 (25.8%) (p < 0.001). Phenotype 1 was characterized by the gastrointestinal type of cancer (26.4%) with respect to phenotype 4, where the most frequent cancer affected the lung (28.8%) (p < 0.001). Phenotype 4 was mainly managed with rapid-onset opioids, while in phenotype 1, many patients were treated with oral, subcutaneous, or intravenous morphine (56.4% and 44.4%, respectively; p = 0.008). The ability to characterize NP-BTcP can offer enormous benefits for the management of this serious aspect of cancer pain. Although requiring validation, this strategy can provide many indications for identifying the diagnostic and therapeutic gaps in NP-BTcP management.