Risk analysis is of paramount importance in maritime transportation due to the particularly hazardous nature of the work. While the International Maritime Organization (IMO) has circulated Formal Safety Assessment (FSA) for the assessment of on-board risk, it has not introduced a specific tool for risk analysis, and a more proactive approach to the assessment of risk is consequently sought by maritime safety researchers. This paper aims to demonstrate how the fuzzy bow-tie method of analysis might be deployed to quantitatively analyse risk. Focussing on the specific context of ship to ship (STS) cargo operations enables specific insights into the method to be gained. The findings of the research can be utilised by maritime safety professionals (STS superintends, mooring masters, tanker safety inspectors, company fleet managers, and tanker shipowners) in order to mitigate potential risks and enhance marine safety during the STS operation.