Robustness research has become popular, however very little is known on its explicit quantification. This paper summarises a quantification method previously published by the main author and proceeds in demonstrating its step-by-step application with a case study tall timber building. A hypothetical 15-storey post-and-beam timber building with a central core is designed for normal loads, and four improved options are designed to account for abnormal loads in order to increase the building’s robustness. A detailed, nonlinear, dynamic Finite Element model is set up in Abaqus® to model three ground floor column removal scenarios, and a Random Forest classifier is set up to propagate uncertainties, to efficiently estimate the probability of certain collapse classes occurring, and to calculate the importance of each input parameter. The results show how design improvements at the whole building scale (e.g., strong floors) have a higher impact on robustness performance than just improving the strength and ductility of some selected connections, although these results are exclusive to the building studied. The case study reinforces the importance of a sound conceptual design for achieving robustness in tall timber buildings.