Erythrocyte (or red blood cell) sedimentation rate (ESR) is a physical derived parameter of blood which is often used in routine health checks and medical diagnosis. For instance, in the case of inflammation, a higher ESR is observed due to the associated increase in fibrinogen and other plasma proteins. It was believed that this increase was due to the formation of larger aggregates of red blood cells (RBCs) caused by the increase in fibrinogen. Indeed, fibrinogen is an agent-fostering aggregation of RBCs and in the Stokes regime-assumed to be observed in blood-larger aggregates sediment faster. However, all models of ESR measurements based on this hypothesis require further specific physical assumptions, not required in any other system. Besides, modern studies in the field of colloidal suspensions have established that attractive particles form percolating aggregates (i.e. aggregates as wide as the container). The sedimentation of these colloids then follows a so-called "colloidal gel collapse". Recently, it has been shown that RBCs actually follow the same behavior. This hypothesis also allows to efficiently and analytically model the sedimentation curve of RBCs, from which robust and physically-meaningful descriptors can be extracted. This manuscript describes how to perform such an analysis, and discusses the benefits of this approach.