The sandpile paradigm is widely used to model aspects of the phenomenology of magnetically confined fusion (MCF) plasmas, including enhanced confinement, edge pedestals and, potentially, the impulsive energy and particle release process known as ELMing. Here we identify new points of contact between ELMing and the systemwide avalanches in a sandpile. We compare the quantified response (F A Calderon et al., Phys. Plasmas 20 042306 (2014)) to increased fuelling of the time sequence of ELM events in a series of similar JET plasmas to the response to increased fuelling of the time sequence of systemwide avalanches in a sandpile model (S C Chapman et al., Phys. Rev. Lett. 86 2814 (2001)) that has well established links to MCF plasma phenomenology. Both the probability density functions of inter-event time intervals, and delay time embeddings of event time sequences, at different fuelling rates, show common features and point to shared underlying physics.