Event rates of BH-EMRIs within z = 1. Predicted theoretical EMRI rates (hatched gray area) from Babak et al. (2017) are compared to those inferred from the QPE formation rate, which have to be interpreted as lower limits as not all EMRIs, even if QPEs are such, are expected to emit eruptions. In the case that QPEs are BH-EMRI, a direct comparison can be made (green 1σ interquantile range); instead, if QPEs are stellar-EMRIs the constraint for BH-EMRIs (orange 1σ interquantile range) requires further extrapolations. Nonetheless, and particularly in the former case, pessimistic EMRI population models would be disfavored, with huge implications for LISA detections.