Earthquake early warning systems based on smartphone networks are emerging as complementary systems to the more expensive systems based on scientific‐grade instruments. Hence, there is a need to better understand their detection capabilities. This article introduces a probabilistic framework for modeling the interaction between a smartphone network and seismic events to provide estimates of the detection probability for a given earthquake and to assess how the network geometry affects the detection delay. The framework was used to study the detection capability of the first operational smartphone‐based earthquake early warning system implemented by the Earthquake Network (EQN) initiative, which started in 2013 and has issued more than 5500 warnings in 25 countries. The analysis showed that the probability of detection of an earthquake depends on the interaction between the network geometry and the earthquake parameters and that the detection probability is greatly affected by the population spatial distribution. Countries that benefit most from the EQN initiative are those without large gaps in the geographic distribution of their population.