Heavy precipitation, often associated with weather phenomena such as tropical cyclones, extratropical cyclones (ETCs), atmospheric rivers (ARs), and mesoscale convective systems (MCSs), can cause significant socio‐economic loss. In this study, we apply atmospheric feature trackers to quantify the contributions of these storm types in observational data sets and climate model short‐range hindcasts. We generate a global hourly storm data set at 0.25° spatial resolution covering 2006–2020, based on the tracking results from TempestExtremes and Python FLEXible object TRacKeR. Our analyses show that these four storm types account for 67% of global annual mean precipitation and 82% of top 1% precipitation extremes, with MCSs mainly over the tropics, and ARs and ETCs over the midlatitudes. The percentage of precipitation contributions from these storms also show strong seasonality over many geographical locations. We further apply the tracking results to the Energy Exascale Earth System Model (E3SM) short‐range hindcasts and evaluate how well these storms are simulated. The evaluation show that E3SM, with ∼1° resolution, significantly underestimates storm‐associated precipitation totals and extremes, especially for MCSs in the tropics. Our analysis also suggests that model fails to capture the correct mean diurnal phases and amplitude of MCS precipitation. This phenomenon‐based approach provides a better understanding of precipitation characteristics and can lead to enhanced model evaluation by revealing underlying problems in model physics related to precipitation processes associated with the heavy‐precipitating storms.