The taxonomic and ecologic composition of Earth’s biota has shifted dramatically through geologic time, with some clades going extinct while others diversified. Here, we derive a metric that quantifies the change in biotic composition due to extinction or origination and show that it equals the product of extinction/origination magnitude and selectivity (variation in magnitude among groups). We also define metrics that describe the extent to which a recovery (1) reinforced or reversed the effects of extinction on biotic composition and (2) changed composition in ways uncorrelated with the extinction. To demonstrate the approach, we analyzed an updated compilation of stratigraphic ranges of marine animal genera. We show that mass extinctions were not more selective than background intervals at the phylum level; rather, they tended to drive greater taxonomic change due to their higher magnitudes. Mass extinctions did not represent a separate class of events with respect to either strength of selectivity or effect. Similar observations apply to origination during recoveries from mass extinctions, and on average, extinction and origination were similarly selective and drove similar amounts of biotic change. Elevated origination during recoveries drove bursts of compositional change that varied considerably in effect. In some cases, origination partially reversed the effects of extinction, returning the biota towards the pre-extinction composition; in others, it reinforced the effects of the extinction, magnifying biotic change. Recoveries were as important as extinction events in shaping the marine biota, and their selectivity deserves systematic study alongside that of extinction.