As endpoints of the hierarchical mass assembly process, the stellar populations of local early-type galaxies encode the evolutionary patterns of galaxies over cosmic time. We use Horizon AGN, a cosmological hydrodynamical simulation, to study the merger histories of local early-types and track how the morphological mix of galaxies that are the progenitors of early-types changes over time. By calculating probabilities for late-type galaxies to be progenitors we provide a framework for alleviating progenitor bias, the bias that occurs if one uses only early-type galaxies (or proxies like the red sequence) to study the progenitor population at earlier epochs. Early-types attain their final morphology at relatively early epochs – by redshift 1, 60 percent of today's early-types have had their last significant merger. Progenitor bias is severe at all but the lowest redshifts: e.g. at redshift 0.6, less than half the stellar mass in today's early-types is actually in progenitors that have early-type morphology. At high redshift, almost all massive late-type galaxies, regardless of their local environment or star formation rate, are progenitors, as are lower-mass galaxies occupying regions of high density. However, at fixed stellar mass, progenitor fractions increase as the star formation rate decreases i.e. late-type galaxies with lower specific star formation rates are more likely to be progenitors (at a given stellar mass). In the impending era of large observational surveys (e.g. LSST, EUCLID, JWST), this study provides a framework for accurate studies of the evolution of local early-type galaxies.