The idea that diversity is a combination of species richness and the so-called "evenness" of count distributions is a bedrock concept in ecology. Researchers often compute stand-alone evenness indices. They also examine Hill numbers related to Shannon's H and Simpson's D because these metrics balance richness and "evenness" to various degrees. But evenness is an operationally problematic abstraction, not a thing out in the world. Evenness indices and Hill numbers in empirical data are overly sensitive to the abundance of dominant species, poorly replicable within communities, highly variable among similar communities, and a weak indicator of latitudinal biodiversity trends. They are inconsistently related to the parameters of key models that might underlie count distributions, and they vary highly in simulation even when these model parameters do not vary. Ecologists would benefit by instead determining which real distributions fit which theoretical models and using estimated parameters to understand community structure and assembly.