A standard model is a theoretical framework that synthesizes observables into a quantitative consensus. Have researchers made progress toward this kind of synthesis for children’s early language learning? Many computational models of early vocabulary learning assume that individual words are learned through an accumulation of environmental input. This assumption is also implicit in empirical work that emphasizes links between language input and learning outcomes. However, models have typically focused on average performance, whereas empirical work has focused on variability. To model individual variability, we relate the tradition of research on accumulator models to item response theory models from psychometrics. This formal connection reveals that currently available data sets do not allow researchers to test the resulting models fully, illustrating a critical need for theory to contribute to shaping new data collection and creating and testing an eventual standard model.