The emergence of language around a child’s first birthday is one of the greatest transformations in human development. Does this transition require a fundamental shift in the child’s knowledge or beliefs, or could it instead be attributable to more gradual changes in processing abilities? We present a simple model of cognitive performance that supports the second conclusion. The premise is that any cognitive operation requires multiple steps, each of which require some time to complete and have some probability of failure. We use meta-analysis to estimate these parameters for two components of simple ostensive word learning: social cue use and word recognition. When combined in our model, these estimates suggest that learning should be very difficult for children younger than around a year, especially with gaze alone. This model takes a first step towards quantifying performance limitations for cognitive development and may be broadly applicable to other developmental changes.