The basic reproductive number --- $R_0$ --- is one of the most common and most commonly misapplied numbers in public health. Nevertheless, estimating $R_0$ for every transmissible pathogen, emerging or endemic, remains a priority for epidemiologists the world over. Although often used to compare outbreaks and forecast pandemic risk, this single number belies the complexity that two different pathogens can exhibit, even when they have the same $R_0$. Here, we show how predicting outbreak size requires both an estimate of $R_0$ and an estimate of the heterogeneity in the number of secondary infections. To facilitate rapid determination of outbreak risk, we propose a reformulation of a classic result from random network theory that relies on contact tracing data to simultaneously determine the first moment ($R_0$) and the higher moments (representing the heterogeneity) in the distribution of secondary infections. Further, we show how this framework is robust in the face of the typically limited amount of data for emerging pathogens. Lastly, we demonstrate that without data on the heterogeneity in secondary infections for emerging pathogens like 2019-nCoV, the uncertainty in outbreak size ranges dramatically, in the case of 2019-nCoV from 5-40% of susceptible individuals. Taken together, our work highlights the critical need for contact tracing during emerging infectious disease outbreaks and the need to look beyond $R_0$ when predicting epidemic size.