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The basic reproductive number -- $R_0$ -- is one of the most common and mostcommonly misapplied numbers in public health. Although often used to compareoutbreaks and forecast pandemic risk, this single number belies the complexitythat two different pathogens can exhibit, even when they have the same $R_0$.Here, we show how to predict outbreak size using estimates of the distributionof secondary infections, leveraging both its average $R_0$ and the underlyingheterogeneity. To do so, we reformulate and extend a classic result from randomnetwork theory that relies on contact tracing data to simultaneously determinethe first moment ($R_0$) and the higher moments (representing theheterogeneity) in the distribution of secondary infections. Further, we showthe different ways in which this framework can be implemented in thedata-scarce reality of emerging pathogens. Lastly, we demonstrate that withoutdata on the heterogeneity in secondary infections for emerging infectiousdiseases like COVID-19, the uncertainty in outbreak size ranges dramatically.Taken together, our work highlights the critical need for contact tracingduring emerging infectious disease outbreaks and the need to look beyond $R_0$when predicting epidemic size.

Beyond $R_0$: Heterogeneity in secondary infections and probabilistic epidemic forecasting