Despite the importance of having robust estimates of the time-asymptotic total number of infections, early estimates of COVID-19 show enormous fluctuations. Using COVID-19 data from different countries, we show that predictions are extremely sensitive to the reporting protocol and crucially depend on the last available data point before the maximum number of daily infections is reached. We propose a physical explanation for this sensitivity, using a susceptible–exposed–infected–recovered model, where the parameters are stochastically perturbed to simulate the difficulty in detecting patients, different confinement measures taken by different countries, as well as changes in the virus characteristics. Our results suggest that there are physical and statistical reasons to assign low confidence to statistical and dynamical fits, despite their apparently good statistical scores. These considerations are general and can be applied to other epidemics. COVID-19 is currently affecting over 180 countries worldwide and poses serious threats to public health as well as economic and social stability of many countries. Modeling and extrapolating in near real-time the evolution of COVID-19 epidemics is a scientific challenge, which requires a deep understanding of the non-linearities undermining the dynamics of the epidemics. Here, we show that real-time predictions of COVID-19 infections are extremely sensitive to errors in data collection and crucially depend on the last available data point. We test these ideas in both statistical (logistic) and dynamical (susceptible–exposed–infected–recovered) models that are currently used to forecast the evolution of the COVID-19 epidemic. Our goal is to show how uncertainties arising from both poor data quality and inadequate estimations of model parameters (incubation, infection, and recovery rates) propagate to long-term extrapolations of infection counts. We provide guidelines for reporting those uncertainties to the scientific community and the general public.