There are many sources of random and systematic error in composition quantification by atom probe, however, often only statistical error is reported. Identification of ions and overlaps or interferences of peaks in the mass spectrum are one major source of uncertainty much larger than counting error. These overlaps can be solved using maximum likelihood estimation (MLE), improving the accuracy of the result, but with an unknown affect on the precision. An analytical expression for the uncertainty of the MLE solution is presented and it is demonstrated to be much more accurate than existing methods. In one example, the commonly used error estimate was 5 times too small. Literature results, containing overlaps, most likely underestimate composition uncertainty because of the complexity of correctly dealing with stochastic effects and error propagation. This is the first paper in atom probe that attempts to robustly address these problems. Using the methods described here, accurate estimation of error, and the minimisation of this could be achieved, providing a key milestone in quantitative atom probe. Accurate estimation of the composition uncertainty in the presence of overlaps is crucial for planning experiments and scientific interpretation of the measurement.