We study the ratio of the cross sections for $t\bar{t}\gamma$ and $t\bar{t}$ production at the LHC. The presence of correlations between theoretical uncertainties of the two processes makes possible a precise determination of this observable. This can help to evidentiate effects of new physics that might reveal themselves only when sufficiently precise theoretical predictions are available. Our analysis is based on fully realistic simulations of $t\bar{t}\gamma$ and $t\bar{t}$ production in the dilepton decay channel, including complete off-shell and non-resonant effects at NLO QCD accuracy. We discuss Standard Model predictions for the LHC Run II at both inclusive and differential level, also quantifying the impact of the theoretical uncertainties related to variation of scales and parton distribution functions.