Expressions for the expected value of the first mode damping ratio are derived from 122 seismic responses from concrete buildings and 81 from steel. The results include dissipation at the soil-structure interface and are appropriate for the situations where this source of dissipation is not included in the model. Comparisons between models of different complexity indicate the appropriateness of using a single regressor, which is taken as the building height. It is shown that the Fisher Information on the damping increases with the number of response cycles and this result is used to define weights for the residuals of the regression. The effective damping in steel buildings, with the exception of very tall structures, is found larger than the 2% typically used in practice, while the 5% assigned to concrete proves to be close to the mean of the data set.