The identification of jets containing b-hadrons, b-tagging, is critical for many ATLAS physics analyses. Its performance is measured in data and the simulation is corrected through simulation-to-data scale factors. However, such measurement only covers a certain jet $p_T$ range, so the b-tagging performance at higher $p_T$ must be evaluated via a simulation-based extrapolation method. This work considers a widely used scheme, the "pseudo-continuous" working points, which constitutes a flexible way to apply a set of different b-tagging requirements within the same ATLAS physics analysis. A brief introduction is given to this scheme and the corresponding simulation-based extrapolation to high $p_T$ jets is presented for the first time. In addition, a new statistical tool, denoted as "eigenvector recomposition", is developed to allow for the correct combination of analyses relying on different b-tagging setups. It correlates common systematic uncertainties related with b-tagging in a mathematically solid way. Its application in the combination of the "boosted" and "resolved" $VH(H\to bb)$ analyses is shown as an example.