The most precise top quark mass measurements use kinematic reconstruction methods, determining the top mass parameter of a Monte Carlo event generator m MC t . Because of hadronization and parton-shower dynamics, relating m MC t to a field theory mass is difficult. We present a calibration procedure to determine this relation using hadron level QCD predictions for observables with kinematic mass sensitivity. The highest precision measurements are based on direct reconstruction methods exploiting kinematic properties related to the top quark mass, and are based on multivariate fits that depend on a maximum amount of information on the top decay final states. This includes template and matrix element fits for distributions such as the measured invariant mass. These observables are highly differential, depending on experimental cuts and jet dynamics. Multipurpose Monte Carlo (MC) event generators are employed to do the analysis, and the results are influenced by both perturbative and nonperturbative QCD effects. Thus, the measured mass is the top mass parameter m MC t contained in the particular MC event generator. Its interpretation may also depend in part on the MC tuning and the observables used in the analysis.The systematic uncertainties from MC modeling are a dominant uncertainty in the above measurements, but do not address how m MC t is related to a mass parameter defined precisely in quantum field theory that can be globally used for higher-order predictions. The relation is nontrivial because it requires an understanding of the interplay between the partonic components of the MC generator (hard matrix elements and parton shower) and the hadronization model. In the context of top quark mass determinations, it is often assumed that MC generators should be considered as models whose partonic components and hadronization models are, through the tuning procedure, capable of describing experimental data to a precision that is higher than that of their partonic input.In the past m MC t has been frequently identified with the pole mass. This is compatible with parton-shower implementations for massive quarks, but a direct identification is disfavored because of sensitivity to nonperturbative effects from below the MC shower cutoff, Λ c ∼ 1 GeV. Also, the pole mass has an OðΛ QCD Þ renormalon ambiguity, while m MC t does not (since partonic information is not employed below Λ c ). It has been argued [4,5] can be calibrated into a field theory mass scheme through a fit of MC predictions to hadron level QCD computations for observables closely related to the distributions that enter the experimental analyses. In this Letter we provide a precise quantitative study on the interpretation of m MC t in terms of the MSR and pole mass schemes based on a hadron level prediction for the variable τ 2 for the production of a boosted top-antitop quark pair in e þ e − annihilation. It is defined aswhere the sum is over the 3-momenta of all final state particles, the maximum defines the thrust axisñ t , and Q is the center-of-ma...