Median purity and completeness across all 98 MW analogs for nine combinations of merger-tracking parameters (see Section 2.2). Each point shows the median values computed over all mergers with peak mass above 10⁹ M_⊙. Completeness is defined as the fraction of particles bound to the merger before infall that are tagged to the merger, while purity is the fraction of particles tagged to the merger that are present in the halo before infall. The combinations vary the lookback time window (1–3 Gyr) and the required fraction of snapshots for which a DM particle must be bound to a subhalo (50%–90%); they are labeled by these two parameters. The blue marker with red edge (2.0 Gyr/70%) denotes the fiducial choice adopted in this work, which maximizes purity while maintaining a completeness above 0.75.