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The problem of bias, meaning over- or underestimation, of the componentperpendicular to the line-of-sight, Bperp, in vector magnetic field maps isdiscussed. Previous works on this topic have illustrated that the problemexists; here we perform novel investigations to quantify the bias, fullyunderstand its source(s), and provide mitigation strategies. First, we developquantitative metrics to measure the Bperp bias and quantify the effect in bothlocal (physical) and native image-plane components. Second we test and evaluatedifferent inversion options and data sources, to systematically characterizethe impacts of choices, including explicitly accounting for the magnetic fillfraction ff. Third we deploy a simple model to test how noise and differentmodels of the bias may manifest. From these three investigations we find thatwhile the bias is dominantly present in under-resolved structures, it is alsopresent in strong-field pixel-filling structures. Noise in the magnetograms canexacerbate the problem, but it is not the primary cause. We show that fittingff explicitly provides significant mitigation, but that other considerationssuch as choice of chi^2 weights and optimization algorithms can impact theresults as well. Finally, we demonstrate a straightforward "quick fix" that canbe applied post-facto but prior to solving the 180deg ambiguity in Bperp, andwhich may be useful when global-scale structures are, e.g., used for modelboundary input. The conclusions of this work support the deployment ofinversion codes that explicitly fit ff or, as with the new SyntHIA neural-net,that are trained on data that did so.

On Identifying and Mitigating Bias in Inferred Measurements for Solar Vector Magnetic Field Data