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We analysed the theoretical foundation of the mixing-length calibration bymeans of classical and global asteroseismic observables of field stars. Wediscussed the soundness of inferring a metallicity dependence of themixing-length parameter. We followed a theoretical approach based on mockdatasets of artificial stars sampled from a grid of stellar models with a fixed$\alpha_{ml}$. [...] We verified that the $\alpha_{ml}$ estimates are affectedby a huge spread, even in the case of perfect agreement between the mock dataand the recovery grid. When the solar heavy-element mixture used to compute themodels is different from that of the artificial stars, we also found ametallicity relationship in which $\alpha_{ml}$ increases by 0.4 for anincrease of 1 dex in [Fe/H]. The origin of this trend was investigatedconsidering the differences in the initial helium abundance Y -- [Fe/H] --initial metallicity Z relation assumed in the models and data. A discrepancybetween the adopted helium-to-metal enrichment ratio caused the appearance ofrelevant spurious trends in the estimated $\alpha_{ml}$. [...] A similar effectwas caused by an offset in the [Fe/H] to Z conversion. An overestimation of[Fe/H] by 0.1 dex in the recovery grid forced an increasing trend of$\alpha_{ml}$ versus [Fe/H] of 0.2 per dex. We also explored the impact of somediscrepancies between the adopted input physics in the recovery grid and mockdata. We observed a trend with [Fe/H] of 0.3 per dex when the effect of themicroscopic diffusion is neglected in the recovery grid [...]. Therefore, anyattempt to calibrate the mixing-length parameter by means of classical andasteroseimic observables of field stars seems to be statistically poorlyreliable. As such, any claim about the dependence of the mixing-length on themetallicity for field stars should be considered cautiously and critically.

Mixing-length calibration from field stars. An investigation on statistical errors, systematic biases, and spurious metallicity trends