g$_{D}$ ∗ Dπ as estimates. Be´ cirevi´ c and Haas recently computed g$_{D}$ ∗ Dπ = 0 . 71(7) in 2-flavor lattice QCD, but this result is from only a single lattice spacing and presents no estimate of the systematic error [67]. Stewart computed the value of g$_{D}$ ∗ Dπ in 1998 by fitting to experimental data [68], and recently updated his result to include the experimental measurement of the D ∗ decay width [69]. His latest determination is g$_{D}$ ∗ Dπ = 0 . 51, but with no error quoted [70]. The most sophisticated extraction of the D $^{∗}$- D - π coupling was performed by Kamenik and Fajfer, and gives g$_{D}$ ∗ Dπ = 0 . 66 +0 . 08 − 0 $_{06}$, where the uncertainty only reflects the error due to counterterms [71]. Finally, we note that the chiral-continuum extrapolations of B -meson quantities by the Fermilab/MILC Collaboration [72] and the HPQCD Collaboration [14] tend to prefer even smaller values of the B $^{∗}$- B - π coupling than those in the literature. Most of the results presented above do not have complete error budgets, and are incon- sistent within the quoted errors, so for this work we take g$_{B}$ ∗ Bπ = 0 . 516 ± 0 . 2 to account for the spread of values. We then vary g$_{B}$ ∗ Bπ within this range to determine how much it changes the central values for f$_{B}$$_{s}$/f$_{B}$$_{d}$ and ξ . This leads to an uncertainty in f$_{B}$$_{s}$/f$_{B}$$_{d}$ of 3 . 2% for both APE and HYP and in ξ of 2 . 1%. In this work we only analyze data at a single, relatively coarse lattice spacing of a ≈ 0 . 11 fm, so we estimate the size of discretization errors with power-counting. As a consistency-check of our estimation procedure, however, we can compare the estimated er- rors in the individual decay constants and matrix elements with the observed differences in those quantities for the APE and HYP-smeared data. This is because, aside from sta- tistical errors, the differences in the values obtained from the two smearings are due to discretization effects and higher-order corrections to the renormalization factors. We find about 15–20% differences in the decay constants and matrix elements obtained from the APE and HYP-smeared data, whereas we estimate by power-counting that discretization errors in f$_{B}$$_{q}$ should be about 15% and in M q should be about 20%. Thus our observations are consistent with the scaling behavior expected from power-counting. We can also compare our power-counting estimates with the findings of the ALPHA Collaboration, who performed a study of f$_{B}$$_{s}$ at several lattice spacings using static b -quarks with similar link-smearings in the quenched approximation [73]. Although ALPHA observes a violation of O ( a $^{2}$) scal- 36 C. Discretization errors